http://comp.chem.tohoku.ac.jp/mediawiki/api.php?action=feedcontributions&feedformat=atom&user=LwangComplexRI: Manual - 利用者の投稿記録 [ja]2026-04-17T11:24:12Z利用者の投稿記録MediaWiki 1.36.2http://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Theory&diff=1035Theory2022-03-04T02:07:51Z<p>Lwang: </p>
<hr />
<div><br />
----<br />
<br />
<div id="ATR-IR data" style="font-size: 200%;font-style:bold;"> Calculated reflectance of ATR-IR from complex refractive index </div><br />
<br />
[[File:Light.png|500px]]<br />
<br />
The experimental geometry is described by the two-layer model in the above Figure, where phase <math>i</math> and phase <math>j</math> represent the substrate and sample, respectively. <br />
The incident light in phase <math>i</math> and transmitted light in phase <math>j</math> are related by Snell's law<br />
: <math> n_i \sin \theta_i = n_j \sin \theta_j </math><br />
<br />
where <math>n_i</math> and <math>n_j</math> are the complex refractive index of substrate and sample. <br />
<math>\theta_i</math> and <math>\theta_j</math> denote the angles of incidence and transmission of IR light, respectively.<br />
<br />
The reflectance of <math>p</math>- and <math>s</math>-polarized lights can be represented as the ratio of reflected to incident light intensities by <ref name = "ref1" /><br />
<br />
: <math> | r_{ij}^p|^2 = \left| \frac{n_j \cos \theta_i - n_i \cos \theta_j}{n_j \cos \theta_i + n_i \cos \theta_j} \right|^2 </math><br />
: <math> | r_{ij}^s|^2 = \left| \frac{n_i \cos \theta_i - n_j \cos \theta_j}{n_i \cos \theta_i + n_j \cos \theta_j} \right|^2 </math><br />
<br />
The angle of transmission <math>\theta_j</math> is derived from Snell's law to be <br />
: <math> \cos \theta_j = \sqrt{1-\frac{n_i^2}{n_j^2} \sin^2 \theta_i} </math><br />
which can be imaginary in the ATR condition. <br />
<br />
In the experiment, the incident angle <math>\theta_i</math> is often fixed, for example, to 45 degree. <br />
Take substate diamond as example, <math>n_i </math> is also known as 2.38. <br />
Therefore, the ATR condition is satisfied in most cases where <math>n_j </math> is smaller than <math> n_i \sin \theta_i = 1.68 </math>.<br />
This situation is held for most liquid samples. <br />
In the total reflection condition, the calculated <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> are unity when <math>n_j </math> is real.<br />
However, <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> become less than unity when the refractive index of the liquid <math>n_j = \eta_j + i \kappa_j </math> is complex.<br />
The reduced reflectance is a consequence of the absorption of evanescent light in the liquid sample. <br />
Therefore, by fitting the experimental reflectance data in ATR-IR spectra, it is able to obtain the complex refractive index of the liquid sample.<br />
<br />
----<br />
<br />
<div id="Fitting procedure" style="font-size: 200%;"> How to Fit the ATR-IR spectra </div><br />
<br />
The purpose of fitting is to determine the frequency-dependent complex refractive index <math>n_j(\nu) </math>.<br />
The complex refractive index of sample is represented with a set of Lorentz functions <br />
: <math> n_j (\nu) = \eta_j (\nu) + i \kappa_j (\nu) = n_j^0 + \sum_{l=1}^{l_\text{max}} \frac{A_l}{\nu_l - \nu - i \Gamma_l} </math><br />
where <math> n_j^0 </math> is the nonresonant refractive index. <br />
<math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> are the amplitude, peak wavenumber and bandwidth of each Lorentz function,<br />
respectively. <math> l_\text{max} </math> is the number of Lorentz functions to be used. <br />
Therefore, the parameters <math> n_j^0 </math>, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> and <math> l_\text{max} </math> were determined from the experimental spectra.<br />
<br />
In the beginning, <math> n_j^0 </math> should be determined before the fitting procedure. <math> n_j^0 </math> is the nonresonant refractive index in the IR wavenumber region. <br />
In the reference paper <ref name = "ref2" />, we use the refractive index values in the visible regions to fit Cauchy's equation.<br />
: <math>n_j^0(\lambda) = A + \frac{B}{{\lambda}^2} + \frac{C}{{\lambda}^4}</math><br />
The obtained parameters <math>A, B, C</math> were used to evaluate the nonresnant refractive index at 5000 <math> \text{cm}^{-1} </math>.<br />
<br />
It is also possible to directly use the refractive index in the visible region, which may involve a very slight deviation in <math> n_j^0 </math>. <ref name = "ref2" /><br />
<br />
After the determination of <math> n_j^0 </math>, other parameters related to the Lorentz functions are determined by minimizing the least-squares residual (LSR) between the experimental reflectance spectra and those of the analytical formulas over the whole wavenumber region of the target vibrational band. The residual is defined by <br />
: <math> \text{LSR} ( \{ A_l, \nu_l, \Gamma_l \} ) = \frac{1}{n} \sum_{\nu_n \in [\nu_\text{min}, \nu_\text{max}]} \left[ |r_{ij}^p (\nu_n)|^2 + |r_{ij}^s (\nu_n)|^2 - 2|r_{ij} (\nu_n)|^2_\mathrm{exp} \right]^2 </math><br />
where <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> are the calculated reflectances in the above section. <br />
<math> |r_{ij} (\nu_n)|^2_\mathrm{exp} </math> is the experimental reflectance of unpolarized light at wavenumber <math> \nu_n </math>. The summation of <math> n </math> is taken for all observed wavenumber points in the target vibrational band.<br />
By minimizing the LSR, the parameters of each Lorentz functions, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math>, were obtained. <br />
The minimization is numerically done in the program, thus the initial parameter of <math> l_\text{max} </math>, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> should be determined.<br />
And the initial parameters also have a large effect on whether the minimization can reach the tolerance and how long the minimization procedure is taken. <br />
All of them can be set manually. <br />
In the following, we will introduce a method to automatically determine the initial parameters.<br />
<br />
----<br />
<br />
<div id="Auto Fitting" style="font-size: 200%;"> Automatically determine the initial parameters in fitting procedure </div><br />
<br />
In order to determine the number of Lorentz functions to be used, we first start with only one Lorentz function and represent the complex refractive index as <br />
: <math> n_j (\nu) = n_j^0 + \frac{A_1}{\nu_1 - \nu - i \Gamma_1} </math><br />
The first Lorentz function is used to fit the strongest adsorption band in the target region. <br />
Thus, the initial parameter for <math> \nu_1 </math> is set to the wavenumber of minimum value of reflectance in the experimental data. <br />
The initial parameter for <math> \Gamma_1 </math> and <math> A_1 </math> are set according to the lineshape of strongest adsorption band in ATR-IR spectra. <br />
<br />
After the first fitting procedure, the strongest adsorption band is expected to be well represented.<br />
Here if the LSR is less than the tolerance, the fitting is finished and no more Lorentz functions are required. <br />
If not, another Lorentz function is added and the complex refractive index become<br />
: <math> n_j (\nu) = n_j^0 + \frac{A_1}{\nu_1 - \nu - i \Gamma_1} + \frac{A_2}{\nu_2 - \nu - i \Gamma_2} </math><br />
The second Lorentz funtion is used to represent major adsorption band in the difference reflectance spectra between the first fitting results and experimental results. <br />
The initial value of <math> \nu_1 </math>, <math> \Gamma_1 </math> and <math> A_1 </math> are set to be the optimized value in the last fitting procedure.<br />
The initial value of <math> \nu_2 </math> is set to the wavenumber of minimum (or maximum) value of difference reflectance spectra. <br />
The initial parameter for <math> \Gamma_2 </math> and <math> A_2 </math> is set to be 15 <math> \text{cm}^{-1} </math> and <math> 0.5 A_1 \text{cm}^{-1} </math>, respectively. <br />
A smaller initial value of <math> A_2 </math> suggests that the second Lorentz function is a minor adsorption band in ATR-IR spectra. <br />
Then all parameters are again optimized using the same fitting procedure. <br />
<br />
The number of Lorentz functions keeps increasing and the whole procedure is repeated until the final LSR reaches the set tolerance.<br />
<br />
----<br />
<br />
<div style="font-size: 200%;"> References </div><br />
<br />
<references><br />
<br />
<ref name = "ref1">"Theory of Sum Frequency Generation Spectroscopy"<br />
Akihiro Morita. Springer Nature Singapore Pte Ltd: 2018 </ref><br />
<ref name = "ref2">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. I Quantitative Spectra"<br />
Ryo Murata, Ken-ichi Inoue, Lin Wang, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9794-9803 (2021).</ref><br />
<br />
</references></div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Input&diff=1034Input2022-03-04T02:05:22Z<p>Lwang: </p>
<hr />
<div><br />
<br />
: [[File:2Newtoppage.png|1500px]]<br />
: This is the typical snapshot of the input of ComplexRI. <br />
: The input of ComplexRI contains two parts. The left part is the information of ATR-IR experimental data. The right part is the control parameters of the complex refractive index fitting procedure. Each part will be explained in the following. <br />
<br />
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<div id="Information of ATR-IR experiment" style="font-size: 200%;"> Information of ATR-IR experiment </div><br />
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<div id="Input01" style="font-size: 150%;"> ①ATR-IR File </div><br />
: Please upload the ATR-IR experimental data in this part. The inside should be like the following.<br />
: [[File:NewFILE01.png|200px]]<br />
: If there are characters at the beginning of the file, they will be ignored. The columns of wavenumber and ATR-IR data should be separated by space or comma. <br />
: For instance, the csv file exported by ATR-IR can be used. <br />
<br />
----<br />
<div id="Input02" style="font-size: 150%;"> ②The order of data </div><br />
: Please select the sort order of your data.<br />
:: Ascending order: The wavenumbers in the input file are in ascending order (left picture). (Default)<br />
:: Descending order: The wavenumbers in the input file are in descending order (right picture). <br />
:[[File:NewFILE01.png|200px]][[File:NewFILE04.png|220px]]<br />
<br />
----<br />
<div id="Input03" style="font-size: 150%;"> ③Reflectance or Absorbance? </div><br />
: Please select the type of your ATR-IR data.<br />
:: Reflectance(%): The Reflectance of ATR-IR spectra in the value of percentage. (Default)<br />
:: Reflectance: The Reflectance of ATR-IR spectra. <br />
:: Absorbance: The Absorbance of ATR-IR spectra.<br />
: The relationships between each data are<br />
:: <math> Reflectance(%)=Reflectance*100 </math><br />
:: <math> Absorbance=-\log_{10}(Reflectance) </math><br />
<br />
----<br />
<div id="Input04" style="font-size: 150%;"> ④The Substrate in ATR-IR </div><br />
: Please select the substrate you used in the ATR-IR experiment. Here, we prepare the three substrates that often used <br />
:: Diamond(Refractive Index = 2.38). (Default)<br />
:: Zinc selenide(Refractive Index = 2.40).<br />
:: Germanium(Refractive Index = 4.0).<br />
: You can also input the refractive index of your substrate by selecting Other in the list.<br />
:[[File:4_other.png|500px]]<br />
<br />
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<div id="Input05" style="font-size: 150%;"> ⑤Incident angle in ATR-IR </div><br />
: Please input the incident angle in your ATR-IR experiment. (Default=45 degree)<br />
<br />
----<br />
<div id="Input06" style="font-size: 150%;"> ⑥Select the column of your data </div><br />
: Please input the column number of the data that you want to analyze in your ATR-IR file. <br />
:: Wavenumber: The column number of wavenumber in your input file. (Default: 1)<br />
:: ATR-IR data: The column number of ATR-IR data in your input file. (Default: 2)<br />
<br />
: For example, an input file like following can be uploaded and column 1 and column 5 can be selected for analyzing. <br />
: [[File:NewFILE03.png|500px]]<br />
: [[File:6_15.png|300px]]<br />
<br />
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<br />
<div id="Control parameters of ComplexRI fitting" style="font-size: 200%;">Control parameters of ComplexRI fitting </div><br />
<br />
----<br />
<div id="Input07" style="font-size: 150%;"> ⑦Title of your job </div><br />
: Please input the title of your job (alphabet). The output results of ComplexRI will be saved in the excel format with the name @Title.xlsx<br />
<br />
----<br />
<div id="Input08" style="font-size: 150%;"> ⑧Input the fitting range </div><br />
: Please input the frequency range (in wavenumber) inside which you want to perform the fitting. ComplexRI will only fit the data inside the range you input here.<br />
:: Minimum wavenumber: The lower boundary of wavenumber. (Default: 1636)<br />
:: Maximum wavenumber: The upper boundary of wavenumber. (Default: 1863)<br />
<br />
---- <br />
<div id="Input09" style="font-size: 150%;"> ⑨Refractive index of target sample in non-resonance region (<math> n_j^0 </math>) </div><br />
: Please input the refractive index of the target sample (<math> n_j^0 </math>) in non-resonance region. (Default=1.360)<br />
: A database of common liquids is prepared for reference. The determination of <math> n_j^0 </math> and some comments about it can be found in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>. <br />
<br />
----<br />
<div id="Input10" style="font-size: 150%;"> ⑩The tolerance of fitting </div><br />
: Please input the tolerance of the fitting procedure. (default: 0.02)<br />
: The fitting will be finished when the calculated residual is less than this value. The details are described in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>.<br />
:: Note: Try to gradually decrease this value if the fitting results are not close to the experiments. This often happens when fit to the weak adsorption bands. Be careful that fitting can not finish if this value is too small.<br />
<br />
----<br />
<div id="Input11" style="font-size: 150%;"> ⑪ Manually set the initial parameters </div><br />
: Please select whether to set the initial fitting parameters by yourself. <br />
:: No: Automatically done by the algorithm (Default)<br />
:: Yes: Manually set the initial parameters by users. <br />
: In the fitting, we use a set of Lorentz functions to represent the complex refractive index <br />
:: <math>n_j=n_j^0+\sum_{l=1}^{l_{max}} \frac{A_l}{\nu_l-\nu-i\gamma_l}</math><br />
: where <math> n_j^0 </math> is input in ⑨. The number of Lorentz functions <math> l_{max} </math>, and the corresponding initial parameters <math> A_l, \nu_l, \gamma_l </math> should be determined.<br />
: By selecting <math> No </math>, it means the initial parameters are automatically guessed by the algorithm explained in <u> [[Theory#Auto Fitting| Automatically determine the initial parameters in fitting procedure]] </u>. <br />
: By selecting <math> Yes </math>, you can manually set <math> l_{max} </math> and <math> A_l, \nu_l, \gamma_l </math> for each Lorentz function by yourself. The units of <math> A_l, \nu_l, \gamma_l </math> are all wavenumber. <math> l_{max} </math> is up to 5.<br />
:: Note: <br />
::: 1. Automatical mode is recommended when using ComplexRI to fit new data. The results also provide useful information for users to further fitting the data by manual mode. <br />
::: 2. In some cases that users want to fit the vibrational regions with multiple weak adsorption bands, the manual mode might be better to represent the very detailed spectra.<br />
: [[File:11yes.png|500px]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Theory&diff=1015Theory2022-02-17T09:02:13Z<p>Lwang: </p>
<hr />
<div><br />
----<br />
<br />
<div id="ATR-IR data" style="font-size: 200%;font-style:bold;"> Calculated reflectance of ATR-IR from complex refractive index </div><br />
<br />
[[File:Light.png|500px]]<br />
<br />
The experimental geometry is described by the two-layer model in the above Figure, where phase <math>i</math> and phase <math>j</math> represent the substrate and sample, respectively. <br />
The incident light in phase <math>i</math> and transmitted light in phase <math>j</math> are related by Snell's law<br />
: <math> n_i \sin \theta_i = n_j \sin \theta_j </math><br />
<br />
where <math>n_i</math> and <math>n_j</math> are the complex refractive index of substrate and sample. <br />
<math>\theta_i</math> and <math>\theta_j</math> denote the angles of incidence and transmission of IR light, respectively.<br />
<br />
The reflectance of <math>p</math>- and <math>s</math>-polarized lights can be represented as the ratio of reflected to incident light intensities by <ref name = "ref1" /><br />
<br />
: <math> | r_{ij}^p|^2 = \left| \frac{n_j \cos \theta_i - n_i \cos \theta_j}{n_j \cos \theta_i + n_i \cos \theta_j} \right|^2 </math><br />
: <math> | r_{ij}^s|^2 = \left| \frac{n_i \cos \theta_i - n_j \cos \theta_j}{n_i \cos \theta_i + n_j \cos \theta_j} \right|^2 </math><br />
<br />
The angle of transmission <math>\theta_j</math> is derived from Snell's law to be <br />
: <math> \cos \theta_j = \sqrt{1-\frac{n_i^2}{n_j^2} \sin^2 \theta_i} </math><br />
which can be imaginary in the ATR condition. <br />
<br />
In the experiment, the incident angle <math>\theta_i</math> is often fixed, for example, to 45 degree. <br />
Take substate diamond as example, <math>n_i </math> is also known as 2.38. <br />
Therefore, the ATR condition is satisfied in most cases where <math>n_j </math> is smaller than <math> n_i \sin \theta_i = 1.68 </math>.<br />
This situation is held for most liquid samples. <br />
In the total reflection condition, the calculated <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> are unity when <math>n_j </math> is real.<br />
However, <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> become less than unity when the refractive index of the liquid <math>n_j = \eta_j + i \kappa_j </math> is complex.<br />
The reduced reflectance is a consequence of the absorption of evanescent light in the liquid sample. <br />
Therefore, by fitting the experimental reflectance data in ATR-IR spectra, it is able to obtain the complex refractive index of the liquid sample.<br />
<br />
----<br />
<br />
<div id="Fitting procedure" style="font-size: 200%;"> How to Fit the ATR-IR spectra </div><br />
<br />
The purpose of fitting is to determine the frequency-dependent complex refractive index <math>n_j(\nu) </math>.<br />
The complex refractive index of sample is represented with a set of Lorentz functions <br />
: <math> n_j (\nu) = \eta_j (\nu) + i \kappa_j (\nu) = n_j^0 + \sum_{l=1}^{l_\text{max}} \frac{A_l}{\nu_l - \nu - i \Gamma_l} </math><br />
where <math> n_j^0 </math> is the nonresonant refractive index. <br />
<math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> are the amplitude, peak wavenumber and bandwidth of each Lorentz function,<br />
respectively. <math> l_\text{max} </math> is the number of Lorentz functions to be used. <br />
Therefore, the parameters <math> n_j^0 </math>, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> and <math> l_\text{max} </math> were determined from the experimental spectra.<br />
<br />
In the beginning, <math> n_j^0 </math> should be determined before the fitting procedure. <math> n_j^0 </math> is the nonresonant refractive index in the IR wavenumber region. <br />
In the reference paper <ref name = "ref2" />, we use the refractive index values in the visible regions to fit Cauchy's equation.<br />
: <math>n_j^0(\lambda) = A + \frac{B}{{\lambda}^2} + \frac{C}{{\lambda}^4}</math><br />
The obtained parameters <math>A, B, C</math> were used to evaluate the nonresnant refractive index at 5000 <math> \text{cm}^{-1} </math>.<br />
<br />
It is also possible to directly use the refractive index in the visible region, which may involve a very slight deviation in <math> n_j^0 </math>. <ref name = "ref2" /><br />
<br />
After the determination of <math> n_j^0 </math>, other parameters related to the Lorentz functions are determined by minimizing the least-squares residual (LSR) between the experimental reflectance spectra and those of the analytical formulas over the whole wavenumber region of the target vibrational band. The residual is defined by <br />
: <math> \text{LSR} ( \{ A_l, \nu_l, \Gamma_l \} ) = \frac{1}{n} \sum_{\nu_n \in [\nu_\text{min}, \nu_\text{max}]} \left[ |r_{ij}^p (\nu_n)|^2 + |r_{ij}^s (\nu_n)|^2 - 2|r_{ij} (\nu_n)|^2_\mathrm{exp} \right]^2 </math><br />
where <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> are the calculated reflectances in the above section. <br />
<math> |r_{ij} (\nu_n)|^2_\mathrm{exp} </math> is the experimental reflectance of unpolarized light at wavenumber <math> \nu_n </math>. The summation of <math> n </math> is taken for all observed wavenumber points in the target vibrational band.<br />
By minimizing the LSR, the parameters of each Lorentz functions, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math>, were obtained. <br />
The minimization is numerically done in the program, thus the initial parameter of <math> l_\text{max} </math>, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> should be determined.<br />
And the initial parameters also have a large effect on whether the minimization can reach the tolerance and how long the minimization procedure is taken. <br />
All of them can be set manually. <br />
In the following, we will introduce a method to automatically determine the initial parameters.<br />
<br />
----<br />
<br />
<div id="Auto Fitting" style="font-size: 200%;"> Automatically determine the initial parameters in fitting procedure </div><br />
<br />
In order to determine the number of Lorentz functions to be used, we first start with only one Lorentz function and represent the complex refractive index as <br />
: <math> n_j (\nu) = n_j^0 + \frac{A_1}{\nu_1 - \nu - i \Gamma_1} </math><br />
The first Lorentz function is used to fit the strongest adsorption band in the target region. <br />
Thus, the initial parameter for <math> \nu_1 </math> is set to the wavenumber of minimum value of reflectance in the experimental data. <br />
The initial parameter for <math> \Gamma_1 </math> and <math> A_1 </math> are set according to the lineshape of strongest adsorption band in ATR-IR spectra. <br />
<br />
After the first fitting procedure, the strongest adsorption band is expected to be well represented.<br />
Here if the LSR is less than the tolerance, the fitting is finished and no more Lorentz functions are required. <br />
If not, another Lorentz function is added and the complex refractive index become<br />
: <math> n_j (\nu) = n_j^0 + \frac{A_1}{\nu_1 - \nu - i \Gamma_1} + \frac{A_2}{\nu_2 - \nu - i \Gamma_2} </math><br />
The second Lorentz funtion is used to represent major adsorption band in the difference reflectance spectra between the first fitting results and experimental results. <br />
The initial value of <math> \nu_1 </math>, <math> \Gamma_1 </math> and <math> A_1 </math> are set to be the optimized value in the last fitting procedure.<br />
The initial value of <math> \nu_2 </math> is set to the wavenumber of minimum (or maximum) value of difference reflectance spectra. <br />
The initial parameter for <math> \Gamma_2 </math> and <math> A_2 </math> is set to be 15 <math> \text{cm}^{-1} </math> and <math> A_1/2 \text{cm}^{-1} </math>, respectively. <br />
A smaller initial value of <math> A_2 </math> suggests that the second Lorentz function is a minor adsorption band in ATR-IR spectra. <br />
Then all parameters are again optimized using the same fitting procedure. <br />
<br />
The number of Lorentz functions keeps increasing and the whole procedure is repeated until the final LSR reaches the set tolerance.<br />
<br />
----<br />
<br />
<div style="font-size: 200%;"> References </div><br />
<br />
<references><br />
<br />
<ref name = "ref1">"Theory of Sum Frequency Generation Spectroscopy"<br />
Akihiro Morita. Springer Nature Singapore Pte Ltd: 2018 </ref><br />
<ref name = "ref2">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. I Quantitative Spectra"<br />
Ryo Murata, Ken-ichi Inoue, Lin Wang, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9794-9803 (2021).</ref><br />
<br />
</references></div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Theory&diff=1014Theory2022-02-17T08:59:11Z<p>Lwang: </p>
<hr />
<div><br />
----<br />
<br />
<div id="ATR-IR data" style="font-size: 200%;font-style:bold;"> Calculated reflectance of ATR-IR from complex refractive index </div><br />
<br />
[[File:Light.png|500px]]<br />
<br />
The experimental geometry is described by the two-layer model in the above Figure, where phase <math>i</math> and phase <math>j</math> represent the substrate and sample, respectively. <br />
The incident light in phase <math>i</math> and transmitted light in phase <math>j</math> are related by Snell's law<br />
: <math> n_i \sin \theta_i = n_j \sin \theta_j </math><br />
<br />
where <math>n_i</math> and <math>n_j</math> are the complex refractive index of substrate and sample. <br />
<math>\theta_i</math> and <math>\theta_j</math> denote the angles of incidence and transmission of IR light, respectively.<br />
<br />
The reflectance of <math>p</math>- and <math>s</math>-polarized lights can be represented as the ratio of reflected to incident light intensities by <ref name = "ref1" /><br />
<br />
: <math> | r_{ij}^p|^2 = \left| \frac{n_j \cos \theta_i - n_i \cos \theta_j}{n_j \cos \theta_i + n_i \cos \theta_j} \right|^2 </math><br />
: <math> | r_{ij}^s|^2 = \left| \frac{n_i \cos \theta_i - n_j \cos \theta_j}{n_i \cos \theta_i + n_j \cos \theta_j} \right|^2 </math><br />
<br />
The angle of transmission <math>\theta_j</math> is derived from Snell's law to be <br />
: <math> \cos \theta_j = \sqrt{1-\frac{n_i^2}{n_j^2} \sin^2 \theta_i} </math><br />
which can be imaginary in the ATR condition. <br />
<br />
In the experiment, the incident angle <math>\theta_i</math> is often fixed, for example, to 45 degree. <br />
Take substate diamond as example, <math>n_i </math> is also known as 2.38. <br />
Therefore, the ATR condition is satisfied in most cases where <math>n_j </math> is smaller than <math> n_i \sin \theta_i = 1.68 </math>.<br />
This situation is held for most liquid samples. <br />
In the total reflection condition, the calculated <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> are unity when <math>n_j </math> is real.<br />
However, <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> become less than unity when the refractive index of the liquid <math>n_j = \eta_j + i \kappa_j </math> is complex.<br />
The reduced reflectance is a consequence of the absorption of evanescent light in the liquid sample. <br />
Therefore, by fitting the experimental reflectance data in ATR-IR spectra, it is able to obtain the complex refractive index of the liquid sample.<br />
<br />
----<br />
<br />
<div id="Fitting procedure" style="font-size: 200%;"> How to Fit the ATR-IR spectra </div><br />
<br />
The purpose of fitting is to determine the frequency-dependent complex refractive index <math>n_j(\nu) </math>.<br />
The complex refractive index of sample is represented with a set of Lorentz functions <br />
: <math> n_j (\nu) = \eta_j (\nu) + i \kappa_j (\nu) = n_j^0 + \sum_{l=1}^{l_\text{max}} \frac{A_l}{\nu_l - \nu - i \Gamma_l} </math><br />
where <math> n_j^0 </math> is the nonresonant refractive index. <br />
<math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> are the amplitude, peak wavenumber and bandwidth of each Lorentz function,<br />
respectively. <math> l_\text{max} </math> is the number of Lorentz functions to be used. <br />
Therefore, the parameters <math> n_j^0 </math>, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> and <math> l_\text{max} </math> were determined from the experimental spectra.<br />
<br />
In the beginning, <math> n_j^0 </math> should be determined before the fitting procedure. <math> n_j^0 </math> is the nonresonant refractive index in the IR wavenumber region. <br />
In the reference paper <ref name = "ref2" />, we use the refractive index values in the visible regions to fit Cauchy's equation.<br />
: <math>n_j^0(\lambda) = A + \frac{B}{{\lambda}^2} + \frac{C}{{\lambda}^4}</math><br />
The obtained parameters <math>A, B, C</math> were used to evaluate the nonresnant refractive index at 5000 <math> \text{cm}^{-1} </math>.<br />
<br />
It is also possible to directly use the refractive index in the visible region, which may involve a very slight deviation in <math> n_j^0 </math>. <ref name = "ref2" /><br />
<br />
After the determination of <math> n_j^0 </math>, other parameters related to the Lorentz functions are determined by minimizing the least-squares residual (LSR) between the experimental reflectance spectra and those of the analytical formulas over the whole wavenumber region of the target vibrational band. The residual is defined by <br />
: <math> \text{LSR} ( \{ A_l, \nu_l, \Gamma_l \} ) = \frac{1}{n} \sum_{\nu_n \in [\nu_\text{min}, \nu_\text{max}]} \left[ |r_{ij}^p (\nu_n)|^2 + |r_{ij}^s (\nu_n)|^2 - 2|r_{ij} (\nu_n)|^2_\mathrm{exp} \right]^2 </math><br />
where <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> are the calculated reflectances in the above section. <br />
<math> |r_{ij} (\nu_n)|^2_\mathrm{exp} </math> is the experimental reflectance of unpolarized light at wavenumber <math> \nu_n </math>. The summation of <math> n </math> is taken for all observed wavenumber points in the target vibrational band.<br />
By minimizing the LSR, the parameters of each Lorentz functions, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math>, were obtained. <br />
The minimization is numerically done in the program, thus the initial parameter of <math> l_\text{max} </math>, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> should be determined.<br />
And the initial parameters also have a large effect on whether the minimization can reach the tolerance and how long the minimization procedure is taken. <br />
All of them can be set manually. <br />
In the following, we will introduce a method to automatically determine the initial parameters.<br />
<br />
----<br />
<br />
<div id="Auto Fitting" style="font-size: 200%;"> Automatically determine the initial parameters in fitting procedure </div><br />
<br />
In order to determine the number of Lorentz functions to be used, we first start with only one Lorentz function and represent the complex refractive index as <br />
: <math> n_j (\nu) = n_j^0 + \frac{A_1}{\nu_1 - \nu - i \Gamma_1} </math><br />
The first Lorentz function is used to fit the strongest adsorption band in the target region. <br />
Thus, the initial parameter for <math> \nu_1 </math> is set to the wavenumber of minimum value of reflectance in the experimental data. <br />
The initial parameter for <math> \Gamma_1 </math> and <math> A_1 </math> is set according to the linesharp of strongest adsorption band in ATR-IR spectra. <br />
<br />
After the first fitting procedure, the strongest adsorption band is expected to be well represented.<br />
Here if the LSR is less than the tolerance, the fitting is finished and no more Lorentz functions are required. <br />
If not, another Lorentz function is added and the complex refractive index become<br />
: <math> n_j (\nu) = n_j^0 + \frac{A_1}{\nu_1 - \nu - i \Gamma_1} + \frac{A_2}{\nu_2 - \nu - i \Gamma_2} </math><br />
The second Lorentz funtion is used to represent major adsorption band in the difference reflectance spectra between the first fitting results and experimental results. <br />
The initial value of <math> \nu_1 </math>, <math> \Gamma_1 </math> and <math> A_1 </math> are set to be the optimized value in the last fitting procedure.<br />
The initial value of <math> \nu_2 </math> is set to the wavenumber of minimum (or maximum) value of difference reflectance spectra. <br />
The initial parameter for <math> \Gamma_2 </math> and <math> A_2 </math> is set to be 15 <math> \text{cm}^{-1} </math> and <math> A_1/2 \text{cm}^{-1} </math>, respectively. <br />
A smaller initial value of <math> A_2 </math> suggests that the second Lorentz function is a minor adsorption band in ATR-IR spectra. <br />
Then all parameters are again optimized using the same fitting procedure. <br />
<br />
The number of Lorentz functions keeps increasing and the whole procedure is repeated until the final LSR reaches the set tolerance.<br />
<br />
----<br />
<br />
<div style="font-size: 200%;"> References </div><br />
<br />
<references><br />
<br />
<ref name = "ref1">"Theory of Sum Frequency Generation Spectroscopy"<br />
Akihiro Morita. Springer Nature Singapore Pte Ltd: 2018 </ref><br />
<ref name = "ref2">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. I Quantitative Spectra"<br />
Ryo Murata, Ken-ichi Inoue, Lin Wang, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9794-9803 (2021).</ref><br />
<br />
</references></div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Input&diff=1013Input2022-02-17T08:51:53Z<p>Lwang: </p>
<hr />
<div><br />
<br />
: [[File:Newtoppage.png|1000px]]<br />
: This is the typical snapshot of the input of ComplexRI. <br />
: The input of ComplexRI contains two parts. The left part is the information of ATR-IR experimental data. The right part is the control parameters of the complex refractive index fitting procedure. Each part will be explained in the following. <br />
<br />
----<br />
<div id="Information of ATR-IR experiment" style="font-size: 200%;"> Information of ATR-IR experiment </div><br />
<br />
----<br />
<div id="Input01" style="font-size: 150%;"> ①ATR-IR File </div><br />
: Please upload the ATR-IR experimental data in this part. The inside should be like the following.<br />
: [[File:NewFILE01.png|200px]]<br />
: If there are characters at the beginning of the file, they will be ignored. The columns of wavenumber and ATR-IR data should be separated by space or comma. <br />
: For instance, the csv file exported by ATR-IR can be used. <br />
<br />
----<br />
<div id="Input02" style="font-size: 150%;"> ②The order of data </div><br />
: Please select the sort order of your data.<br />
:: Ascending order: The wavenumbers in the input file are in ascending order (left picture). (Default)<br />
:: Descending order: The wavenumbers in the input file are in descending order (right picture). <br />
:[[File:NewFILE01.png|200px]][[File:NewFILE04.png|220px]]<br />
<br />
----<br />
<div id="Input03" style="font-size: 150%;"> ③Reflectance or Absorbance? </div><br />
: Please select the type of your ATR-IR data.<br />
:: Reflectance(%): The Reflectance of ATR-IR spectra in the value of percentage. (Default)<br />
:: Reflectance: The Reflectance of ATR-IR spectra. <br />
:: Absorbance: The Absorbance of ATR-IR spectra.<br />
: The relationships between each data are<br />
:: <math> Reflectance(%)=Reflectance*100 </math><br />
:: <math> Absorbance=-\log_{10}(Reflectance) </math><br />
<br />
----<br />
<div id="Input04" style="font-size: 150%;"> ④The Substrate in ATR-IR </div><br />
: Please select the substrate you used in the ATR-IR experiment. Here, we prepare the three substrates that often used <br />
:: Diamond(Refractive Index = 2.38). (Default)<br />
:: Zinc selenide(Refractive Index = 2.40).<br />
:: Germanium(Refractive Index = 4.0).<br />
: You can also input the refractive index of your substrate by selecting Other in the list.<br />
:[[File:4_other.png|500px]]<br />
<br />
----<br />
<div id="Input05" style="font-size: 150%;"> ⑤Incident angle in ATR-IR </div><br />
: Please input the incident angle in your ATR-IR experiment. (Default=45 degree)<br />
<br />
----<br />
<div id="Input06" style="font-size: 150%;"> ⑥Select the column of your data </div><br />
: Please input the column number of the data that you want to analyze in your ATR-IR file. <br />
:: Wavenumber: The column number of wavenumber in your input file. (Default: 1)<br />
:: ATR-IR data: The column number of ATR-IR data in your input file. (Default: 2)<br />
<br />
: For example, an input file like following can be uploaded and column 1 and column 5 can be selected for analyzing. <br />
: [[File:NewFILE03.png|500px]]<br />
: [[File:6_15.png|300px]]<br />
<br />
----<br />
<br />
<div id="Control parameters of ComplexRI fitting" style="font-size: 200%;">Control parameters of ComplexRI fitting </div><br />
<br />
----<br />
<div id="Input07" style="font-size: 150%;"> ⑦Title of your job </div><br />
: Please input the title of your job (alphabet). The output results of ComplexRI will be saved in the excel format with the name @Title.xlsx<br />
<br />
----<br />
<div id="Input08" style="font-size: 150%;"> ⑧Input the fitting range </div><br />
: Please input the frequency range (in wavenumber) inside which you want to perform the fitting. ComplexRI will only fit the data inside the range you input here.<br />
:: Minimum wavenumber: The lower boundary of wavenumber. (Default: 1636)<br />
:: Maximum wavenumber: The upper boundary of wavenumber. (Default: 1863)<br />
<br />
---- <br />
<div id="Input09" style="font-size: 150%;"> ⑨Refractive index of target sample in non-resonance region (<math> n_j^0 </math>) </div><br />
: Please input the refractive index of the target sample (<math> n_j^0 </math>) in non-resonance region. (Default=1.360)<br />
: The determination of <math> n_j^0 </math> and some comments about it can be found in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>. <br />
<br />
----<br />
<div id="Input10" style="font-size: 150%;"> ⑩The tolerance of fitting </div><br />
: Please input the tolerance of the fitting procedure. (default: 0.02)<br />
: The fitting will be finished when the calculated residual is less than this value. The details are described in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>.<br />
:: Note: Try to gradually decrease this value if the fitting results are not close to the experiments. This often happens when fit to the weak adsorption bands. Be careful that fitting can not finish if this value is too small.<br />
<br />
----<br />
<div id="Input11" style="font-size: 150%;"> ⑪ Manually set the initial parameters </div><br />
: Please select whether to set the initial fitting parameters by yourself. <br />
:: No: Automatically done by the algorithm (Default)<br />
:: Yes: Manually set the initial parameters by users. <br />
: In the fitting, we use a set of Lorentz functions to represent the complex refractive index <br />
:: <math>n_j=n_j^0+\sum_{l=1}^{l_{max}} \frac{A_l}{\nu_l-\nu-i\gamma_l}</math><br />
: where <math> n_j^0 </math> is input in ⑨. The number of Lorentz functions <math> l_{max} </math>, and the corresponding initial parameters <math> A_l, \nu_l, \gamma_l </math> should be determined.<br />
: By selecting <math> No </math>, it means the initial parameters are automatically guessed by the algorithm explained in <u> [[Theory#Auto Fitting| Automatically determine the initial parameters in fitting procedure]] </u>. <br />
: By selecting <math> Yes </math>, you can manually set <math> l_{max} </math> and <math> A_l, \nu_l, \gamma_l </math> for each Lorentz function by yourself. The units of <math> A_l, \nu_l, \gamma_l </math> are all wavenumber. <math> l_{max} </math> is up to 5.<br />
:: Note: <br />
::: 1. Automatical mode is recommended when using ComplexRI to fit new data. The results also provide useful information for users to further fitting the data by manual mode. <br />
::: 2. In some cases that users want to fit the vibrational regions with multiple weak adsorption bands, the manual mode might be better to represent the very detailed spectra.<br />
: [[File:11yes.png|500px]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Input&diff=1012Input2022-02-16T04:49:11Z<p>Lwang: </p>
<hr />
<div><br />
<br />
: [[File:Newtoppage.png|1000px]]<br />
: This is the typical snapshot of the input of ComplexRI. <br />
: The input of ComplexRI contains two parts. The left part is the information of ATR-IR experimental data. The right part is the control parameters of the complex refractive index fitting procedure. Each part will be explained in the following. <br />
<br />
----<br />
<div id="Information of ATR-IR experiment" style="font-size: 200%;"> Information of ATR-IR experiment </div><br />
<br />
----<br />
<div id="Input01" style="font-size: 150%;"> ①ATR-IR File </div><br />
: Please upload the ATR-IR experimental data in this part. The inside should be like the following.<br />
: [[File:NewFILE01.png|200px]]<br />
: If there are characters at the beginning of the file, they will be ignored. The columns of wavenumber and ATR-IR data should be separated by space or comma. <br />
: For instance, the csv file exported by ATR-IR can be used. <br />
<br />
----<br />
<div id="Input02" style="font-size: 150%;"> ②The order of data </div><br />
: Please select the sort order of your data.<br />
:: Ascending order: The wavenumbers in the input file are in ascending order (left picture). (Default)<br />
:: Descending order: The wavenumbers in the input file are in descending order (right picture). <br />
:[[File:NewFILE01.png|200px]][[File:NewFILE04.png|220px]]<br />
<br />
----<br />
<div id="Input03" style="font-size: 150%;"> ③Reflectance or Absorbance? </div><br />
: Please select the type of your ATR-IR data.<br />
:: Reflectance(%): The Reflectance of ATR-IR spectra in the value of percentage. (Default)<br />
:: Reflectance: The Reflectance of ATR-IR spectra. <br />
:: Absorbance: The Absorbance of ATR-IR spectra.<br />
: The relationships between each data are<br />
:: <math> Reflectance(%)=Reflectance*100 </math><br />
:: <math> Absorbance=-\log_{10}(Reflectance) </math><br />
<br />
----<br />
<div id="Input04" style="font-size: 150%;"> ④The Substrate in ATR-IR </div><br />
: Please select the substrate you used in the ATR-IR experiment. Here, we prepare the three substrates that often used <br />
:: Diamond(Refractive Index = 2.38). (Default)<br />
:: Zinc selenide(Refractive Index = 2.40).<br />
:: Germanium(Refractive Index = 4.0).<br />
: You can also input the refractive index of your substrate by selecting Other in the list.<br />
:[[File:4_other.png|500px]]<br />
<br />
----<br />
<div id="Input05" style="font-size: 150%;"> ⑤Incident angle in ATR-IR </div><br />
: Please input the incident angle in your ATR-IR experiment. (Default=45 degree)<br />
<br />
----<br />
<div id="Input06" style="font-size: 150%;"> ⑥Select the column of your data </div><br />
: Please input the column number of the data that you want to analyze in your ATR-IR file. <br />
:: Wavenumber: The column number of wavenumber in your input file. (Default: 1)<br />
:: ATR-IR data: The column number of ATR-IR data in your input file. (Default: 2)<br />
<br />
: For example, an input file like following can be uploaded and column 1 and column 5 can be selected for analyzing. <br />
: [[File:NewFILE03.png|500px]]<br />
: [[File:6_15.png|300px]]<br />
<br />
----<br />
<br />
<div id="Control parameters of ComplexRI fitting" style="font-size: 200%;">Control parameters of ComplexRI fitting </div><br />
<br />
----<br />
<div id="Input07" style="font-size: 150%;"> ⑦Title of your job </div><br />
: Please input the title of your job (alphabet). The output results of ComplexRI will be saved in the excel format with the name @Title.xlsx<br />
<br />
----<br />
<div id="Input08" style="font-size: 150%;"> ⑧Input the fitting range </div><br />
: Please input the frequency range (in wavenumber) inside which you want to perform the fitting. ComplexRI will only fit the data inside the range you input here.<br />
:: Minimum wavenumber: The lower boundary of wavenumber. (Default: 1636)<br />
:: Maximum wavenumber: The upper boundary of wavenumber. (Default: 1863)<br />
<br />
---- <br />
<div id="Input09" style="font-size: 150%;"> ⑨Refractive index of target sample in non-resonance region (<math> n_j^0 </math>) </div><br />
: Please input the refractive index of the target sample (<math> n_j^0 </math>) in non-resonance region. (Default=1.360)<br />
: The determination of <math> n_j^0 </math> and some comments about it can be found in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>. <br />
<br />
----<br />
<div id="Input10" style="font-size: 150%;"> ⑩The tolerance of fitting </div><br />
: Please input the tolerance of the fitting procedure. (default: 0.02)<br />
: The fitting will be finished when the calculated residual is less than this value. The details are described in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>.<br />
:: Note: Fitting can not finish if this value is too small. You should increase this value when dealing with vibrational regions containing complicated vibrational bands. <br />
<br />
----<br />
<div id="Input11" style="font-size: 150%;"> ⑪ Manually set the initial parameters </div><br />
: Please select whether to set the initial fitting parameters by yourself. <br />
:: No: Automatically done by the algorithm (Default)<br />
:: Yes: Manually set the initial parameters by users. <br />
: In the fitting, we use a set of Lorentz functions to represent the complex refractive index <br />
:: <math>n_j=n_j^0+\sum_{l=1}^{l_{max}} \frac{A_l}{\nu_l-\nu-i\gamma_l}</math><br />
: where <math> n_j^0 </math> is input in ⑨. The number of Lorentz functions <math> l_{max} </math>, and the corresponding initial parameters <math> A_l, \nu_l, \gamma_l </math> should be determined.<br />
: By selecting <math> No </math>, it means the initial parameters are automatically guessed by the algorithm explained in <u> [[Theory#Auto Fitting| Automatically determine the initial parameters in fitting procedure]] </u>. <br />
: By selecting <math> Yes </math>, you can manually set <math> l_{max} </math> and <math> A_l, \nu_l, \gamma_l </math> for each Lorentz function by yourself. The units of <math> A_l, \nu_l, \gamma_l </math> are all wavenumber. <math> l_{max} </math> is up to 5.<br />
:: Note: <br />
::: 1. Automatical mode is recommended when using ComplexRI to fit new data. The results also provide useful information for users to further fitting the data by manual mode. <br />
::: 2. Automatical mode is designed to deal with the strong adsorption band. If uses want to fit to the vibrational regions with weak adsorption bands, manual mode might be better to represent the very detailed spectra.<br />
: [[File:11yes.png|500px]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=%E5%85%A5%E5%8A%9B&diff=1011入力2022-02-16T04:48:19Z<p>Lwang: </p>
<hr />
<div><br />
<br />
: [[File:Newtoppage.png|1000px]]<br />
: これはComplexRIの標準入力のスナップショットです。<br />
: ComplexRIの入力は大きく二つに分類されます。左の部分は、ATR-IR実験の情報に関する部分、右の部分は複素屈折率のフィッティングのパラメータを調整する部分です。以下では、それぞれについて説明します。<br />
<br />
----<br />
<div id="Information of ATR-IR experiment" style="font-size: 200%;"> Information of ATR-IR experiment </div><br />
<br />
----<br />
<div id="Input01" style="font-size: 150%;"> ①ATR-IR File </div><br />
: ここでは、ATR-IRの実験データをアップロードしてください。中身は以下のようになっている必要があります。<br />
: [[File:NewFILE01.png|200px]]<br />
: ファイルの先頭に文字がある場合、それらは無視されます。各列は空白またはコンマで区切られている。<br />
: 例えば、ATR-IRでエクスポートしたcsvファイルを使用できます。<br />
<br />
----<br />
<div id="Input02" style="font-size: 150%;"> ②The order of data </div><br />
: データの並び方を入力してください。<br />
:: Ascending order: 波数が昇順 (下の図の左側)。(デフォルト)<br />
:: Descending order:波数が降順 (下の図の右側)。 <br />
:[[File:NewFILE01.png|200px]][[File:NewFILE04.png|220px]]<br />
<br />
----<br />
<div id="Input03" style="font-size: 150%;"> ③Reflectance or Absorbance? </div><br />
: ATR-IRのデータの種類を選択してください。<br />
:: Reflectance(%): 反射率のスペクトル。単位は(%)。(デフォルト)<br />
:: Reflectance: 反射率のスペクトル。<br />
:: Absorbance: 吸光度スペクトル。<br />
: それぞれのデータは以下の関係を持っています。<br />
:: <math> Reflectance(%)=Reflectance*100 </math><br />
:: <math> Absorbance=-\log_{10}(Reflectance) </math><br />
<br />
----<br />
<div id="Input04" style="font-size: 150%;"> ④The Substrate in ATR-IR </div><br />
: ATR-IR実験で使用した基板の屈折率を入力してください。ここには、よく使われる３つの基板は選択として用意します。<br />
:: Diamond(Refractive Index = 2.38) (デフォルト)<br />
:: Zinc selenide(Refractive Index = 2.40)<br />
:: Germanium(Refractive Index = 4.0).<br />
:Otherを使うことで基板の屈折率の値を入力することもできます。<br />
:[[File:4_other.png|500px]]<br />
<br />
----<br />
<div id="Input05" style="font-size: 150%;"> ⑤Incident angle in ATR-IR </div><br />
: ATR-IR実験のIR光の入射角を入力してください。(デフォルト=45°)<br />
<br />
----<br />
<div id="Input06" style="font-size: 150%;"> ⑥Select the column of your data </div><br />
: 入力ファイルの中で解析したいデータの列番号を入力してください。<br />
:: Wavenumber: 波数の列番号。 (デフォルト: 1)<br />
:: ATR-IR data: 反射率もしくは吸光度の列番号。(デフォルト: 2)<br />
<br />
: 例えば、以下のようなファイルをアップロードした場合は、１列目と５列目を選んで解析に用いることができる。 <br />
: [[File:NewFILE03.png|500px]]<br />
: [[File:6_15.png|300px]]<br />
<br />
----<br />
<br />
<div id="Control parameters of ComplexRI fitting" style="font-size: 200%;">Control parameters of ComplexRI fitting </div><br />
<br />
----<br />
<div id="Input07" style="font-size: 150%;"> ⑦Title of your job </div><br />
: 今回の解析に名前を付けてください。<span color=”red”>(※半角入力)</span>。 結果は@Title.xlsxという名前のエクセルファイルに保存されます。<br />
<br />
----<br />
<div id="Input08" style="font-size: 150%;"> ⑧Input the fitting range </div><br />
: フィッティングを行う範囲を波数単位で入力してください。ComplexRIはこの範囲でのみ解析を行います。<br />
:: Minimum wavenumber: 波数の下限。 (デフォルト: 1636)<br />
:: Maximum wavenumber: 波数の上限。 (デフォルト: 1863)<br />
<br />
---- <br />
<div id="Input09" style="font-size: 150%;"> ⑨Refractive index of target sample in non-resonance region (<math> n_j^0 </math>) </div><br />
: 対象分子の非共鳴領域における屈折率(<math> n_j^0 </math>)を入力してください。(デフォルト＝1.360)<br />
: 詳細は<u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>で説明しています。<br />
<br />
----<br />
<div id="Input10" style="font-size: 150%;"> ⑩The tolerance of fitting </div><br />
: フィッティングの収束判定のしきい値を指定してください。(デフォルト: 0.02)<br />
: 最小二乗法の残差は与えられた値よりも小さくなったらフィッティングが終了します。<br />
: 詳細は<u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>で説明しています。<br />
:<span style color="red">注意!! この入力値が小さすぎると解析が終わらないことがあります。 </span><br />
<br />
----<br />
<div id="Input11" style="font-size: 150%;"> ⑪ Manually set the initial parameters </div><br />
: フィッティング関数のパラメータの初期値を自分で設定するかを選択してください。<br />
:: No: 内部で自動的に設定されます。(デフォルト)<br />
:: Yes: ユーザーが入力します。<br />
: フィッティングにおいて、複素屈折率はローレンツ関数を用いて表しています。<br />
:: <math>n_j=n_j^0+\sum_{l=1}^{l_{max}} \frac{A_l}{\nu_l-\nu-i\gamma_l}</math><br />
: <math> n_j^0 </math> ⑨での入力になっています。ローレンツ関数の本数<math> l_{max} </math>とそれに対応するパラメータ <math> A_l, \nu_l, \gamma_l </math> 初期値を決定する必要があります。<br />
: <math> No </math>を選んだ場合、パラメータの初期値は<u> [[Theory#Auto Fitting| Automatically determine the initial parameters in fitting procedure]] </u>で説明されているようなアルゴリズムで自動的に決定されます。<br />
: <math> Yes </math>を選んだ場合、<math> l_{max} </math> と それぞれのローレンツ関数に対する<math> A_l, \nu_l, \gamma_l </math>の初期値を自分で設定することが可能です。<math> A_l, \nu_l, \gamma_l </math> の単位は<math>cm^{-1}</math>で<math> l_{max} </math>の最大値は５になっています。<br />
: [[File:11yes.png|500px]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Input&diff=1010Input2022-02-16T04:47:12Z<p>Lwang: </p>
<hr />
<div><br />
<br />
: [[File:Newtoppage.png|1000px]]<br />
: This is the typical snapshot of the input of ComplexRI. <br />
: The input of ComplexRI contains two parts. The left part is the information of ATR-IR experimental data. The right part is the control parameters of the complex refractive index fitting procedure. Each part will be explained in the following. <br />
<br />
----<br />
<div id="Information of ATR-IR experiment" style="font-size: 200%;"> Information of ATR-IR experiment </div><br />
<br />
----<br />
<div id="Input01" style="font-size: 150%;"> ①ATR-IR File </div><br />
: Please upload the ATR-IR experimental data in this part. The inside should be like the following.<br />
: [[File:NewFILE01.png|200px]]<br />
: If there are characters at the beginning of the file, they will be ignored. The columns of wavenumber and ATR-IR data should be separated by space or comma. <br />
: For instance, the csv file exported by ATR-IR can be used. <br />
<br />
----<br />
<div id="Input02" style="font-size: 150%;"> ②The order of data </div><br />
: Please select the sort order of your data.<br />
:: Ascending order: The wavenumbers in the input file are in ascending order (left picture). (Default)<br />
:: Descending order: The wavenumbers in the input file are in descending order (right picture). <br />
:[[File:NewFILE01.png|200px]][[File:NewFILE04.png|220px]]<br />
<br />
----<br />
<div id="Input03" style="font-size: 150%;"> ③Reflectance or Absorptance? </div><br />
: Please select the type of your ATR-IR data.<br />
:: Reflectance(%): The Reflectance of ATR-IR spectra in the value of percentage. (Default)<br />
:: Reflectance: The Reflectance of ATR-IR spectra. <br />
:: Absorbance: The Absorbance of ATR-IR spectra.<br />
: The relationships between each data are<br />
:: <math> Reflectance(%)=Reflectance*100 </math><br />
:: <math> Absorbance=-\log_{10}(Reflectance) </math><br />
<br />
----<br />
<div id="Input04" style="font-size: 150%;"> ④The Substrate in ATR-IR </div><br />
: Please select the substrate you used in the ATR-IR experiment. Here, we prepare the three substrates that often used <br />
:: Diamond(Refractive Index = 2.38). (Default)<br />
:: Zinc selenide(Refractive Index = 2.40).<br />
:: Germanium(Refractive Index = 4.0).<br />
: You can also input the refractive index of your substrate by selecting Other in the list.<br />
:[[File:4_other.png|500px]]<br />
<br />
----<br />
<div id="Input05" style="font-size: 150%;"> ⑤Incident angle in ATR-IR </div><br />
: Please input the incident angle in your ATR-IR experiment. (Default=45 degree)<br />
<br />
----<br />
<div id="Input06" style="font-size: 150%;"> ⑥Select the column of your data </div><br />
: Please input the column number of the data that you want to analyze in your ATR-IR file. <br />
:: Wavenumber: The column number of wavenumber in your input file. (Default: 1)<br />
:: ATR-IR data: The column number of ATR-IR data in your input file. (Default: 2)<br />
<br />
: For example, an input file like following can be uploaded and column 1 and column 5 can be selected for analyzing. <br />
: [[File:NewFILE03.png|500px]]<br />
: [[File:6_15.png|300px]]<br />
<br />
----<br />
<br />
<div id="Control parameters of ComplexRI fitting" style="font-size: 200%;">Control parameters of ComplexRI fitting </div><br />
<br />
----<br />
<div id="Input07" style="font-size: 150%;"> ⑦Title of your job </div><br />
: Please input the title of your job (alphabet). The output results of ComplexRI will be saved in the excel format with the name @Title.xlsx<br />
<br />
----<br />
<div id="Input08" style="font-size: 150%;"> ⑧Input the fitting range </div><br />
: Please input the frequency range (in wavenumber) inside which you want to perform the fitting. ComplexRI will only fit the data inside the range you input here.<br />
:: Minimum wavenumber: The lower boundary of wavenumber. (Default: 1636)<br />
:: Maximum wavenumber: The upper boundary of wavenumber. (Default: 1863)<br />
<br />
---- <br />
<div id="Input09" style="font-size: 150%;"> ⑨Refractive index of target sample in non-resonance region (<math> n_j^0 </math>) </div><br />
: Please input the refractive index of the target sample (<math> n_j^0 </math>) in non-resonance region. (Default=1.360)<br />
: The determination of <math> n_j^0 </math> and some comments about it can be found in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>. <br />
<br />
----<br />
<div id="Input10" style="font-size: 150%;"> ⑩The tolerance of fitting </div><br />
: Please input the tolerance of the fitting procedure. (default: 0.02)<br />
: The fitting will be finished when the calculated residual is less than this value. The details are described in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>.<br />
:: Note: Fitting can not finish if this value is too small. You should increase this value when dealing with vibrational regions containing complicated vibrational bands. <br />
<br />
----<br />
<div id="Input11" style="font-size: 150%;"> ⑪ Manually set the initial parameters </div><br />
: Please select whether to set the initial fitting parameters by yourself. <br />
:: No: Automatically done by the algorithm (Default)<br />
:: Yes: Manually set the initial parameters by users. <br />
: In the fitting, we use a set of Lorentz functions to represent the complex refractive index <br />
:: <math>n_j=n_j^0+\sum_{l=1}^{l_{max}} \frac{A_l}{\nu_l-\nu-i\gamma_l}</math><br />
: where <math> n_j^0 </math> is input in ⑨. The number of Lorentz functions <math> l_{max} </math>, and the corresponding initial parameters <math> A_l, \nu_l, \gamma_l </math> should be determined.<br />
: By selecting <math> No </math>, it means the initial parameters are automatically guessed by the algorithm explained in <u> [[Theory#Auto Fitting| Automatically determine the initial parameters in fitting procedure]] </u>. <br />
: By selecting <math> Yes </math>, you can manually set <math> l_{max} </math> and <math> A_l, \nu_l, \gamma_l </math> for each Lorentz function by yourself. The units of <math> A_l, \nu_l, \gamma_l </math> are all wavenumber. <math> l_{max} </math> is up to 5.<br />
:: Note: <br />
::: 1. Automatical mode is recommended when using ComplexRI to fit new data. The results also provide useful information for users to further fitting the data by manual mode. <br />
::: 2. Automatical mode is designed to deal with the strong adsorption band. If uses want to fit to the vibrational regions with weak adsorption bands, manual mode might be better to represent the very detailed spectra.<br />
: [[File:11yes.png|500px]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=%E5%85%A5%E5%8A%9B&diff=1009入力2022-02-16T02:14:21Z<p>Lwang: </p>
<hr />
<div><br />
<br />
: [[File:Newtoppage.png|1000px]]<br />
: これはComplexRIの標準入力のスナップショットです。<br />
: ComplexRIの入力は大きく二つに分類されます。左の部分は、ATR-IR実験の情報に関する部分、右の部分は複素屈折率のフィッティングのパラメータを調整する部分です。以下では、それぞれについて説明します。<br />
<br />
----<br />
<div id="Information of ATR-IR experiment" style="font-size: 200%;"> Information of ATR-IR experiment </div><br />
<br />
----<br />
<div id="Input01" style="font-size: 150%;"> ①ATR-IR File </div><br />
: ここでは、ATR-IRの実験データをアップロードしてください。中身は以下のようになっている必要があります。<br />
: [[File:NewFILE01.png|200px]]<br />
: ファイルの先頭に文字がある場合、それらは無視されます。各列は空白またはコンマで区切られている。<br />
: 例えば、ATR-IRでエクスポートしたcsvファイルを使用できます。<br />
<br />
----<br />
<div id="Input02" style="font-size: 150%;"> ②The order of data </div><br />
: データの並び方を入力してください。<br />
:: Ascending order: 波数が昇順 (下の図の左側)。(デフォルト)<br />
:: Descending order:波数が降順 (下の図の右側)。 <br />
:[[File:NewFILE01.png|200px]][[File:NewFILE04.png|220px]]<br />
<br />
----<br />
<div id="Input03" style="font-size: 150%;"> ③Reflectance or Absorptance? </div><br />
: ATR-IRのデータの種類を選択してください。<br />
:: Reflectance(%): 反射率のスペクトル。単位は(%)。(デフォルト)<br />
:: Reflectance: 反射率のスペクトル。<br />
:: Absorptance: 吸光度スペクトル。<br />
: それぞれのデータは以下の関係を持っています。<br />
:: <math> Reflectance(%)=Reflectance*100 </math><br />
:: <math> Absorptance=-\log_{10}(Reflectance) </math><br />
<br />
----<br />
<div id="Input04" style="font-size: 150%;"> ④The Substrate in ATR-IR </div><br />
: ATR-IR実験で使用した基板の屈折率を入力してください。ここには、よく使われる３つの基板は選択として用意します。<br />
:: Diamond(Refractive Index = 2.38) (デフォルト)<br />
:: Zinc selenide(Refractive Index = 2.40)<br />
:: Germanium(Refractive Index = 4.0).<br />
:Otherを使うことで基板の屈折率の値を入力することもできます。<br />
:[[File:4_other.png|500px]]<br />
<br />
----<br />
<div id="Input05" style="font-size: 150%;"> ⑤Incident angle in ATR-IR </div><br />
: ATR-IR実験のIR光の入射角を入力してください。(デフォルト=45°)<br />
<br />
----<br />
<div id="Input06" style="font-size: 150%;"> ⑥Select the column of your data </div><br />
: 入力ファイルの中で解析したいデータの列番号を入力してください。<br />
:: Wavenumber: 波数の列番号。 (デフォルト: 1)<br />
:: ATR-IR data: 反射率もしくは吸光度の列番号。(デフォルト: 2)<br />
<br />
: 例えば、以下のようなファイルをアップロードした場合は、１列目と５列目を選んで解析に用いることができる。 <br />
: [[File:NewFILE03.png|500px]]<br />
: [[File:6_15.png|300px]]<br />
<br />
----<br />
<br />
<div id="Control parameters of ComplexRI fitting" style="font-size: 200%;">Control parameters of ComplexRI fitting </div><br />
<br />
----<br />
<div id="Input07" style="font-size: 150%;"> ⑦Title of your job </div><br />
: 今回の解析に名前を付けてください。<span color=”red”>(※半角入力)</span>。 結果は@Title.xlsxという名前のエクセルファイルに保存されます。<br />
<br />
----<br />
<div id="Input08" style="font-size: 150%;"> ⑧Input the fitting range </div><br />
: フィッティングを行う範囲を波数単位で入力してください。ComplexRIはこの範囲でのみ解析を行います。<br />
:: Minimum wavenumber: 波数の下限。 (デフォルト: 1636)<br />
:: Maximum wavenumber: 波数の上限。 (デフォルト: 1863)<br />
<br />
---- <br />
<div id="Input09" style="font-size: 150%;"> ⑨Refractive index of target sample in non-resonance region (<math> n_j^0 </math>) </div><br />
: 対象分子の非共鳴領域における屈折率(<math> n_j^0 </math>)を入力してください。(デフォルト＝1.360)<br />
: 詳細は<u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>で説明しています。<br />
<br />
----<br />
<div id="Input10" style="font-size: 150%;"> ⑩The tolerance of fitting </div><br />
: フィッティングの収束判定のしきい値を指定してください。(デフォルト: 0.02)<br />
: 最小二乗法の残差は与えられた値よりも小さくなったらフィッティングが終了します。<br />
: 詳細は<u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>で説明しています。<br />
:<span style color="red">注意!! この入力値が小さすぎると解析が終わらないことがあります。 </span><br />
<br />
----<br />
<div id="Input11" style="font-size: 150%;"> ⑪ Manually set the initial parameters </div><br />
: フィッティング関数のパラメータの初期値を自分で設定するかを選択してください。<br />
:: No: 内部で自動的に設定されます。(デフォルト)<br />
:: Yes: ユーザーが入力します。<br />
: フィッティングにおいて、複素屈折率はローレンツ関数を用いて表しています。<br />
:: <math>n_j=n_j^0+\sum_{l=1}^{l_{max}} \frac{A_l}{\nu_l-\nu-i\gamma_l}</math><br />
: <math> n_j^0 </math> ⑨での入力になっています。ローレンツ関数の本数<math> l_{max} </math>とそれに対応するパラメータ <math> A_l, \nu_l, \gamma_l </math> 初期値を決定する必要があります。<br />
: <math> No </math>を選んだ場合、パラメータの初期値は<u> [[Theory#Auto Fitting| Automatically determine the initial parameters in fitting procedure]] </u>で説明されているようなアルゴリズムで自動的に決定されます。<br />
: <math> Yes </math>を選んだ場合、<math> l_{max} </math> と それぞれのローレンツ関数に対する<math> A_l, \nu_l, \gamma_l </math>の初期値を自分で設定することが可能です。<math> A_l, \nu_l, \gamma_l </math> の単位は<math>cm^{-1}</math>で<math> l_{max} </math>の最大値は５になっています。<br />
: [[File:11yes.png|500px]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Input&diff=1008Input2022-02-16T02:05:46Z<p>Lwang: </p>
<hr />
<div><br />
<br />
: [[File:Newtoppage.png|1000px]]<br />
: This is the typical snapshot of the input of ComplexRI. <br />
: The input of ComplexRI contains two parts. The left part is the information of ATR-IR experimental data. The right part is the control parameters of the complex refractive index fitting procedure. Each part will be explained in the following. <br />
<br />
----<br />
<div id="Information of ATR-IR experiment" style="font-size: 200%;"> Information of ATR-IR experiment </div><br />
<br />
----<br />
<div id="Input01" style="font-size: 150%;"> ①ATR-IR File </div><br />
: Please upload the ATR-IR experimental data in this part. The inside should be like the following.<br />
: [[File:NewFILE01.png|200px]]<br />
: If there are characters at the beginning of the file, they will be ignored. The columns of wavenumber and ATR-IR data should be separated by space or comma. <br />
: For instance, the csv file exported by ATR-IR can be used. <br />
<br />
----<br />
<div id="Input02" style="font-size: 150%;"> ②The order of data </div><br />
: Please select the sort order of your data.<br />
:: Ascending order: The wavenumbers in the input file are in ascending order (left picture). (Default)<br />
:: Descending order: The wavenumbers in the input file are in descending order (right picture). <br />
:[[File:NewFILE01.png|200px]][[File:NewFILE04.png|220px]]<br />
<br />
----<br />
<div id="Input03" style="font-size: 150%;"> ③Reflectance or Absorptance? </div><br />
: Please select the type of your ATR-IR data.<br />
:: Reflectance(%): The Reflectance of ATR-IR spectra in the value of percentage. (Default)<br />
:: Reflectance: The Reflectance of ATR-IR spectra. <br />
:: Absorptance: The Absorptance of ATR-IR spectra.<br />
: The relationships between each data are<br />
:: <math> Reflectance(%)=Reflectance*100 </math><br />
:: <math> Absorptance=-\log_{10}(Reflectance) </math><br />
<br />
----<br />
<div id="Input04" style="font-size: 150%;"> ④The Substrate in ATR-IR </div><br />
: Please select the substrate you used in the ATR-IR experiment. Here, we prepare the three substrates that often used <br />
:: Diamond(Refractive Index = 2.38). (Default)<br />
:: Zinc selenide(Refractive Index = 2.40).<br />
:: Germanium(Refractive Index = 4.0).<br />
: You can also input the refractive index of your substrate by selecting Other in the list.<br />
:[[File:4_other.png|500px]]<br />
<br />
----<br />
<div id="Input05" style="font-size: 150%;"> ⑤Incident angle in ATR-IR </div><br />
: Please input the incident angle in your ATR-IR experiment. (Default=45 degree)<br />
<br />
----<br />
<div id="Input06" style="font-size: 150%;"> ⑥Select the column of your data </div><br />
: Please input the column number of the data that you want to analyze in your ATR-IR file. <br />
:: Wavenumber: The column number of wavenumber in your input file. (Default: 1)<br />
:: ATR-IR data: The column number of ATR-IR data in your input file. (Default: 2)<br />
<br />
: For example, an input file like following can be uploaded and column 1 and column 5 can be selected for analyzing. <br />
: [[File:NewFILE03.png|500px]]<br />
: [[File:6_15.png|300px]]<br />
<br />
----<br />
<br />
<div id="Control parameters of ComplexRI fitting" style="font-size: 200%;">Control parameters of ComplexRI fitting </div><br />
<br />
----<br />
<div id="Input07" style="font-size: 150%;"> ⑦Title of your job </div><br />
: Please input the title of your job (alphabet). The output results of ComplexRI will be saved in the excel format with the name @Title.xlsx<br />
<br />
----<br />
<div id="Input08" style="font-size: 150%;"> ⑧Input the fitting range </div><br />
: Please input the frequency range (in wavenumber) inside which you want to perform the fitting. ComplexRI will only fit the data inside the range you input here.<br />
:: Minimum wavenumber: The lower boundary of wavenumber. (Default: 1636)<br />
:: Maximum wavenumber: The upper boundary of wavenumber. (Default: 1863)<br />
<br />
---- <br />
<div id="Input09" style="font-size: 150%;"> ⑨Refractive index of target sample in non-resonance region (<math> n_j^0 </math>) </div><br />
: Please input the refractive index of the target sample (<math> n_j^0 </math>) in non-resonance region. (Default=1.360)<br />
: The determination of <math> n_j^0 </math> and some comments about it can be found in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>. <br />
<br />
----<br />
<div id="Input10" style="font-size: 150%;"> ⑩The tolerance of fitting </div><br />
: Please input the tolerance of the fitting procedure. (default: 0.02)<br />
: The fitting will be finished when the calculated residual is less than this value. The details are described in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>.<br />
:: Note: Fitting can not finish if this value is too small. You should increase this value when dealing with vibrational regions containing complicated vibrational bands. <br />
<br />
----<br />
<div id="Input11" style="font-size: 150%;"> ⑪ Manually set the initial parameters </div><br />
: Please select whether to set the initial fitting parameters by yourself. <br />
:: No: Automatically done by the algorithm (Default)<br />
:: Yes: Manually set the initial parameters by users. <br />
: In the fitting, we use a set of Lorentz functions to represent the complex refractive index <br />
:: <math>n_j=n_j^0+\sum_{l=1}^{l_{max}} \frac{A_l}{\nu_l-\nu-i\gamma_l}</math><br />
: where <math> n_j^0 </math> is input in ⑨. The number of Lorentz functions <math> l_{max} </math>, and the corresponding initial parameters <math> A_l, \nu_l, \gamma_l </math> should be determined.<br />
: By selecting <math> No </math>, it means the initial parameters are automatically guessed by the algorithm explained in <u> [[Theory#Auto Fitting| Automatically determine the initial parameters in fitting procedure]] </u>. <br />
: By selecting <math> Yes </math>, you can manually set <math> l_{max} </math> and <math> A_l, \nu_l, \gamma_l </math> for each Lorentz function by yourself. The units of <math> A_l, \nu_l, \gamma_l </math> are all wavenumber. <math> l_{max} </math> is up to 5.<br />
:: Note: <br />
::: 1. Automatical mode is recommended when using ComplexRI to fit new data. The results also provide useful information for users to further fitting the data by manual mode. <br />
::: 2. Automatical mode is designed to deal with the strong adsorption band. If uses want to fit to the vibrational regions with weak adsorption bands, manual mode might be better to represent the very detailed spectra.<br />
: [[File:11yes.png|500px]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Input&diff=1007Input2022-02-16T02:04:39Z<p>Lwang: </p>
<hr />
<div><br />
<br />
: [[File:Newtoppage.png|1000px]]<br />
: This is the typical snapshot of the input of ComplexRI. <br />
: The input of ComplexRI contains two parts. The left part is the information of ATR-IR experimental data. The right part is the control parameters of the complex refractive index fitting procedure. Each part will be explained in the following. <br />
<br />
----<br />
<div id="Information of ATR-IR experiment" style="font-size: 200%;"> Information of ATR-IR experiment </div><br />
<br />
----<br />
<div id="Input01" style="font-size: 150%;"> ①ATR-IR File </div><br />
: Please upload the ATR-IR experimental data in this part. The inside should be like the following.<br />
: [[File:NewFILE01.png|200px]]<br />
: If there are characters at the beginning of the file, they will be ignored. The columns of wavenumber and ATR-IR data should be separated by space or comma. <br />
: For instance, the csv file exported by ATR-IR can be used. <br />
<br />
----<br />
<div id="Input02" style="font-size: 150%;"> ②The order of data </div><br />
: Please select the sort order of your data.<br />
:: Ascending order: The wavenumbers in the input file are in ascending order (left picture). (Default)<br />
:: Descending order: The wavenumbers in the input file are in descending order (right picture). <br />
:[[File:NewFILE01.png|200px]][[File:NewFILE04.png|220px]]<br />
<br />
----<br />
<div id="Input03" style="font-size: 150%;"> ③Reflectance or Absorptance? </div><br />
: Please select the type of your ATR-IR data.<br />
:: Reflectance(%): The Reflectance of ATR-IR spectra in the value of percentage. (Default)<br />
:: Reflectance: The Reflectance of ATR-IR spectra. <br />
:: Absorptance: The Absorptance of ATR-IR spectra.<br />
: The relationships between each data are<br />
:: <math> Reflectance(%)=Reflectance*100 </math><br />
:: <math> Absorptance=-\log_{10}(Reflectance) </math><br />
<br />
----<br />
<div id="Input04" style="font-size: 150%;"> ④The Substrate in ATR-IR </div><br />
: Please select the substrate you used in the ATR-IR experiment. Here, we prepare the three substrates that often used <br />
:: Diamond(Refractive Index = 2.38). (Default)<br />
:: Zinc selenide(Refractive Index = 2.40).<br />
:: Germanium(Refractive Index = 4.0).<br />
: You can also input the refractive index of your substrate by selecting Other in the list.<br />
:[[File:4_other.png|500px]]<br />
<br />
----<br />
<div id="Input05" style="font-size: 150%;"> ⑤Incident angle in ATR-IR </div><br />
: Please input the incident angle in your ATR-IR experiment. (Default=45 degree)<br />
<br />
----<br />
<div id="Input06" style="font-size: 150%;"> ⑥Select the column of your data </div><br />
: Please input the column number of the data that you want to analyze in your ATR-IR file. <br />
:: Wavenumber: The column number of wavenumber in your input file. (Default: 1)<br />
:: ATR-IR data: The column number of ATR-IR data in your input file. (Default: 2)<br />
<br />
: For example, an input file like following can be uploaded and column 1 and column 5 can be selected for analyzing. <br />
: [[File:NewFILE03.png|500px]]<br />
: [[File:6_15.png|300px]]<br />
<br />
----<br />
<br />
<div id="Control parameters of ComplexRI fitting" style="font-size: 200%;">Control parameters of ComplexRI fitting </div><br />
<br />
----<br />
<div id="Input07" style="font-size: 150%;"> ⑦Title of your job </div><br />
: Please input the title of your job (alphabet). The output results of ComplexRI will be saved in the excel format with the name @Title.xlsx<br />
<br />
----<br />
<div id="Input08" style="font-size: 150%;"> ⑧Input the fitting range </div><br />
: Please input the frequency range (in wavenumber) inside which you want to perform the fitting. ComplexRI will only fit the data inside the range you input here.<br />
:: Minimum wavenumber: The lower boundary of wavenumber. (Default: 1636)<br />
:: Maximum wavenumber: The upper boundary of wavenumber. (Default: 1863)<br />
<br />
---- <br />
<div id="Input09" style="font-size: 150%;"> ⑨Refractive index of target sample in non-resonance region (<math> n_j^0 </math>) </div><br />
: Please input the refractive index of the target sample (<math> n_j^0 </math>) in non-resonance region. (Default=1.360)<br />
: The determination of <math> n_j^0 </math> and some comments about it can be found in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>. <br />
<br />
----<br />
<div id="Input10" style="font-size: 150%;"> ⑩The tolerance of fitting </div><br />
: Please input the tolerance of the fitting procedure. (default: 0.02)<br />
: The fitting will be finished when the calculated residual is less than this value. The details are described in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>.<br />
:: Note: Fitting can not finish if this value is too small. You should increase this value when dealing with vibrational regions containing complicated vibrational bands. <br />
<br />
----<br />
<div id="Input11" style="font-size: 150%;"> ⑪ Manually set the initial parameters </div><br />
: Please select whether to set the initial fitting parameters by yourself. <br />
:: No: Automatically done by the algorithm (Default)<br />
:: Yes: Manually set the initial parameters by users. <br />
: In the fitting, we use a set of Lorentz functions to represent the complex refractive index <br />
:: <math>n_j=n_j^0+\sum_{l=1}^{l_{max}} \frac{A_l}{\nu_l-\nu-i\gamma_l}</math><br />
: where <math> n_j^0 </math> is input in ⑨. The number of Lorentz functions <math> l_{max} </math>, and the corresponding initial parameters <math> A_l, \nu_l, \gamma_l </math> should be determined.<br />
: By selecting <math> No </math>, it means the initial parameters are automatically guessed by the algorithm explained in <u> [[Theory#Auto Fitting| Automatically determine the initial parameters in fitting procedure]] </u>. <br />
: By selecting <math> Yes </math>, you can manually set <math> l_{max} </math> and <math> A_l, \nu_l, \gamma_l </math> for each Lorentz function by yourself. The units of <math> A_l, \nu_l, \gamma_l </math> are all wavenumber. <math> l_{max} </math> is up to 5.<br />
:: Note: <br />
::: 1. Automatical mode is recommended when you use ComplexRI to fit new data. The results also provide useful information for you to further fitting the data by manual mode. <br />
::: 2. Automatical mode is designed to deal with the strong adsorption band. If uses want to fit to the vibrational regions with weak adsorption bands, manual mode might be better to represent the very detailed spectra.<br />
: [[File:11yes.png|500px]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Input&diff=1006Input2022-02-16T02:03:31Z<p>Lwang: </p>
<hr />
<div><br />
<br />
: [[File:Newtoppage.png|1000px]]<br />
: This is the typical snapshot of the input of ComplexRI. <br />
: The input of ComplexRI contains two parts. The left part is the information of ATR-IR experimental data. The right part is the control parameters of the complex refractive index fitting procedure. Each part will be explained in the following. <br />
<br />
----<br />
<div id="Information of ATR-IR experiment" style="font-size: 200%;"> Information of ATR-IR experiment </div><br />
<br />
----<br />
<div id="Input01" style="font-size: 150%;"> ①ATR-IR File </div><br />
: Please upload the ATR-IR experimental data in this part. The inside should be like the following.<br />
: [[File:NewFILE01.png|200px]]<br />
: If there are characters at the beginning of the file, they will be ignored. The columns of wavenumber and ATR-IR data should be separated by space or comma. <br />
: For instance, the csv file exported by ATR-IR can be used. <br />
<br />
----<br />
<div id="Input02" style="font-size: 150%;"> ②The order of data </div><br />
: Please select the sort order of your data.<br />
:: Ascending order: The wavenumbers in the input file are in ascending order (left picture). (Default)<br />
:: Descending order: The wavenumbers in the input file are in descending order (right picture). <br />
:[[File:NewFILE01.png|200px]][[File:NewFILE04.png|220px]]<br />
<br />
----<br />
<div id="Input03" style="font-size: 150%;"> ③Reflectance or Absorptance? </div><br />
: Please select the type of your ATR-IR data.<br />
:: Reflectance(%): The Reflectance of ATR-IR spectra in the value of percentage. (Default)<br />
:: Reflectance: The Reflectance of ATR-IR spectra. <br />
:: Absorptance: The Absorptance of ATR-IR spectra.<br />
: The relationships between each data are<br />
:: <math> Reflectance(%)=Reflectance*100 </math><br />
:: <math> Absorptance=-\log_{10}(Reflectance) </math><br />
<br />
----<br />
<div id="Input04" style="font-size: 150%;"> ④The Substrate in ATR-IR </div><br />
: Please select the substrate you used in the ATR-IR experiment. Here, we prepare the three substrates that often used <br />
:: Diamond(Refractive Index = 2.38). (Default)<br />
:: Zinc selenide(Refractive Index = 2.40).<br />
:: Germanium(Refractive Index = 4.0).<br />
: You can also input the refractive index of your substrate by selecting Other in the list.<br />
:[[File:4_other.png|500px]]<br />
<br />
----<br />
<div id="Input05" style="font-size: 150%;"> ⑤Incident angle in ATR-IR </div><br />
: Please input the incident angle in your ATR-IR experiment. (Default=45 degree)<br />
<br />
----<br />
<div id="Input06" style="font-size: 150%;"> ⑥Select the column of your data </div><br />
: Please input the column number of the data that you want to analyze in your ATR-IR file. <br />
:: Wavenumber: The column number of wavenumber in your input file. (Default: 1)<br />
:: ATR-IR data: The column number of ATR-IR data in your input file. (Default: 2)<br />
<br />
: For example, an input file like following can be uploaded and column 1 and column 5 can be selected for analyzing. <br />
: [[File:NewFILE03.png|500px]]<br />
: [[File:6_15.png|300px]]<br />
<br />
----<br />
<br />
<div id="Control parameters of ComplexRI fitting" style="font-size: 200%;">Control parameters of ComplexRI fitting </div><br />
<br />
----<br />
<div id="Input07" style="font-size: 150%;"> ⑦Title of your job </div><br />
: Please input the title of your job (alphabet). The output results of ComplexRI will be saved in the excel format with the name @Title.xlsx<br />
<br />
----<br />
<div id="Input08" style="font-size: 150%;"> ⑧Input the fitting range </div><br />
: Please input the frequency range (in wavenumber) inside which you want to perform the fitting. ComplexRI will only fit the data inside the range you input here.<br />
:: Minimum wavenumber: The lower boundary of wavenumber. (Default: 1636)<br />
:: Maximum wavenumber: The upper boundary of wavenumber. (Default: 1863)<br />
<br />
---- <br />
<div id="Input09" style="font-size: 150%;"> ⑨Refractive index of target sample in non-resonance region (<math> n_j^0 </math>) </div><br />
: Please input the refractive index of the target sample (<math> n_j^0 </math>) in non-resonance region. (Default=1.360)<br />
: The determination of <math> n_j^0 </math> and some comments about it can be found in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>. <br />
<br />
----<br />
<div id="Input10" style="font-size: 150%;"> ⑩The tolerance of fitting </div><br />
: Please input the tolerance of the fitting procedure. (default: 0.02)<br />
: The fitting will be finished when the calculated residual is less than this value. The details are described in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>.<br />
:: Note: Fitting can not finish if this value is too small. You should increase this value when dealing with vibrational regions containing complicated vibrational bands. <br />
<br />
----<br />
<div id="Input11" style="font-size: 150%;"> ⑪ Manually set the initial parameters </div><br />
: Please select whether to set the initial fitting parameters by yourself. <br />
:: No: Automatically done by the algorithm (Default)<br />
:: Yes: Manually set the initial parameters by users. <br />
: In the fitting, we use a set of Lorentz functions to represent the complex refractive index <br />
:: <math>n_j=n_j^0+\sum_{l=1}^{l_{max}} \frac{A_l}{\nu_l-\nu-i\gamma_l}</math><br />
: where <math> n_j^0 </math> is input in ⑨. The number of Lorentz functions <math> l_{max} </math>, and the corresponding initial parameters <math> A_l, \nu_l, \gamma_l </math> should be determined.<br />
: By selecting <math> No </math>, it means the initial parameters are automatically guessed by the algorithm explained in <u> [[Theory#Auto Fitting| Automatically determine the initial parameters in fitting procedure]] </u>. <br />
: By selecting <math> Yes </math>, you can manually set <math> l_{max} </math> and <math> A_l, \nu_l, \gamma_l </math> for each Lorentz function by yourself. The units of <math> A_l, \nu_l, \gamma_l </math> are all wavenumber. <math> l_{max} </math> is up to 5.<br />
:: Note: 1. Automatical mode is recommended when you use ComplexRI to fit new data. The results also provide useful information for you to further fitting the data by manual mode. <br />
:: 2. Automatical mode is designed to deal with the strong adsorption band. If uses want to fit to the vibrational regions with weak adsorption bands, manual mode might be better to represent the very detailed spectra.<br />
: [[File:11yes.png|500px]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Input&diff=1005Input2022-02-16T01:58:08Z<p>Lwang: </p>
<hr />
<div><br />
<br />
: [[File:Newtoppage.png|1000px]]<br />
: This is the typical snapshot of the input of ComplexRI. <br />
: The input of ComplexRI contains two parts. The left part is the information of ATR-IR experimental data. The right part is the control parameters of the complex refractive index fitting procedure. Each part will be explained in the following. <br />
<br />
----<br />
<div id="Information of ATR-IR experiment" style="font-size: 200%;"> Information of ATR-IR experiment </div><br />
<br />
----<br />
<div id="Input01" style="font-size: 150%;"> ①ATR-IR File </div><br />
: Please upload the ATR-IR experimental data in this part. The inside should be like the following.<br />
: [[File:NewFILE01.png|200px]]<br />
: If there are characters at the beginning of the file, they will be ignored. The columns of wavenumber and ATR-IR data should be separated by space or comma. <br />
: For instance, the csv file exported by ATR-IR can be used. <br />
<br />
----<br />
<div id="Input02" style="font-size: 150%;"> ②The order of data </div><br />
: Please select the sort order of your data.<br />
:: Ascending order: The wavenumbers in the input file are in ascending order (left picture). (Default)<br />
:: Descending order: The wavenumbers in the input file are in descending order (right picture). <br />
:[[File:NewFILE01.png|200px]][[File:NewFILE04.png|220px]]<br />
<br />
----<br />
<div id="Input03" style="font-size: 150%;"> ③Reflectance or Absorptance? </div><br />
: Please select the type of your ATR-IR data.<br />
:: Reflectance(%): The Reflectance of ATR-IR spectra in the value of percentage. (Default)<br />
:: Reflectance: The Reflectance of ATR-IR spectra. <br />
:: Absorptance: The Absorptance of ATR-IR spectra.<br />
: The relationships between each data are<br />
:: <math> Reflectance(%)=Reflectance*100 </math><br />
:: <math> Absorptance=-\log_{10}(Reflectance) </math><br />
<br />
----<br />
<div id="Input04" style="font-size: 150%;"> ④The Substrate in ATR-IR </div><br />
: Please select the substrate you used in the ATR-IR experiment. Here, we prepare the three substrates that often used <br />
:: Diamond(Refractive Index = 2.38). (Default)<br />
:: Zinc selenide(Refractive Index = 2.40).<br />
:: Germanium(Refractive Index = 4.0).<br />
: You can also input the refractive index of your substrate by selecting Other in the list.<br />
:[[File:4_other.png|500px]]<br />
<br />
----<br />
<div id="Input05" style="font-size: 150%;"> ⑤Incident angle in ATR-IR </div><br />
: Please input the incident angle in your ATR-IR experiment. (Default=45 degree)<br />
<br />
----<br />
<div id="Input06" style="font-size: 150%;"> ⑥Select the column of your data </div><br />
: Please input the column number of the data that you want to analyze in your ATR-IR file. <br />
:: Wavenumber: The column number of wavenumber in your input file. (Default: 1)<br />
:: ATR-IR data: The column number of ATR-IR data in your input file. (Default: 2)<br />
<br />
: For example, an input file like following can be uploaded and column 1 and column 5 can be selected for analyzing. <br />
: [[File:NewFILE03.png|500px]]<br />
: [[File:6_15.png|300px]]<br />
<br />
----<br />
<br />
<div id="Control parameters of ComplexRI fitting" style="font-size: 200%;">Control parameters of ComplexRI fitting </div><br />
<br />
----<br />
<div id="Input07" style="font-size: 150%;"> ⑦Title of your job </div><br />
: Please input the title of your job (alphabet). The output results of ComplexRI will be saved in the excel format with the name @Title.xlsx<br />
<br />
----<br />
<div id="Input08" style="font-size: 150%;"> ⑧Input the fitting range </div><br />
: Please input the frequency range (in wavenumber) inside which you want to perform the fitting. ComplexRI will only fit the data inside the range you input here.<br />
:: Minimum wavenumber: The lower boundary of wavenumber. (Default: 1636)<br />
:: Maximum wavenumber: The upper boundary of wavenumber. (Default: 1863)<br />
<br />
---- <br />
<div id="Input09" style="font-size: 150%;"> ⑨Refractive index of target sample in non-resonance region (<math> n_j^0 </math>) </div><br />
: Please input the refractive index of the target sample (<math> n_j^0 </math>) in non-resonance region. (Default=1.360)<br />
: The determination of <math> n_j^0 </math> and some comments about it can be found in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>. <br />
<br />
----<br />
<div id="Input10" style="font-size: 150%;"> ⑩The tolerance of fitting </div><br />
: Please input the tolerance of the fitting procedure. (default: 0.02)<br />
: The fitting will be finished when the calculated residual is less than this value. The details are described in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>.<br />
:: Note: Fitting can not finish if this value is too small. You should increase this value when dealing with vibrational regions containing complicated vibrational bands. <br />
<br />
----<br />
<div id="Input11" style="font-size: 150%;"> ⑪ Manually set the initial parameters </div><br />
: Please select whether to set the initial fitting parameters by yourself. <br />
:: No: Automatically done by the algorithm (Default)<br />
:: Yes: Manually set the initial parameters by users. <br />
: In the fitting, we use a set of Lorentz functions to represent the complex refractive index <br />
:: <math>n_j=n_j^0+\sum_{l=1}^{l_{max}} \frac{A_l}{\nu_l-\nu-i\gamma_l}</math><br />
: where <math> n_j^0 </math> is input in ⑨. The number of Lorentz functions <math> l_{max} </math>, and the corresponding initial parameters <math> A_l, \nu_l, \gamma_l </math> should be determined.<br />
: By selecting <math> No </math>, it means the initial parameters are automatically guessed by the algorithm explained in <u> [[Theory#Auto Fitting| Automatically determine the initial parameters in fitting procedure]] </u>. <br />
: By selecting <math> Yes </math>, you can manually set <math> l_{max} </math> and <math> A_l, \nu_l, \gamma_l </math> for each Lorentz function by yourself. The units of <math> A_l, \nu_l, \gamma_l </math> are all wavenumber. <math> l_{max} </math> is up to 5.<br />
:: Note: Automatical mode is recommended when you use ComplexRI to fit new data. The results also provide useful information for you to further fitting the data by manual mode. <br />
: [[File:11yes.png|500px]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=MediaWiki:Sidebar&diff=1004MediaWiki:Sidebar2022-02-15T02:27:59Z<p>Lwang: </p>
<hr />
<div><br />
* navigation<br />
* ComplexRI Manual<br />
** ComplexRI Manual#Tutorial|Tutorial<br />
** ComplexRI Manual#Manual|Manual<br />
** ComplexRI Manual#Theory|Theory<br />
<br />
* ComplexRI Manual (Japanese)<br />
** ComplexRI Manual (Japanese)#チュートリアル|チュートリアル<br />
** ComplexRI Manual (Japanese)#マニュアル|マニュアル<br />
** ComplexRI Manual (Japanese)#理論|理論<br />
<br />
* その他<br />
** mainpage|mainpage-description<br />
** recentchanges-url|recentchanges<br />
** randompage-url|randompage<br />
** helppage|help-mediawiki<br />
* SEARCH<br />
* TOOLBOX<br />
* LANGUAGES</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=ComplexRI_Manual_(Japanese)&diff=1003ComplexRI Manual (Japanese)2022-02-15T02:27:20Z<p>Lwang: </p>
<hr />
<div><br />
== チュートリアル ==<br />
<br />
ComplexRIを初めて使用するときは、このチュートリアルに従うことをお勧めします。<br />
<br />
: [[チュートリアル01|チュートリアル01]]<br />
: [[チュートリアル02|チュートリアル02]]<br />
<br />
----<br />
<br />
<br />
<br />
== マニュアル ==<br />
<br />
ComplexRIの入力と出力の詳細な説明。<br />
<br />
: [[入力|ComplexRIの入力]]<br />
: [[出力|ComplexRIの出力]]<br />
<br />
----<br />
<br />
<br />
<br />
== 理論 ==<br />
<br />
ComplexRIのフィッティング手順における理論の詳細な説明。<br />
<br />
: [[Theory#ATR-IR data|1. Calculated reflectance of ATR-IR from complex refractive index]]<br />
: [[Theory#Fitting procedure|2. How to Fit the ATR-IR spectra]]<br />
: [[Theory#Auto Fitting|3. Automatically determine the initial parameters in fitting procedure]]<br />
<br />
----<br />
<br />
[http://comp.chem.tohoku.ac.jp/mediawiki/index.php/en/ComplexRI Top of this page]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Input&diff=1002Input2022-02-15T02:17:53Z<p>Lwang: </p>
<hr />
<div><br />
<br />
: [[File:Newtoppage.png|1000px]]<br />
: This is the typical snapshot of the input of ComplexRI. <br />
: The input of ComplexRI contains two parts. The left part is the information of ATR-IR experimental data. The right part is the control parameters of the complex refractive index fitting procedure. Each part will be explained in the following. <br />
<br />
----<br />
<div id="Information of ATR-IR experiment" style="font-size: 200%;"> Information of ATR-IR experiment </div><br />
<br />
----<br />
<div id="Input01" style="font-size: 150%;"> ①ATR-IR File </div><br />
: Please upload the ATR-IR experimental data in this part. The inside should be like the following.<br />
: [[File:NewFILE01.png|200px]]<br />
: There are two rules for the format of input file.<br />
: (1). The format of input file must be txt.<br />
: (2). The columns are separated by the space.<br />
<br />
----<br />
<div id="Input02" style="font-size: 150%;"> ②The order of data </div><br />
: Please select the sort order of your data.<br />
:: Ascending order: The wavenumbers in the input file are in ascending order (left picture). (Default)<br />
:: Descending order: The wavenumbers in the input file are in descending order (right picture). <br />
:[[File:NewFILE01.png|200px]][[File:NewFILE04.png|220px]]<br />
<br />
----<br />
<div id="Input03" style="font-size: 150%;"> ③Reflectance or Absorptance? </div><br />
: Please select the type of your ATR-IR data.<br />
:: Reflectance(%): The Reflectance of ATR-IR spectra in the value of percentage. (Default)<br />
:: Reflectance: The Reflectance of ATR-IR spectra. <br />
:: Absorptance: The Absorptance of ATR-IR spectra.<br />
: The relationships between each data are<br />
:: <math> Reflectance(%)=Reflectance*100 </math><br />
:: <math> Absorptance=-\log_{10}(Reflectance) </math><br />
<br />
----<br />
<div id="Input04" style="font-size: 150%;"> ④The Substrate in ATR-IR </div><br />
: Please select the substrate you used in the ATR-IR experiment. Here, we prepare the three substrates that often used <br />
:: Diamond(Refractive Index = 2.38). (Default)<br />
:: Zinc selenide(Refractive Index = 2.40).<br />
:: Germanium(Refractive Index = 4.0).<br />
: You can also input the refractive index of your substrate by selecting Other in the list.<br />
:[[File:4_other.png|500px]]<br />
<br />
----<br />
<div id="Input05" style="font-size: 150%;"> ⑤Incident angle in ATR-IR </div><br />
: Please input the incident angle in your ATR-IR experiment. (Default=45 degree)<br />
<br />
----<br />
<div id="Input06" style="font-size: 150%;"> ⑥Select the column of your data </div><br />
: Please input the column number of the data that you want to analyze in your ATR-IR file. <br />
:: Wavenumber: The column number of wavenumber in your input file. (Default: 1)<br />
:: ATR-IR data: The column number of ATR-IR data in your input file. (Default: 2)<br />
<br />
: For example, an input file like following can be uploaded and column 1 and column 5 can be selected for analyzing. <br />
: [[File:NewFILE03.png|500px]]<br />
: [[File:6_15.png|300px]]<br />
<br />
----<br />
<br />
<div id="Control parameters of ComplexRI fitting" style="font-size: 200%;">Control parameters of ComplexRI fitting </div><br />
<br />
----<br />
<div id="Input07" style="font-size: 150%;"> ⑦Title of your job </div><br />
: Please input the title of your job (alphabet). The output results of ComplexRI will be saved in the excel format with the name @Title.xlsx<br />
<br />
----<br />
<div id="Input08" style="font-size: 150%;"> ⑧Input the fitting range </div><br />
: Please input the frequency range (in wavenumber) inside which you want to perform the fitting. ComplexRI will only fit the data inside the range you input here.<br />
:: Minimum wavenumber: The lower boundary of wavenumber. (Default: 1636)<br />
:: Maximum wavenumber: The upper boundary of wavenumber. (Default: 1863)<br />
<br />
---- <br />
<div id="Input09" style="font-size: 150%;"> ⑨Refractive index of target sample in non-resonance region (<math> n_j^0 </math>) </div><br />
: Please input the refractive index of the target sample (<math> n_j^0 </math>) in non-resonance region. (Default=1.360)<br />
: The determination of <math> n_j^0 </math> and some comments about it can be found in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>. <br />
<br />
----<br />
<div id="Input10" style="font-size: 150%;"> ⑩The tolerance of fitting </div><br />
: Please input the tolerance of the fitting procedure. (default: 0.02)<br />
: The fitting will be finished when the calculated residual is less than this value. The details are described in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>.<br />
:: Note: Fitting can not finish if this value is too small. You should increase this value when dealing with vibrational regions containing complicated vibrational bands. <br />
<br />
----<br />
<div id="Input11" style="font-size: 150%;"> ⑪ Manually set the initial parameters </div><br />
: Please select whether to set the initial fitting parameters by yourself. <br />
:: No: Automatically done by the algorithm (Default)<br />
:: Yes: Manually set the initial parameters by users. <br />
: In the fitting, we use a set of Lorentz functions to represent the complex refractive index <br />
:: <math>n_j=n_j^0+\sum_{l=1}^{l_{max}} \frac{A_l}{\nu_l-\nu-i\gamma_l}</math><br />
: where <math> n_j^0 </math> is input in ⑨. The number of Lorentz functions <math> l_{max} </math>, and the corresponding initial parameters <math> A_l, \nu_l, \gamma_l </math> should be determined.<br />
: By selecting <math> No </math>, it means the initial parameters are automatically guessed by the algorithm explained in <u> [[Theory#Auto Fitting| Automatically determine the initial parameters in fitting procedure]] </u>. <br />
: By selecting <math> Yes </math>, you can manually set <math> l_{max} </math> and <math> A_l, \nu_l, \gamma_l </math> for each Lorentz function by yourself. The units of <math> A_l, \nu_l, \gamma_l </math> are all wavenumber. <math> l_{max} </math> is up to 5.<br />
:: Note: Automatical mode is recommended when you use ComplexRI to fit new data. The results also provide useful information for you to further fitting the data by manual mode. <br />
: [[File:11yes.png|500px]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Theory&diff=1001Theory2022-02-15T02:05:10Z<p>Lwang: </p>
<hr />
<div><br />
----<br />
<br />
<div id="ATR-IR data" style="font-size: 200%;font-style:bold;"> Calculated reflectance of ATR-IR from complex refractive index </div><br />
<br />
[[File:Light.png|500px]]<br />
<br />
The experimental geometry is described by the two-layer model in the above Figure, where phase <math>i</math> and phase <math>j</math> represent the substrate and sample, respectively. <br />
The incident light in phase <math>i</math> and transmitted light in phase <math>j</math> are related by Snell's law<br />
: <math> n_i \sin \theta_i = n_j \sin \theta_j </math><br />
<br />
where <math>n_i</math> and <math>n_j</math> are the complex refractive index of substrate and sample. <br />
<math>\theta_i</math> and <math>\theta_j</math> denote the angles of incidence and transmission of IR light, respectively.<br />
<br />
The reflectance of <math>p</math>- and <math>s</math>-polarized lights can be represented as the ratio of reflected to incident light intensities by <ref name = "ref1" /><br />
<br />
: <math> | r_{ij}^p|^2 = \left| \frac{n_j \cos \theta_i - n_i \cos \theta_j}{n_j \cos \theta_i + n_i \cos \theta_j} \right|^2 </math><br />
: <math> | r_{ij}^s|^2 = \left| \frac{n_i \cos \theta_i - n_j \cos \theta_j}{n_i \cos \theta_i + n_j \cos \theta_j} \right|^2 </math><br />
<br />
The angle of transmission <math>\theta_j</math> is derived from Snell's law to be <br />
: <math> \cos \theta_j = \sqrt{1-\frac{n_i^2}{n_j^2} \sin^2 \theta_i} </math><br />
which can be imaginary in the ATR condition. <br />
<br />
In the experiment, the incident angle <math>\theta_i</math> is often fixed, for example, to 45 degree. <br />
Take substate diamond as example, <math>n_i </math> is also known as 2.38. <br />
Therefore, the ATR condition is satisfied in most cases where <math>n_j </math> is smaller than <math> n_i \sin \theta_i = 1.68 </math>.<br />
This situation is held for most liquid samples. <br />
In the total reflection condition, the calculated <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> are unity when <math>n_j </math> is real.<br />
However, <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> become less than unity when the refractive index of the liquid <math>n_j = \eta_j + i \kappa_j </math> is complex.<br />
The reduced reflectance is a consequence of the absorption of evanescent light in the liquid sample. <br />
Therefore, by fitting the experimental reflectance data in ATR-IR spectra, it is able to obtain the complex refractive index of the liquid sample.<br />
<br />
----<br />
<br />
<div id="Fitting procedure" style="font-size: 200%;"> How to Fit the ATR-IR spectra </div><br />
<br />
The purpose of fitting is to determine the frequency-dependent complex refractive index <math>n_j(\nu) </math>.<br />
The complex refractive index of sample is represented with a set of Lorentz functions <br />
: <math> n_j (\nu) = \eta_j (\nu) + i \kappa_j (\nu) = n_j^0 + \sum_{l=1}^{l_\text{max}} \frac{A_l}{\nu_l - \nu - i \Gamma_l} </math><br />
where <math> n_j^0 </math> is the nonresonant refractive index. <br />
<math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> are the amplitude, peak wavenumber and bandwidth of each Lorentz function,<br />
respectively. <math> l_\text{max} </math> is the number of Lorentz functions to be used. <br />
Therefore, the parameters <math> n_j^0 </math>, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> and <math> l_\text{max} </math> were determined from the experimental spectra.<br />
<br />
In the beginning, <math> n_j^0 </math> should be determined before the fitting procedure. <math> n_j^0 </math> is the nonresonant refractive index in the IR wavenumber region. <br />
In the reference paper <ref name = "ref2" />, we use the refractive index values in the visible regions to fit Cauchy's equation.<br />
: <math>n_j^0(\lambda) = A + \frac{B}{{\lambda}^2} + \frac{C}{{\lambda}^4}</math><br />
The obtained parameters <math>A, B, C</math> were used to evaluate the nonresnant refractive index at 5000 <math> \text{cm}^{-1} </math>.<br />
It is also possible to directly use the refractive index in the visible region, which may involve a slightly deviation in <math> n_j^0 </math>. <ref name = "ref2" /><br />
<br />
After the determination of <math> n_j^0 </math>, other parameters related to the Lorentz functions are determined by minimizing the least-squares residual (LSR) between the experimental reflectance spectra and those of the analytical formulas over the whole wavenumber region of the target vibrational band. The residual is defined by <br />
: <math> \text{LSR} ( \{ A_l, \nu_l, \Gamma_l \} ) = \frac{1}{n} \sum_{\nu_n \in [\nu_\text{min}, \nu_\text{max}]} \left[ |r_{ij}^p (\nu_n)|^2 + |r_{ij}^s (\nu_n)|^2 - 2|r_{ij} (\nu_n)|^2_\mathrm{exp} \right]^2 </math><br />
where <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> are the calculated reflectances in the above section. <br />
<math> |r_{ij} (\nu_n)|^2_\mathrm{exp} </math> is the experimental reflectance of unpolarized light at wavenumber <math> \nu_n </math>. The summation of <math> n </math> is taken for all observed wavenumber points in the target vibrational band.<br />
By minimizing the LSR, the parameters of each Lorentz functions, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math>, were obtained. <br />
The minimization is numerically done in the program, thus the initial parameter of <math> l_\text{max} </math>, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> should be determined.<br />
And the initial parameters also have a large effect on whether the minimization can reach the tolerance and how long the minimization procedure is taken. <br />
All of them can be set manually. <br />
In the following, we will introduce a method to automatically determine the initial parameters.<br />
<br />
----<br />
<br />
<div id="Auto Fitting" style="font-size: 200%;"> Automatically determine the initial parameters in fitting procedure </div><br />
<br />
In order to determine the number of Lorentz functions to be used, we first start with only one Lorentz function and represent the complex refractive index as <br />
: <math> n_j (\nu) = n_j^0 + \frac{A_1}{\nu_1 - \nu - i \Gamma_1} </math><br />
The first Lorentz function is used to fit the strongest adsorption band in the target region. <br />
Thus, the initial parameter for <math> \nu_1 </math> is set to the wavenumber of minimum value of reflectance in the experimental data. <br />
The initial parameter for <math> \Gamma_1 </math> and <math> A_1 </math> is set to be 15 <math> \text{cm}^{-1} </math> and 7.5 <math> \text{cm}^{-1} </math>, respectively.<br />
These parameters are estimated from the parameters of very strong adsorption bands of commonly used liquids. <ref name = "ref2" /><br />
<br />
After the first fitting procedure, the strongest adsorption band is expected to be well represented.<br />
Here if the LSR is less than the tolerance, the fitting is finished and no more Lorentz functions are required. <br />
If not, another Lorentz function is added and the complex refractive index become<br />
: <math> n_j (\nu) = n_j^0 + \frac{A_1}{\nu_1 - \nu - i \Gamma_1} + \frac{A_2}{\nu_2 - \nu - i \Gamma_2} </math><br />
The second Lorentz funtion is used to represent major adsorption band in the difference reflectance spectra between the first fitting results and experimental results. <br />
The initial value of <math> \nu_1 </math>, <math> \Gamma_1 </math> and <math> A_1 </math> are set to be the optimized value in the last fitting procedure.<br />
The initial value of <math> \nu_2 </math> is set to the wavenumber of minimum (or maximum) value of difference reflectance spectra. <br />
The initial parameter for <math> \Gamma_2 </math> and <math> A_2 </math> is set to be 15 <math> \text{cm}^{-1} </math> and 3.75 <math> \text{cm}^{-1} </math>, respectively. <br />
A smaller initial value of <math> A_2 </math> suggests that the second Lorentz function is a minor adsorption band in ATR-IR spectra. <br />
Then all parameters are again optimized using the same fitting procedure. <br />
<br />
The number of Lorentz functions keeps increasing and the whole procedure is repeated until the final LSR reaches the set tolerance.<br />
<br />
----<br />
<br />
<div style="font-size: 200%;"> References </div><br />
<br />
<references><br />
<br />
<ref name = "ref1">"Theory of Sum Frequency Generation Spectroscopy"<br />
Akihiro Morita. Springer Nature Singapore Pte Ltd: 2018 </ref><br />
<ref name = "ref2">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. I Quantitative Spectra"<br />
Ryo Murata, Ken-ichi Inoue, Lin Wang, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9794-9803 (2021).</ref><br />
<br />
</references></div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Tutorial02&diff=1000Tutorial022022-02-15T02:02:27Z<p>Lwang: </p>
<hr />
<div><div><span id="Tutorial02" style="font-size: 150%;"> Fitting the complex refractive index by manual mode </span> </div><br />
----<br />
: In this tutorial, we will use the C-C-O asymmetric stretching region of ethanol as an example. The initial parameters in the fitting procedure are set by users. <br />
: The ATR-IR experimental data file in this tutorial can be downloaded <u><htmltag tagname="a" href="https://comp.chem.tohoku.ac.jp/media/Tutorial/data_ethanol.txt" target="_blank">Here</htmltag></u>. Use Ctrl + s to save the file in your local computer. The file name is “data_ethanol.txt”. <br />
: Then, please move to the Main Package page.<br />
[[File:Nav-Main.png|1000px]]<br />
: Upload the“data_ethanol.txt” in ① and set the other parameters according to the following figure. (For the meanings of each part, please refer to ➡[[ComplexRI Manual#Manual#Manual|Manual]].)<br />
:[[File:5Newtutorial02.png|1600px]]<br />
: Now, please click the “Execute Fitting” to start fitting. <br />
<div id="Results of Tutorial02" style="font-size: 150%;"> Results of Tutorial02</div><br />
----<br />
: The Result should be like follows.<br />
[[File:5Newres_tuto02.png|750px]]<br />
: The meaning of each output can be found in ➡[[ComplexRI Manual#Manual#Manual|Manual]]<br />
<br />
[[Tutorial01|Tutorial01]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Tutorial01&diff=999Tutorial012022-02-15T02:00:26Z<p>Lwang: </p>
<hr />
<div><div><span id="Tutorial01" style="font-size: 150%;"> Fitting the complex refractive index by automatic mode </span> </div><br />
----<br />
: In this tutorial, we will use the C=O stretching region of dimethyl carbonate (DMC) as an example. The initial parameters in the fitting procedure are automatically determined by ComplexRI. <br />
: The ATR-IR experimental data file in this tutorial can be downloaded <u><htmltag tagname="a" href="https://comp.chem.tohoku.ac.jp/media/Tutorial/data_DMC_2col.txt" target="_blank">Here</htmltag></u>. Use Ctrl + s to save the file in your local computer. The file name is “data_DMC_2col.txt”.<br />
: Then, please move to the Main Package page.<br />
[[File:Nav-Main.png|1000px]]<br />
: Upload the“data_DMC_2col.txt” in ① and set the other parameters according to the following figure. (For the meanings of each part, please refer to ➡[[ComplexRI Manual#Manual|Manual]].)<br />
:[[File:Newtutorial01.png|1500px]]<br />
: Now, please click the “Execute Fitting” to start fitting. <br />
<div id="Results of Tutorial01" style="font-size: 150%;"> Results of Tutorial01</div><br />
----<br />
: The Result should be like follows.<br />
[[File:2Newres_tuto01.png|750px]]<br />
: The meaning of each output can be found in ➡[[ComplexRI Manual#Manual|Manual]]<br />
<br />
[[Tutorial02|Tutorial02]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=ComplexRI_Manual&diff=998ComplexRI Manual2022-02-15T01:54:42Z<p>Lwang: </p>
<hr />
<div><br />
== Tutorial ==<br />
<br />
We prepared two examples to help users get familiar with ComplexRI.<br />
Users are recommended to follow this tutorial when using ComplexRI for the first time.<br />
<br />
: [[Tutorial01|Tutorial01：Fitting C=O stretching region of dimethyl carbonate]]<br />
: [[Tutorial02|Tutorial02：Fitting C-C-O asymmetric stretching region of ethanol]]<br />
<br />
----<br />
<br />
<br />
<br />
==Manual==<br />
<br />
A detailed explanation of the input and output of ComplexRI can be found here.<br />
<br />
: [[Input|Input of ComplexRI]]<br />
: [[Output|Output of ComplexRI]]<br />
<br />
----<br />
<br />
<br />
<br />
==Theory==<br />
<br />
A detailed description of the theory in the fitting procedure of ComplexRI can be found here. <br />
<br />
: [[Theory#ATR-IR data|1. Calculated reflectance of ATR-IR from complex refractive index]]<br />
: [[Theory#Fitting procedure|2. How to Fit the ATR-IR spectra]]<br />
: [[Theory#Auto Fitting|3. Automatically determine the initial parameters in fitting procedure]]<br />
<br />
----<br />
<br />
[http://comp.chem.tohoku.ac.jp/mediawiki/index.php/en/ComplexRI Top of this page]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=ComplexRI_Manual&diff=997ComplexRI Manual2022-02-15T01:48:04Z<p>Lwang: </p>
<hr />
<div><br />
== Tutorial ==<br />
<br />
We prepared two examples to help users get familiar with ComplexRI.<br />
Users are recommended to follow this tutorial when using ComplexRI for the first time.<br />
<br />
: [[Tutorial01|Tutorial01：Fitting C=O stretching region of dimethyl carbonate]]<br />
: [[Tutorial02|Tutorial02：Fitting C-C-O asymmetric stretching region of ethanol]]<br />
<br />
----<br />
<br />
==Manual==<br />
<br />
A detailed explanation of the input and output of ComplexRI can be found here.<br />
<br />
: [[Input|Input of ComplexRI]]<br />
: [[Output|Output of ComplexRI]]<br />
<br />
----<br />
<br />
==Theory==<br />
<br />
A detailed description of the theory in the fitting procedure of ComplexRI can be found here. <br />
<br />
: [[Theory#ATR-IR data|1. Calculated reflectance of ATR-IR from complex refractive index]]<br />
: [[Theory#Fitting procedure|2. How to Fit the ATR-IR spectra]]<br />
: [[Theory#Auto Fitting|3. Automatically determine the initial parameters in fitting procedure]]<br />
<br />
----<br />
<br />
[http://comp.chem.tohoku.ac.jp/mediawiki/index.php/en/ComplexRI Top of this page]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Input&diff=993Input2022-02-14T08:30:12Z<p>Lwang: </p>
<hr />
<div><br />
<br />
: [[File:Newtoppage.png|1000px]]<br />
: This is the typical snapshot of the input of ComplexRI. <br />
: The input of ComplexRI contains two parts. The left part is the information of ATR-IR experimental data. The right part is the control parameters of the complex refractive index fitting procedure. Each part will be explained in the following. <br />
<br />
----<br />
<div id="Information of ATR-IR experiment" style="font-size: 200%;"> Information of ATR-IR experiment </div><br />
<br />
----<br />
<div id="Input01" style="font-size: 150%;"> ①ATR-IR File </div><br />
: Please upload the ATR-IR experimental data in this part. The inside should be like the following.<br />
: [[File:NewFILE01.png|200px]]<br />
: There are two rules for the format of input file.<br />
: (1). The format of input file must be txt.<br />
: (2). The columns are separated by the space.<br />
<br />
----<br />
<div id="Input02" style="font-size: 150%;"> ②The order of data </div><br />
: Please select the sort order of your data.<br />
:: Ascending order: The wavenumbers in the input file are in ascending order (left picture). (Default)<br />
:: Descending order: The wavenumbers in the input file are in descending order (right picture). <br />
:[[File:NewFILE01.png|200px]][[File:NewFILE04.png|220px]]<br />
<br />
----<br />
<div id="Input03" style="font-size: 150%;"> ③Reflectance or Absorptance? </div><br />
: Please select the type of your ATR-IR data.<br />
:: Reflectance(%): The Reflectance of ATR-IR spectra in the value of percentage. (Default)<br />
:: Reflectance: The Reflectance of ATR-IR spectra. <br />
:: Absorptance: The Absorptance of ATR-IR spectra.<br />
: The relationships between each data are<br />
:: <math> Reflectance(%)=Reflectance*100 </math><br />
:: <math> Absorptance=-\log_{10}(Reflectance) </math><br />
<br />
----<br />
<div id="Input04" style="font-size: 150%;"> ④The Substrate in ATR-IR </div><br />
: Please select the substrate you used in the ATR-IR experiment. Here, we prepare the three substrates that often used <br />
:: Diamond(Refractive Index = 2.38). (Default)<br />
:: Zinc selenide(Refractive Index = 2.40).<br />
:: Germanium(Refractive Index = 4.0).<br />
: You can also input the refractive index of your substrate by selecting Other in the list.<br />
:[[File:4_other.png|500px]]<br />
<br />
----<br />
<div id="Input05" style="font-size: 150%;"> ⑤Incident angle in ATR-IR </div><br />
: Please input the incident angle in your ATR-IR experiment. (Default=45 degree)<br />
<br />
----<br />
<div id="Input06" style="font-size: 150%;"> ⑥Select the column of your data </div><br />
: Please input the column number of the data that you want to analyze in your ATR-IR file. <br />
:: Wavenumber: The column number of wavenumber in your input file. (Default: 1)<br />
:: ATR-IR data: The column number of ATR-IR data in your input file. (Default: 2)<br />
<br />
: For example, an input file like following can be uploaded and column 1 and column 5 can be selected for analyzing. <br />
: [[File:NewFILE03.png|500px]]<br />
: [[File:6_15.png|300px]]<br />
<br />
----<br />
<br />
<div id="Control parameters of ComplexRI fitting" style="font-size: 200%;">Control parameters of ComplexRI fitting </div><br />
<br />
----<br />
<div id="Input07" style="font-size: 150%;"> ⑦Title of your job </div><br />
: Please input the title of your job (alphabet). The output results of ComplexRI will be saved in the excel format with the name @Title.xlsx<br />
<br />
----<br />
<div id="Input08" style="font-size: 150%;"> ⑧Input the fitting range </div><br />
: Please input the frequency range (in wavenumber) inside which you want to perform the fitting. ComplexRI will only fit the data inside the range you input here.<br />
:: Minimum wavenumber: The lower boundary of wavenumber. (Default: 1636)<br />
:: Maximum wavenumber: The upper boundary of wavenumber. (Default: 1863)<br />
<br />
---- <br />
<div id="Input09" style="font-size: 150%;"> ⑨Refractive index of target sample in non-resonance region (<math> n_j^0 </math>) </div><br />
: Please input the refractive index of the target sample (<math> n_j^0 </math>) in non-resonance region. (Default=1.360)<br />
: The determination of <math> n_j^0 </math> and some comments about it can be found in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>. <br />
<br />
----<br />
<div id="Input10" style="font-size: 150%;"> ⑩The tolerance of fitting </div><br />
: Please input the tolerance of fitting procedure. (default: 0.02)<br />
: The fitting will be finished when the calculated residual is less than this value. <br />
: The details are described in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>.<br />
:<span style color="red">Notice!! Fitting can not finish if this value is too small. </span><br />
<br />
----<br />
<div id="Input11" style="font-size: 150%;"> ⑪ Manually set the initial parameters </div><br />
: Please select whether to set the initial fitting parameters by yourself. <br />
:: No: Automatically done by the algorithm (Default)<br />
:: Yes: Manually set the initial parameters by users. <br />
: In the fitting, we use a set of Lorentz functions to represent the complex refractive index <br />
:: <math>n_j=n_j^0+\sum_{l=1}^{l_{max}} \frac{A_l}{\nu_l-\nu-i\gamma_l}</math><br />
: where <math> n_j^0 </math> is input in ⑨. The number of Lorentz functions <math> l_{max} </math>, and the corresponding initial parameters <math> A_l, \nu_l, \gamma_l </math> should be determined.<br />
: By selecting <math> No </math>, it means the initial parameters are automatically guessed by the algorithm explained in <u> [[Theory#Auto Fitting| Automatically determine the initial parameters in fitting procedure]] </u>. <br />
: By selecting <math> Yes </math>, you can manually set <math> l_{max} </math> and <math> A_l, \nu_l, \gamma_l </math> for each Lorentz function by yourself. The units of <math> A_l, \nu_l, \gamma_l </math> are all wavenumber. <math> l_{max} </math> is up to 5. <br />
: [[File:11yes.png|500px]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Input&diff=988Input2022-02-14T08:20:38Z<p>Lwang: </p>
<hr />
<div><br />
<br />
: [[File:Newtoppage.png|1000px]]<br />
: This is the typical snapshot of the input of ComplexRI. <br />
: The input of ComplexRI contains two parts. The left part is the information of ATR-IR experimental data. The right part is the control parameters of the complex refractive index fitting procedure. Each part will be explained in the following. <br />
<br />
----<br />
<div id="Information of ATR-IR experiment" style="font-size: 200%;"> Information of ATR-IR experiment </div><br />
<br />
----<br />
<div id="Input01" style="font-size: 150%;"> ①ATR-IR File </div><br />
: Please upload the ATR-IR experimental data in this part. The inside should be like the following.<br />
: [[File:NewFILE01.png|200px]]<br />
: There are two rules for the format of input file.<br />
: (1). The format of input file must be txt.<br />
: (2). The columns are separated by the space.<br />
<br />
----<br />
<div id="Input02" style="font-size: 150%;"> ②The order of data </div><br />
: Please select the sort order of your data.<br />
:: Ascending order: The wavenumbers in the input file are in ascending order (left picture). (Default)<br />
:: Descending order: The wavenumbers in the input file are in descending order (right picture). <br />
:[[File:NewFILE01.png|200px]][[File:NewFILE04.png|220px]]<br />
<br />
----<br />
<div id="Input03" style="font-size: 150%;"> ③Reflectance or Absorptance? </div><br />
: Please select the type of your ATR-IR data.<br />
:: Reflectance(%): The Reflectance of ATR-IR spectra in the value of percentage. (Default)<br />
:: Reflectance: The Reflectance of ATR-IR spectra. <br />
:: Absorptance: The Absorptance of ATR-IR spectra.<br />
: The relationships between each data are<br />
:: <math> Reflectance(%)=Reflectance*100 </math><br />
:: <math> Absorptance=-\log_{10}(Reflectance) </math><br />
<br />
----<br />
<div id="Input04" style="font-size: 150%;"> ④The Substrate in ATR-IR </div><br />
: Please select the substrate you used in the ATR-IR experiment. Here, we prepare the three substrates that often used <br />
:: Diamond(Refractive Index = 2.38). (Default)<br />
:: Zinc selenide(Refractive Index = 2.40).<br />
:: Germanium(Refractive Index = 4.0).<br />
: You can also input the refractive index of your substrate by selecting Others in the list.<br />
:[[File:4_other.png|500px]]<br />
<br />
----<br />
<div id="Input05" style="font-size: 150%;"> ⑤Incident angle in ATR-IR </div><br />
: Please input the incident angle in your ATR-IR experiment. (Default=45 degree)<br />
<br />
----<br />
<div id="Input06" style="font-size: 150%;"> ⑥Select the column of your data </div><br />
: Please input the column number of the data that you want to analyze in your ATR-IR file. <br />
:: Wavenumber: The column number of wavenumber in your input file. (Default: 1)<br />
:: ATR-IR data: The column number of ATR-IR data in your input file. (Default: 2)<br />
<br />
: For example, an input file like following can be uploaded and column 1 and column 5 can be selected for analyzing. <br />
: [[File:NewFILE03.png|500px]]<br />
: [[File:6_15.png|300px]]<br />
<br />
----<br />
<br />
<div id="Control parameters of ComplexRI fitting" style="font-size: 200%;">Control parameters of ComplexRI fitting </div><br />
<br />
----<br />
<div id="Input07" style="font-size: 150%;"> ⑦Title of your job </div><br />
: Please input the title of your job (alphabet). The output results of ComplexRI will be saved in the excel format with the name @Title.xlsx<br />
<br />
----<br />
<div id="Input08" style="font-size: 150%;"> ⑧Input the fitting range </div><br />
: Please input the frequency range (in wavenumber) inside which you want to perform the fitting. ComplexRI will only fit the data inside the range you input here.<br />
:: Minimum wavenumber: The lower boundary of wavenumber. (Default: 1636)<br />
:: Maximum wavenumber: The upper boundary of wavenumber. (Default: 1863)<br />
<br />
---- <br />
<div id="Input09" style="font-size: 150%;"> ⑨Refractive index of target sample in non-resonance region (<math> n_j^0 </math>) </div><br />
: Please input the refractive index of the target sample (<math> n_j^0 </math>) in non-resonance region. (Default=1.360)<br />
: The determination of <math> n_j^0 </math> and some comments about it can be found in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>. <br />
<br />
----<br />
<div id="Input10" style="font-size: 150%;"> ⑩The tolerance of fitting </div><br />
: Please input the tolerance of fitting procedure. (default: 0.02)<br />
: The fitting will be finished when the calculated residual is less than this value. <br />
: The details are described in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>.<br />
:<span style color="red">Notice!! Fitting can not finish if this value is too small. </span><br />
<br />
----<br />
<div id="Input11" style="font-size: 150%;"> ⑪ Manually set the initial parameters </div><br />
: Please select whether to set the initial fitting parameters by yourself. <br />
:: No: Automatically done by the algorithm (Default)<br />
:: Yes: Manually set the initial parameters by users. <br />
: In the fitting, we use a set of Lorentz functions to represent the complex refractive index <br />
:: <math>n_j=n_j^0+\sum_{l=1}^{l_{max}} \frac{A_l}{\nu_l-\nu-i\gamma_l}</math><br />
: where <math> n_j^0 </math> is input in ⑨. The number of Lorentz functions <math> l_{max} </math>, and the corresponding initial parameters <math> A_l, \nu_l, \gamma_l </math> should be determined.<br />
: By selecting <math> No </math>, it means the initial parameters are automatically guessed by the algorithm explained in <u> [[Theory#Auto Fitting| Automatically determine the initial parameters in fitting procedure]] </u>. <br />
: By selecting <math> Yes </math>, you can manually set <math> l_{max} </math> and <math> A_l, \nu_l, \gamma_l </math> for each Lorentz function by yourself. The units of <math> A_l, \nu_l, \gamma_l </math> are all wavenumber. <math> l_{max} </math> is up to 5. <br />
: [[File:11yes.png|500px]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Tutorial02&diff=984Tutorial022022-02-14T08:11:47Z<p>Lwang: </p>
<hr />
<div><div><span id="Tutorial02" style="font-size: 150%;"> Fitting the complex refractive index by manual mode </span> </div><br />
----<br />
: In this tutorial, we will use the C-C-O asymmetric stretching region of ethanol as an example to show the manually fitting procedure in ComplexRI.<br />
: The ATR-IR experimental data file in this tutorial can be downloaded <u><htmltag tagname="a" href="https://comp.chem.tohoku.ac.jp/media/Tutorial/data_ethanol.txt" target="_blank">Here</htmltag></u>. Use Ctrl + s to save the file in your local computer. The file name is “data_ethanol.txt”. <br />
: Then, please move to the Main Package page.<br />
[[File:Main.png|1000px]]<br />
: Upload the“data_ethanol.txt” in ① and set the other parameters according to the following figure. (For the meanings of each part, please refer to ➡[[En/ComplexRI#Manual|Manual]].)<br />
:[[File:5Newtutorial02.png|1600px]]<br />
: Now, please click the “Execute Fitting” to start fitting. <br />
<div id="Results of Tutorial02" style="font-size: 150%;"> Results of Tutorial02</div><br />
----<br />
: The Result should be like follows.<br />
[[File:5Newres_tuto02.png|750px]]<br />
: The meaning of each output can be found in ➡[[En/ComplexRI#Manual|Manual]]<br />
<br />
[[Tutorial01|Tutorial01]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Tutorial01&diff=983Tutorial012022-02-14T08:10:37Z<p>Lwang: </p>
<hr />
<div><div><span id="Tutorial01" style="font-size: 150%;"> Fitting the complex refractive index by automatic mode </span> </div><br />
----<br />
: In this tutorial, we will use the C=O stretching region of dimethyl carbonate (DMC) as an example to show the automatic fitting procedure in ComplexRI.<br />
: The ATR-IR experimental data file in this tutorial can be downloaded <u><htmltag tagname="a" href="https://comp.chem.tohoku.ac.jp/media/Tutorial/data_DMC_2col.txt" target="_blank">Here</htmltag></u>. Use Ctrl + s to save the file in your local computer. The file name is “data_DMC_2col.txt”.<br />
: Then, please move to the Main Package page.<br />
[[File:Main.png|1000px]]<br />
: Upload the“data_DMC_2col.txt” in ① and set the other parameters according to the following figure. (For the meanings of each part, please refer to ➡[[En/ComplexRI#Manual|Manual]].)<br />
:[[File:Newtutorial01.png|1500px]]<br />
: Now, please click the “Execute Fitting” to start fitting. <br />
<div id="Results of Tutorial01" style="font-size: 150%;"> Results of Tutorial01</div><br />
----<br />
: The Result should be like follows.<br />
[[File:2Newres_tuto01.png|750px]]<br />
: The meaning of each output can be found in ➡[[En/ComplexRI#Manual|Manual]]<br />
<br />
[[Tutorial02|Tutorial02]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Tutorial01&diff=982Tutorial012022-02-14T08:09:30Z<p>Lwang: </p>
<hr />
<div><div><span id="Tutorial01" style="font-size: 150%;"> Fitting the complex refractive index by automatic mode </span> </div><br />
----<br />
: In this tutorial, we will use the C=O stretching region of dimethyl carbonate (DMC) as an example to show the automatic fitting procedure in ComplexRI.<br />
: The ATR-IR experimental data file in this tutorial can be downloaded <u><htmltag tagname="a" href="https://comp.chem.tohoku.ac.jp/media/Tutorial/data_DMC_2col.txt" target="_blank">Here</htmltag></u>. Use Ctrl + s to save the file in your local computer.<br />
: Then, please move to the Main Package page.<br />
[[File:Main.png|1000px]]<br />
: Upload the“data_DMC_2col.txt” in ① and set the other parameters according to the following figure. (For the meanings of each part, please refer to ➡[[En/ComplexRI#Manual|Manual]].)<br />
:[[File:Newtutorial01.png|1500px]]<br />
: Now, please click the “Execute Fitting” to start fitting. <br />
<div id="Results of Tutorial01" style="font-size: 150%;"> Results of Tutorial01</div><br />
----<br />
: The Result should be like follows.<br />
[[File:2Newres_tuto01.png|750px]]<br />
: The meaning of each output can be found in ➡[[En/ComplexRI#Manual|Manual]]<br />
<br />
[[Tutorial02|Tutorial02]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Theory&diff=969Theory2022-02-14T05:09:25Z<p>Lwang: </p>
<hr />
<div><br />
----<br />
<br />
<div id="ATR-IR data" style="font-size: 200%;font-style:bold;"> Calculated reflectance of ATR-IR from complex refractive index </div><br />
<br />
[[File:Light.png|500px]]<br />
<br />
The experimental geometry is described by the two-layer model in the above Figure, where phase <math>i</math> and phase <math>j</math> represent the substrate and sample, respectively. <br />
The incident light in phase <math>i</math> and transmitted light in phase <math>j</math> are related by Snell's law<br />
: <math> n_i \sin \theta_i = n_j \sin \theta_j </math><br />
<br />
where <math>n_i</math> and <math>n_j</math> are the complex refractive index of substrate and sample. <br />
<math>\theta_i</math> and <math>\theta_j</math> denote the angles of incidence and transmission of IR light, respectively.<br />
<br />
The reflectance of <math>p</math>- and <math>s</math>-polarized lights can be represented as the ratio of reflected to incident light intensities by <ref name = "ref1" /><br />
<br />
: <math> | r_{ij}^p|^2 = \left| \frac{n_j \cos \theta_i - n_i \cos \theta_j}{n_j \cos \theta_i + n_i \cos \theta_j} \right|^2 </math><br />
: <math> | r_{ij}^s|^2 = \left| \frac{n_i \cos \theta_i - n_j \cos \theta_j}{n_i \cos \theta_i + n_j \cos \theta_j} \right|^2 </math><br />
<br />
The angle of transmission <math>\theta_j</math> is derived from Snell's law to be <br />
: <math> \cos \theta_j = \sqrt{1-\frac{n_i^2}{n_j^2} \sin^2 \theta_i} </math><br />
which can be imaginary in the ATR condition. <br />
<br />
In the experiment, the incident angle <math>\theta_i</math> is often fixed, for example, to 45 degree. <br />
Take substate diamond as example, <math>n_i </math> is also known as 2.38. <br />
Therefore, the ATR condition is satisfied in most cases where <math>n_j </math> is smaller than <math> n_i \sin \theta_i = 1.68 </math>.<br />
This situation is held for most liquid samples. <br />
In the total reflection condition, the calculated <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> are unity when <math>n_j </math> is real.<br />
However, <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> become less than unity when the refractive index of the liquid <math>n_j = \eta_j + i \kappa_j </math> is complex.<br />
The reduced reflectance is a consequence of the absorption of evanescent light in the liquid sample. <br />
Therefore, by fitting the experimental reflectance data in ATR-IR spectra, it is able to obtain the complex refractive index of the liquid sample.<br />
<br />
----<br />
<br />
<div id="Fitting procedure" style="font-size: 200%;"> How to Fit the ATR-IR spectra </div><br />
<br />
The purpose of fitting is to determine the frequency-dependent complex refractive index <math>n_j(\nu) </math>.<br />
The complex refractive index of sample is represented with a set of Lorentz functions <br />
: <math> n_j (\nu) = \eta_j (\nu) + i \kappa_j (\nu) = n_j^0 + \sum_{l=1}^{l_\text{max}} \frac{A_l}{\nu_l - \nu - i \Gamma_l} </math><br />
where <math> n_j^0 </math> is the nonresonant refractive index. <br />
<math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> are the amplitude, peak wavenumber and bandwidth of each Lorentz function,<br />
respectively. <math> l_\text{max} </math> is the number of Lorentz functions to be used. <br />
Therefore, the parameters <math> n_j^0 </math>, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> and <math> l_\text{max} </math> were determined from the experimental spectra.<br />
<br />
In the beginning, <math> n_j^0 </math> should be determined before the fitting procedure. <math> n_j^0 </math> is the nonresonant refractive index in the IR wavenumber region. <br />
In the reference paper <ref name = "ref2" />, we use the refractive index values in the visible regions to fit Cauchy's equation.<br />
: <math>n_j^0(\lambda) = A + \frac{B}{{\lambda}^2} + \frac{C}{{\lambda}^4}</math><br />
The obtained parameters <math>A, B, C</math> were used to evaluate the nonresnant refractive index at 5000 <math> \text{cm}^{-1} </math>.<br />
It is also possible to directly use the refractive index in the visible region, which may involve some deviation in <math> n_j^0 </math>. <ref name = "ref2" /><br />
<br />
After the determination of <math> n_j^0 </math>, other parameters related to the Lorentz functions are determined by minimizing the least-squares residual (LSR) between the experimental reflectance spectra and those of the analytical formulas over the whole wavenumber region of the target vibrational band. The residual is defined by <br />
: <math> \text{LSR} ( \{ A_l, \nu_l, \Gamma_l \} ) = \frac{1}{n} \sum_{\nu_n \in [\nu_\text{min}, \nu_\text{max}]} \left[ |r_{ij}^p (\nu_n)|^2 + |r_{ij}^s (\nu_n)|^2 - 2|r_{ij} (\nu_n)|^2_\mathrm{exp} \right]^2 </math><br />
where <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> are the calculated reflectances in the above section. <br />
<math> |r_{ij} (\nu_n)|^2_\mathrm{exp} </math> is the experimental reflectance of unpolarized light at wavenumber <math> \nu_n </math>. The summation of <math> n </math> is taken for all observed wavenumber points in the target vibrational band.<br />
By minimizing the LSR, the parameters of each Lorentz functions, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math>, were obtained. <br />
The minimization is numerically done in the program, thus the initial parameter of <math> l_\text{max} </math>, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> should be determined.<br />
And the initial parameters also have a large effect on whether the minimization can reach the tolerance and how long the minimization procedure is taken. <br />
All of them can be set manually. <br />
In the following, we will introduce a method to automatically determine the initial parameters.<br />
<br />
----<br />
<br />
<div id="Auto Fitting" style="font-size: 200%;"> Automatically determine the initial parameters in fitting procedure </div><br />
<br />
In order to determine the number of Lorentz functions to be used, we first start with only one Lorentz function and represent the complex refractive index as <br />
: <math> n_j (\nu) = n_j^0 + \frac{A_1}{\nu_1 - \nu - i \Gamma_1} </math><br />
The first Lorentz function is used to fit the strongest adsorption band in the target region. <br />
Thus, the initial parameter for <math> \nu_1 </math> is set to the wavenumber of minimum value of reflectance in the experimental data. <br />
The initial parameter for <math> \Gamma_1 </math> and <math> A_1 </math> is set to be 15 <math> \text{cm}^{-1} </math> and 7.5 <math> \text{cm}^{-1} </math>, respectively.<br />
These parameters are estimated from the parameters of very strong adsorption bands of commonly used liquids. <ref name = "ref2" /><br />
<br />
After the first fitting procedure, the strongest adsorption band is expected to be well represented.<br />
Here if the LSR is less than the tolerance, the fitting is finished and no more Lorentz functions are required. <br />
If not, another Lorentz function is added and the complex refractive index become<br />
: <math> n_j (\nu) = n_j^0 + \frac{A_1}{\nu_1 - \nu - i \Gamma_1} + \frac{A_2}{\nu_2 - \nu - i \Gamma_2} </math><br />
The second Lorentz funtion is used to represent major adsorption band in the difference reflectance spectra between the first fitting results and experimental results. <br />
The initial value of <math> \nu_1 </math>, <math> \Gamma_1 </math> and <math> A_1 </math> are set to be the optimized value in the last fitting procedure.<br />
The initial value of <math> \nu_2 </math> is set to the wavenumber of minimum (or maximum) value of difference reflectance spectra. <br />
The initial parameter for <math> \Gamma_2 </math> and <math> A_2 </math> is set to be 15 <math> \text{cm}^{-1} </math> and 3.75 <math> \text{cm}^{-1} </math>, respectively. <br />
A smaller initial value of <math> A_2 </math> suggests that the second Lorentz function is a minor adsorption band in ATR-IR spectra. <br />
Then all parameters are again optimized using the same fitting procedure. <br />
<br />
The number of Lorentz functions keeps increasing and the whole procedure is repeated until the final LSR reaches the set tolerance.<br />
<br />
----<br />
<br />
<div style="font-size: 200%;"> References </div><br />
<br />
<references><br />
<br />
<ref name = "ref1">"Theory of Sum Frequency Generation Spectroscopy"<br />
Akihiro Morita. Springer Nature Singapore Pte Ltd: 2018 </ref><br />
<ref name = "ref2">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. I Quantitative Spectra"<br />
Ryo Murata, Ken-ichi Inoue, Lin Wang, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9794-9803 (2021).</ref><br />
<br />
</references></div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Jp/ComplexRI&diff=965Jp/ComplexRI2022-02-14T02:25:49Z<p>Lwang: </p>
<hr />
<div><br />
==マニュアル==<br />
<br />
{|class="wikitable"<br />
! 入力 <br />
|-<br />
|[[入力#Information of ATR-IR experiment|Information of ATR-IR experiment]]<br />
|-<br />
|[[入力#Control parameters of ComplexRI fitting|Control parameters of ComplexRI fitting]]<br />
|}<br />
<br />
{|class="wikitable"<br />
! 出力 <br />
|-<br />
|[[出力#標準出力|標準出力]] <br />
|-<br />
|[[出力#結果のダウンロード|結果のダウンロード]] <br />
|}<br />
<br />
----<br />
<br />
== チュートリアル ==<br />
{|class="wikitable"<br />
! 使用例<br />
|-<br />
|チュートリアル01： [[チュートリアル01|Automatic Mode]]<br />
|-<br />
|チュートリアル02： [[チュートリアル02|Manual Mode]]<br />
|}<br />
<br />
----<br />
<br />
==理論==<br />
<br />
{|class="wikitable"<br />
|-<br />
|[[Theory#ATR-IR data|Calculated reflectance of ATR-IR from complex refractive index]]<br />
|-<br />
|[[Theory#Fitting procedure| How to Fit the ATR-IR spectra]]<br />
|-<br />
|[[Theory#Auto Fitting|Automatically determine the initial parameters in fitting procedure]]<br />
|}<br />
<br />
----<br />
<br />
[http://comp.chem.tohoku.ac.jp/mediawiki/index.php/en/ComplexRI Top of this page]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=MediaWiki:Sidebar&diff=964MediaWiki:Sidebar2022-02-14T02:12:32Z<p>Lwang: </p>
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* navigation<br />
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* LANGUAGES</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=MediaWiki:Sidebar&diff=963MediaWiki:Sidebar2022-02-14T02:07:13Z<p>Lwang: </p>
<hr />
<div><br />
* navigation<br />
* ComplexRI Manual (English)<br />
** En/ComplexRI#Manual|Manual<br />
** En/ComplexRI#Tutorial|Tutorial<br />
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<br />
* ComplexRI Manual (Japanese)<br />
** Jp/ComplexRI#マニュアル|マニュアル<br />
** Jp/ComplexRI#チュートリアル|チュートリアル<br />
** Jp/ComplexRI#理論|理論<br />
<br />
* その他<br />
** mainpage|mainpage-description<br />
** recentchanges-url|recentchanges<br />
** randompage-url|randompage<br />
** helppage|help-mediawiki<br />
* SEARCH<br />
* TOOLBOX<br />
* LANGUAGES</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Jp/ComplexRI&diff=962Jp/ComplexRI2022-02-14T02:06:27Z<p>Lwang: </p>
<hr />
<div><br />
==マニュアル==<br />
<br />
{|class="wikitable"<br />
! 入力 <br />
|-<br />
|[[入力#Information of ATR-IR experiment|Information of ATR-IR experiment]]<br />
|-<br />
|[[入力#Control parameters of ComplexRI fitting|Control parameters of ComplexRI fitting]]<br />
|}<br />
<br />
{|class="wikitable"<br />
! 出力 <br />
|-<br />
|[[出力#標準出力|標準出力]] <br />
|-<br />
|[[出力#結果のダウンロード|結果のダウンロード]] <br />
|}<br />
<br />
----<br />
<br />
== チュートリアル ==<br />
{|class="wikitable"<br />
! 使用例<br />
|-<br />
|チュートリアル01： [[チュートリアル01|Automatic Mode]]<br />
|-<br />
|チュートリアル02： [[チュートリアル02|Manual Mode]]<br />
|}<br />
<br />
----<br />
<br />
<br />
==理論==<br />
<br />
{|class="wikitable"<br />
|-<br />
|[[Theory#ATR-IR data|Calculated reflectance of ATR-IR from complex refractive index]]<br />
|-<br />
|[[Theory#Fitting procedure| How to Fit the ATR-IR spectra]]<br />
|-<br />
|[[Theory#Auto Fitting|Automatically determine the initial parameters in fitting procedure]]<br />
|}<br />
<br />
----<br />
<br />
[http://comp.chem.tohoku.ac.jp/mediawiki/index.php/en/ComplexRI Top of this page]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=MediaWiki:Sidebar&diff=961MediaWiki:Sidebar2022-02-14T02:04:33Z<p>Lwang: </p>
<hr />
<div><br />
* navigation<br />
* ComplexRI Manual (English)<br />
** En/ComplexRI#Manual|Manual<br />
** En/ComplexRI#Tutorial|Tutorial<br />
** En/ComplexRI#Theory|Theory<br />
<br />
* ComplexRI Manual (Japanese)<br />
** Jp/ComplexRI#概要|概要<br />
** Jp/ComplexRI#作成の沿革|作成の沿革<br />
** Jp/ComplexRI#チュートリアル|チュートリアル<br />
** Jp/ComplexRI#マニュアル|マニュアル<br />
** Jp/ComplexRI#理論|理論<br />
** Jp/ComplexRI#よくある質問|よくある質問<br />
<br />
* その他<br />
** mainpage|mainpage-description<br />
** recentchanges-url|recentchanges<br />
** randompage-url|randompage<br />
** helppage|help-mediawiki<br />
* SEARCH<br />
* TOOLBOX<br />
* LANGUAGES</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=MediaWiki:Sidebar&diff=960MediaWiki:Sidebar2022-02-14T02:04:19Z<p>Lwang: </p>
<hr />
<div><br />
* navigation<br />
* ComplexRI Manual(English)<br />
** En/ComplexRI#Manual|Manual<br />
** En/ComplexRI#Tutorial|Tutorial<br />
** En/ComplexRI#Theory|Theory<br />
<br />
* ComplexRI Manual(Japanese)<br />
** Jp/ComplexRI#概要|概要<br />
** Jp/ComplexRI#作成の沿革|作成の沿革<br />
** Jp/ComplexRI#チュートリアル|チュートリアル<br />
** Jp/ComplexRI#マニュアル|マニュアル<br />
** Jp/ComplexRI#理論|理論<br />
** Jp/ComplexRI#よくある質問|よくある質問<br />
<br />
* その他<br />
** mainpage|mainpage-description<br />
** recentchanges-url|recentchanges<br />
** randompage-url|randompage<br />
** helppage|help-mediawiki<br />
* SEARCH<br />
* TOOLBOX<br />
* LANGUAGES</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=MediaWiki:Sidebar&diff=959MediaWiki:Sidebar2022-02-14T02:02:40Z<p>Lwang: </p>
<hr />
<div><br />
* navigation<br />
* ComplexRI Manual Page<br />
** En/ComplexRI#Manual|Manual<br />
** En/ComplexRI#Tutorial|Tutorial<br />
** En/ComplexRI#Theory|Theory<br />
<br />
* 日本語/ComplexRI<br />
** Jp/ComplexRI#概要|概要<br />
** Jp/ComplexRI#作成の沿革|作成の沿革<br />
** Jp/ComplexRI#チュートリアル|チュートリアル<br />
** Jp/ComplexRI#マニュアル|マニュアル<br />
** Jp/ComplexRI#理論|理論<br />
** Jp/ComplexRI#よくある質問|よくある質問<br />
<br />
* その他<br />
** mainpage|mainpage-description<br />
** recentchanges-url|recentchanges<br />
** randompage-url|randompage<br />
** helppage|help-mediawiki<br />
* SEARCH<br />
* TOOLBOX<br />
* LANGUAGES</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=En/ComplexRI&diff=958En/ComplexRI2022-02-14T01:54:09Z<p>Lwang: </p>
<hr />
<div><br />
==Manual==<br />
<br />
{|class="wikitable"<br />
! Input of ComplexRI<br />
|-<br />
|[[Input#Information of ATR-IR experiment|Information of ATR-IR experiment]]<br />
|-<br />
|[[Input#Control parameters of ComplexRI fitting|Control parameters of ComplexRI fitting]]<br />
|}<br />
<br />
{|class="wikitable"<br />
! Output of ComplexRI<br />
|-<br />
|[[Output#Stardard output of ComplexRI|Stardard output of ComplexRI]] <br />
|-<br />
|[[Output#Download your results|Download your results]] <br />
|}<br />
<br />
----<br />
<br />
== Tutorial ==<br />
{|class="wikitable"<br />
! Examples to use ComplexRI<br />
|-<br />
| Tutorial01：[[Tutorial01| Automatic Mode]]<br />
|-<br />
| Tutorial02： [[Tutorial02|Manual Mode]]<br />
|}<br />
<br />
----<br />
<br />
==Theory==<br />
<br />
{|class="wikitable"<br />
|-<br />
|[[Theory#ATR-IR data|Calculated reflectance of ATR-IR from complex refractive index]]<br />
|-<br />
|[[Theory#Fitting procedure| How to Fit the ATR-IR spectra]]<br />
|-<br />
|[[Theory#Auto Fitting|Automatically determine the initial parameters in fitting procedure]]<br />
|}<br />
<br />
----<br />
<br />
[http://comp.chem.tohoku.ac.jp/mediawiki/index.php/en/ComplexRI Top of this page]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=En/ComplexRI&diff=957En/ComplexRI2022-02-14T01:53:52Z<p>Lwang: </p>
<hr />
<div>__NOTOC__<br />
<br />
==Manual==<br />
<br />
{|class="wikitable"<br />
! Input of ComplexRI<br />
|-<br />
|[[Input#Information of ATR-IR experiment|Information of ATR-IR experiment]]<br />
|-<br />
|[[Input#Control parameters of ComplexRI fitting|Control parameters of ComplexRI fitting]]<br />
|}<br />
<br />
{|class="wikitable"<br />
! Output of ComplexRI<br />
|-<br />
|[[Output#Stardard output of ComplexRI|Stardard output of ComplexRI]] <br />
|-<br />
|[[Output#Download your results|Download your results]] <br />
|}<br />
<br />
----<br />
<br />
== Tutorial ==<br />
{|class="wikitable"<br />
! Examples to use ComplexRI<br />
|-<br />
| Tutorial01：[[Tutorial01| Automatic Mode]]<br />
|-<br />
| Tutorial02： [[Tutorial02|Manual Mode]]<br />
|}<br />
<br />
----<br />
<br />
==Theory==<br />
<br />
{|class="wikitable"<br />
|-<br />
|[[Theory#ATR-IR data|Calculated reflectance of ATR-IR from complex refractive index]]<br />
|-<br />
|[[Theory#Fitting procedure| How to Fit the ATR-IR spectra]]<br />
|-<br />
|[[Theory#Auto Fitting|Automatically determine the initial parameters in fitting procedure]]<br />
|}<br />
<br />
----<br />
<br />
[http://comp.chem.tohoku.ac.jp/mediawiki/index.php/en/ComplexRI Top of this page]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=En/ComplexRI&diff=956En/ComplexRI2022-02-14T01:51:40Z<p>Lwang: </p>
<hr />
<div>__NOTOC__<br />
<br />
{|class="wikitable"<br />
! Index<br />
|-<br />
|[[#Tutorial|Tutorial]]<br />
|-<br />
|[[#Manual|Manual]]<br />
|-<br />
|[[#Theory|Theory]]<br />
|}<br />
<br />
== Tutorial ==<br />
{|class="wikitable"<br />
! Examples to use ComplexRI<br />
|-<br />
| Tutorial01：[[Tutorial01| Automatic Mode]]<br />
|-<br />
| Tutorial02： [[Tutorial02|Manual Mode]]<br />
|}<br />
<br />
----<br />
<br />
==Manual==<br />
<br />
{|class="wikitable"<br />
! Input of ComplexRI<br />
|-<br />
|[[Input#Information of ATR-IR experiment|Information of ATR-IR experiment]]<br />
|-<br />
|[[Input#Control parameters of ComplexRI fitting|Control parameters of ComplexRI fitting]]<br />
|}<br />
<br />
{|class="wikitable"<br />
! Output of ComplexRI<br />
|-<br />
|[[Output#Stardard output of ComplexRI|Stardard output of ComplexRI]] <br />
|-<br />
|[[Output#Download your results|Download your results]] <br />
|}<br />
<br />
----<br />
<br />
==Theory==<br />
<br />
{|class="wikitable"<br />
|-<br />
|[[Theory#ATR-IR data|Calculated reflectance of ATR-IR from complex refractive index]]<br />
|-<br />
|[[Theory#Fitting procedure| How to Fit the ATR-IR spectra]]<br />
|-<br />
|[[Theory#Auto Fitting|Automatically determine the initial parameters in fitting procedure]]<br />
|}<br />
<br />
----<br />
<br />
[http://comp.chem.tohoku.ac.jp/mediawiki/index.php/en/ComplexRI Top of this page]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=En/ComplexRI&diff=955En/ComplexRI2022-02-14T01:50:31Z<p>Lwang: </p>
<hr />
<div>__NOTOC__<br />
<br />
{|class="wikitable"<br />
! Index<br />
|-<br />
|[[#Tutorial|Tutorial]]<br />
|-<br />
|[[#Manual|Manual]]<br />
|-<br />
|[[#Theory|Theory]]<br />
|-<br />
|[[#FAQ|FAQ]]<br />
|}<br />
<br />
== Tutorial ==<br />
{|class="wikitable"<br />
! Examples to use ComplexRI<br />
|-<br />
| Tutorial01：[[Tutorial01| Automatic Mode]]<br />
|-<br />
| Tutorial02： [[Tutorial02|Manual Mode]]<br />
|}<br />
<br />
----<br />
<br />
==Manual==<br />
<br />
{|class="wikitable"<br />
! Input of ComplexRI<br />
|-<br />
|[[Input#Information of ATR-IR experiment|Information of ATR-IR experiment]]<br />
|-<br />
|[[Input#Control parameters of ComplexRI fitting|Control parameters of ComplexRI fitting]]<br />
|}<br />
<br />
{|class="wikitable"<br />
! Output of ComplexRI<br />
|-<br />
|[[Output#Stardard output of ComplexRI|Stardard output of ComplexRI]] <br />
|-<br />
|[[Output#Download your results|Download your results]] <br />
|}<br />
<br />
----<br />
<br />
==Theory==<br />
<br />
{|class="wikitable"<br />
|-<br />
|[[Theory#ATR-IR data|Calculated reflectance of ATR-IR from complex refractive index]]<br />
|-<br />
|[[Theory#Fitting procedure| How to Fit the ATR-IR spectra]]<br />
|-<br />
|[[Theory#Auto Fitting|Automatically determine the initial parameters in fitting procedure]]<br />
|}<br />
<br />
----<br />
<br />
[http://comp.chem.tohoku.ac.jp/mediawiki/index.php/en/ComplexRI Top of this page]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=En/ComplexRI&diff=953En/ComplexRI2022-01-25T01:54:52Z<p>Lwang: </p>
<hr />
<div>__NOTOC__<br />
<br />
<span style="font-size: 100%; color:red;">※Chrome browser is recommend to read this page. </span><br />
<br />
{|class="wikitable"<br />
! Index<br />
|-<br />
|[[#Overview|Overview]]<br />
|-<br />
|[[#Developing History|Developing History]]<br />
|-<br />
|[[#Tutorial|Tutorial]]<br />
|-<br />
|[[#Manual|Manual]]<br />
|-<br />
|[[#Theory|Theory]]<br />
|-<br />
|[[#FAQ|FAQ]]<br />
|}<br />
<br />
== Overview ==<br />
The complex refractive index is a basic property in the study of light-matter interactions and spectroscopy. Especially in the sum frequency generation (SFG) vibrational spectroscopy studies, the analysis of SFG spectra requires detailed information of the Fresnel factors in the typical three-layer interface model. Studies <ref name = "ref1" /> have shown that the dispersion of the Fresnel factor may become significant and seriously change the analysis results of SFG spectra. The dispersion of Fresnel factors in SFG spectra originates from the complex refractive index of the liquid. However, the complex refractive index in the Infrared region is somehow unavailable for most commonly used liquids in SFG studies. Therefore, we have developed ComplexRI software package to obtain the complex refractive index of any liquids by using the ATR-IR spectra. The output of ComplexRI is the complex refractive index in IR region. Users can specify the target vibrational regions.<br />
<br />
==Developing History==<br />
The development of ComplexRI was done by Lin Wang, Ryo Murata, Teppei Kamimura, Akihiro Morita in the lab of computational molecular science at Tohoku University. <br />
<br />
The main code was first developed by Wang in 2019 when he investigated the dispersion of Fresnel factor in electrode/electrolyte interfaces. <ref name = "ref1" /> In 2020, Murata and Wang further extended the code and generated a complex refractive index database with about 20 commonly used liquids in SFG studies. <ref name = "ref2" /> Wang used the database and discussed the general influence of dispersion of Fresnel factor in the SFG spectra analysis. <ref name = "ref3" />. In 2021, the program code was summarized and opened to the website by Kamimura under the supervise of Wang and Morita. The automatic fitting procedure is updated. Kamimura and Wang also created the MediaWiki manual page for ComplexRI. <br />
<br />
Many thanks to the experimental collaborators during the development.<br />
: Dr. Satoshi Nihonyanagi (RIKEN), Dr. Ken-ichi Inoue (Tohoku Univ.), Prof. Shen Ye (Tohoku Univ.), Dr. Tahei Tahara (RIKEN). <br />
<br />
<br />
== Tutorial ==<br />
{|class="wikitable"<br />
! Examples to use ComplexRI<br />
|-<br />
| Tutorial01：[[Tutorial01| Automatic Mode]]<br />
|-<br />
| Tutorial02： [[Tutorial02|Manual Mode]]<br />
|}<br />
<br />
----<br />
<br />
==Manual==<br />
<br />
{|class="wikitable"<br />
! Input of ComplexRI<br />
|-<br />
|[[Input#Information of ATR-IR experiment|Information of ATR-IR experiment]]<br />
|-<br />
|[[Input#Control parameters of ComplexRI fitting|Control parameters of ComplexRI fitting]]<br />
|}<br />
<br />
{|class="wikitable"<br />
! Output of ComplexRI<br />
|-<br />
|[[Output#Stardard output of ComplexRI|Stardard output of ComplexRI]] <br />
|-<br />
|[[Output#Download your results|Download your results]] <br />
|}<br />
<br />
----<br />
<br />
==Theory==<br />
<br />
{|class="wikitable"<br />
|-<br />
|[[Theory#ATR-IR data|Calculated reflectance of ATR-IR from complex refractive index]]<br />
|-<br />
|[[Theory#Fitting procedure| How to Fit the ATR-IR spectra]]<br />
|-<br />
|[[Theory#Auto Fitting|Automatically determine the initial parameters in fitting procedure]]<br />
|}<br />
<br />
----<br />
<br />
==FAQ==<br />
<br />
<div style="font-size: 150%;"> 1. How to cite ComplexRI </div><br />
<br />
: If ComplexRI is helpful, please cite the following references.<br />
<br />
<references><br />
<ref name = "ref1">"Effect of Frequency-Dependent Fresnel Factor on the Vibrational Sum Frequency Generation Spectra for Liquid/Solid Interfaces"<br />
Lin Wang, Satoshi Nihonyanagi, Ken-ichi Inoue, Kei Nishikawa, Akihiro Morita, Shen Ye, Tahei Tahara, J. Phys. Chem. C, 123(25) 15665-15673 (2019).</ref><br />
<ref name = "ref2">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. I Quantitative Spectra"<br />
Ryo Murata, Ken-ichi Inoue, Lin Wang, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9794-9803 (2021).</ref><br />
<ref name = "ref3">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. II Implication to Sum Frequency Generation Spectroscopy"<br />
Lin Wang, Ryo Murata, Ken-ichi Inoue, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9804-9810 (2021).</ref><br />
<br />
</references><br />
<br />
[http://comp.chem.tohoku.ac.jp/mediawiki/index.php/en/ComplexRI Top of this page]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=En/ComplexRI&diff=952En/ComplexRI2022-01-25T01:53:56Z<p>Lwang: </p>
<hr />
<div>__NOTOC__<br />
<br />
<span style="font-size: 100%; color:red;">※Chrome browser is recommend to read this page. </span><br />
<br />
{|class="wikitable"<br />
! Index<br />
|-<br />
|[[#Overview|Overview]]<br />
|-<br />
|[[#Developing History|Developing History]]<br />
|-<br />
|[[#Tutorial|Tutorial]]<br />
|-<br />
|[[#Manual|Manual]]<br />
|-<br />
|[[#Theory|Theory]]<br />
|-<br />
|[[#FAQ|FAQ]]<br />
|}<br />
<br />
== Overview ==<br />
The complex refractive index is a basic property in the study of light-matter interactions and spectroscopy. Especially in the sum frequency generation (SFG) vibrational spectroscopy studies, the analysis of SFG spectra requires detailed information of the Fresnel factors in the typical three-layer interface model. The dispersion of Fresnel factors in SFG spectra originates from the complex refractive index of the liquid. Studies <ref name = "ref1" /> have shown that the dispersion of the Fresnel factor may become significant and seriously change the analysis results of SFG spectra. However, the complex refractive index in the Infrared region is somehow unavailable for most commonly used liquids in SFG studies. Therefore, we have developed ComplexRI software package to obtain the complex refractive index of any liquids by using the ATR-IR spectra. The output of ComplexRI is the complex refractive index in IR region. Users can specify the target vibrational regions.<br />
<br />
==Developing History==<br />
The development of ComplexRI was done by Lin Wang, Ryo Murata, Teppei Kamimura, Akihiro Morita in the lab of computational molecular science at Tohoku University. <br />
<br />
The main code was first developed by Wang in 2019 when he investigated the dispersion of Fresnel factor in electrode/electrolyte interfaces. <ref name = "ref1" /> In 2020, Murata and Wang further extended the code and generated a complex refractive index database with about 20 commonly used liquids in SFG studies. <ref name = "ref2" /> Wang used the database and discussed the general influence of dispersion of Fresnel factor in the SFG spectra analysis. <ref name = "ref3" />. In 2021, the program code was summarized and opened to the website by Kamimura under the supervise of Wang and Morita. The automatic fitting procedure is updated. Kamimura and Wang also created the MediaWiki manual page for ComplexRI. <br />
<br />
Many thanks to the experimental collaborators during the development.<br />
: Dr. Satoshi Nihonyanagi (RIKEN), Dr. Ken-ichi Inoue (Tohoku Univ.), Prof. Shen Ye (Tohoku Univ.), Dr. Tahei Tahara (RIKEN). <br />
<br />
<br />
== Tutorial ==<br />
{|class="wikitable"<br />
! Examples to use ComplexRI<br />
|-<br />
| Tutorial01：[[Tutorial01| Automatic Mode]]<br />
|-<br />
| Tutorial02： [[Tutorial02|Manual Mode]]<br />
|}<br />
<br />
----<br />
<br />
==Manual==<br />
<br />
{|class="wikitable"<br />
! Input of ComplexRI<br />
|-<br />
|[[Input#Information of ATR-IR experiment|Information of ATR-IR experiment]]<br />
|-<br />
|[[Input#Control parameters of ComplexRI fitting|Control parameters of ComplexRI fitting]]<br />
|}<br />
<br />
{|class="wikitable"<br />
! Output of ComplexRI<br />
|-<br />
|[[Output#Stardard output of ComplexRI|Stardard output of ComplexRI]] <br />
|-<br />
|[[Output#Download your results|Download your results]] <br />
|}<br />
<br />
----<br />
<br />
==Theory==<br />
<br />
{|class="wikitable"<br />
|-<br />
|[[Theory#ATR-IR data|Calculated reflectance of ATR-IR from complex refractive index]]<br />
|-<br />
|[[Theory#Fitting procedure| How to Fit the ATR-IR spectra]]<br />
|-<br />
|[[Theory#Auto Fitting|Automatically determine the initial parameters in fitting procedure]]<br />
|}<br />
<br />
----<br />
<br />
==FAQ==<br />
<br />
<div style="font-size: 150%;"> 1. How to cite ComplexRI </div><br />
<br />
: If ComplexRI is helpful, please cite the following references.<br />
<br />
<references><br />
<ref name = "ref1">"Effect of Frequency-Dependent Fresnel Factor on the Vibrational Sum Frequency Generation Spectra for Liquid/Solid Interfaces"<br />
Lin Wang, Satoshi Nihonyanagi, Ken-ichi Inoue, Kei Nishikawa, Akihiro Morita, Shen Ye, Tahei Tahara, J. Phys. Chem. C, 123(25) 15665-15673 (2019).</ref><br />
<ref name = "ref2">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. I Quantitative Spectra"<br />
Ryo Murata, Ken-ichi Inoue, Lin Wang, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9794-9803 (2021).</ref><br />
<ref name = "ref3">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. II Implication to Sum Frequency Generation Spectroscopy"<br />
Lin Wang, Ryo Murata, Ken-ichi Inoue, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9804-9810 (2021).</ref><br />
<br />
</references><br />
<br />
[http://comp.chem.tohoku.ac.jp/mediawiki/index.php/en/ComplexRI Top of this page]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=En/ComplexRI&diff=951En/ComplexRI2022-01-25T01:51:29Z<p>Lwang: </p>
<hr />
<div>__NOTOC__<br />
<br />
<span style="font-size: 100%; color:red;">※Chrome browser is recommend to read this page. </span><br />
<br />
{|class="wikitable"<br />
! Index<br />
|-<br />
|[[#Overview|Overview]]<br />
|-<br />
|[[#Developing History|Developing History]]<br />
|-<br />
|[[#Tutorial|Tutorial]]<br />
|-<br />
|[[#Manual|Manual]]<br />
|-<br />
|[[#Theory|Theory]]<br />
|-<br />
|[[#FAQ|FAQ]]<br />
|}<br />
<br />
== Overview ==<br />
The complex refractive index is a basic property in the study of light-matter interactions and spectroscopy. Especially in the sum frequency generation (SFG) vibrational spectroscopy studies, the analysis of SFG spectra requires detailed information of the Fresnel factors in the typical three-layer interface model. The dispersion of Fresnel factors in SFG spectra originates from the complex refractive index of the liquid. However, the complex refractive index in the Infrared region is somehow unavailable for most commonly used liquids in SFG studies. Studies <ref name = "ref1" /> have shown that the dispersion of the Fresnel factor may become significant and seriously change the analysis results of SFG spectra. Therefore, we have developed ComplexRI software package to obtain the complex refractive index of any liquids by using the ATR-IR spectra. The output of ComplexRI is the complex refractive index in IR region. Users can specify the target vibrational regions.<br />
<br />
==Developing History==<br />
The development of ComplexRI was done by Lin Wang, Ryo Murata, Teppei Kamimura, Akihiro Morita in the lab of computational molecular science at Tohoku University. <br />
<br />
The main code was first developed by Wang in 2019 when he investigated the dispersion of Fresnel factor in electrode/electrolyte interfaces. <ref name = "ref1" /> In 2020, Murata and Wang further extended the code and generated a complex refractive index database with about 20 commonly used liquids in SFG studies. <ref name = "ref2" /> Wang used the database and discussed the general influence of dispersion of Fresnel factor in the SFG spectra analysis. <ref name = "ref3" />. In 2021, the program code was summarized and opened to the website by Kamimura under the supervise of Wang and Morita. The automatic fitting procedure is updated. Kamimura and Wang also created the MediaWiki manual page for ComplexRI. <br />
<br />
Many thanks to the experimental collaborators during the development.<br />
: Dr. Satoshi Nihonyanagi (RIKEN), Dr. Ken-ichi Inoue (Tohoku Univ.), Prof. Shen Ye (Tohoku Univ.), Dr. Tahei Tahara (RIKEN). <br />
<br />
<br />
== Tutorial ==<br />
{|class="wikitable"<br />
! Examples to use ComplexRI<br />
|-<br />
| Tutorial01：[[Tutorial01| Automatic Mode]]<br />
|-<br />
| Tutorial02： [[Tutorial02|Manual Mode]]<br />
|}<br />
<br />
----<br />
<br />
==Manual==<br />
<br />
{|class="wikitable"<br />
! Input of ComplexRI<br />
|-<br />
|[[Input#Information of ATR-IR experiment|Information of ATR-IR experiment]]<br />
|-<br />
|[[Input#Control parameters of ComplexRI fitting|Control parameters of ComplexRI fitting]]<br />
|}<br />
<br />
{|class="wikitable"<br />
! Output of ComplexRI<br />
|-<br />
|[[Output#Stardard output of ComplexRI|Stardard output of ComplexRI]] <br />
|-<br />
|[[Output#Download your results|Download your results]] <br />
|}<br />
<br />
----<br />
<br />
==Theory==<br />
<br />
{|class="wikitable"<br />
|-<br />
|[[Theory#ATR-IR data|Calculated reflectance of ATR-IR from complex refractive index]]<br />
|-<br />
|[[Theory#Fitting procedure| How to Fit the ATR-IR spectra]]<br />
|-<br />
|[[Theory#Auto Fitting|Automatically determine the initial parameters in fitting procedure]]<br />
|}<br />
<br />
----<br />
<br />
==FAQ==<br />
<br />
<div style="font-size: 150%;"> 1. How to cite ComplexRI </div><br />
<br />
: If ComplexRI is helpful, please cite the following references.<br />
<br />
<references><br />
<ref name = "ref1">"Effect of Frequency-Dependent Fresnel Factor on the Vibrational Sum Frequency Generation Spectra for Liquid/Solid Interfaces"<br />
Lin Wang, Satoshi Nihonyanagi, Ken-ichi Inoue, Kei Nishikawa, Akihiro Morita, Shen Ye, Tahei Tahara, J. Phys. Chem. C, 123(25) 15665-15673 (2019).</ref><br />
<ref name = "ref2">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. I Quantitative Spectra"<br />
Ryo Murata, Ken-ichi Inoue, Lin Wang, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9794-9803 (2021).</ref><br />
<ref name = "ref3">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. II Implication to Sum Frequency Generation Spectroscopy"<br />
Lin Wang, Ryo Murata, Ken-ichi Inoue, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9804-9810 (2021).</ref><br />
<br />
</references><br />
<br />
[http://comp.chem.tohoku.ac.jp/mediawiki/index.php/en/ComplexRI Top of this page]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Theory&diff=944Theory2022-01-25T01:15:53Z<p>Lwang: </p>
<hr />
<div><br />
<div id="ATR-IR data" style="font-size: 200%;"> Calculated reflectance of ATR-IR from complex refractive index </div><br />
<br />
----<br />
[[File:Light.png|500px]]<br />
<br />
The experimental geometry is described by the two-layer model in the above Figure, where phase <math>i</math> and phase <math>j</math> represent the substrate and sample, respectively. <br />
The incident light in phase <math>i</math> and transmitted light in phase <math>j</math> are related by Snell's law<br />
: <math> n_i \sin \theta_i = n_j \sin \theta_j </math><br />
<br />
where <math>n_i</math> and <math>n_j</math> are the complex refractive index of substrate and sample. <br />
<math>\theta_i</math> and <math>\theta_j</math> denote the angles of incidence and transmission of IR light, respectively.<br />
<br />
The reflectance of <math>p</math>- and <math>s</math>-polarized lights can be represented as the ratio of reflected to incident light intensities by <ref name = "ref1" /><br />
<br />
: <math> | r_{ij}^p|^2 = \left| \frac{n_j \cos \theta_i - n_i \cos \theta_j}{n_j \cos \theta_i + n_i \cos \theta_j} \right|^2 </math><br />
: <math> | r_{ij}^s|^2 = \left| \frac{n_i \cos \theta_i - n_j \cos \theta_j}{n_i \cos \theta_i + n_j \cos \theta_j} \right|^2 </math><br />
<br />
The angle of transmission <math>\theta_j</math> is derived from Snell's law to be <br />
: <math> \cos \theta_j = \sqrt{1-\frac{n_i^2}{n_j^2} \sin^2 \theta_i} </math><br />
which can be imaginary in the ATR condition. <br />
<br />
In the experiment, the incident angle <math>\theta_i</math> is often fixed, for example, to 45 degree. <br />
Take substate diamond as example, <math>n_i </math> is also known as 2.38. <br />
Therefore, the ATR condition is satisfied in most cases where <math>n_j </math> is smaller than <math> n_i \sin \theta_i = 1.68 </math>.<br />
This situation is held for most liquid samples. <br />
In the total reflection condition, the calculated <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> are unity when <math>n_j </math> is real.<br />
However, <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> become less than unity when the refractive index of the liquid <math>n_j = \eta_j + i \kappa_j </math> is complex.<br />
The reduced reflectance is a consequence of the absorption of evanescent light in the liquid sample. <br />
Therefore, by fitting the experimental reflectance data in ATR-IR spectra, it is able to obtain the complex refractive index of the liquid sample.<br />
<br />
----<br />
<br />
<div id="Fitting procedure" style="font-size: 200%;"> How to Fit the ATR-IR spectra </div><br />
<br />
The purpose of fitting is to determine the frequency-dependent complex refractive index <math>n_j(\nu) </math>.<br />
The complex refractive index of sample is represented with a set of Lorentz functions <br />
: <math> n_j (\nu) = \eta_j (\nu) + i \kappa_j (\nu) = n_j^0 + \sum_{l=1}^{l_\text{max}} \frac{A_l}{\nu_l - \nu - i \Gamma_l} </math><br />
where <math> n_j^0 </math> is the nonresonant refractive index. <br />
<math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> are the amplitude, peak wavenumber and bandwidth of each Lorentz function,<br />
respectively. <math> l_\text{max} </math> is the number of Lorentz functions to be used. <br />
Therefore, the parameters <math> n_j^0 </math>, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> and <math> l_\text{max} </math> were determined from the experimental spectra.<br />
<br />
In the beginning, <math> n_j^0 </math> should be determined before the fitting procedure. <math> n_j^0 </math> is the nonresonant refractive index in the IR wavenumber region. <br />
In the reference paper <ref name = "ref2" />, we use the refractive index values in the visible regions to fit Cauchy's equation.<br />
: <math>n_j^0(\lambda) = A + \frac{B}{{\lambda}^2} + \frac{C}{{\lambda}^4}</math><br />
The obtained parameters <math>A, B, C</math> were used to evaluate the nonresnant refractive index at 5000 <math> \text{cm}^{-1} </math>.<br />
It is also possible to directly use the refractive index in the visible region, which may involve some deviation in <math> n_j^0 </math>. <ref name = "ref2" /><br />
<br />
After the determination of <math> n_j^0 </math>, other parameters related to the Lorentz functions are determined by minimizing the least-squares residual (LSR) between the experimental reflectance spectra and those of the analytical formulas over the whole wavenumber region of the target vibrational band. The residual is defined by <br />
: <math> \text{LSR} ( \{ A_l, \nu_l, \Gamma_l \} ) = \frac{1}{n} \sum_{\nu_n \in [\nu_\text{min}, \nu_\text{max}]} \left[ |r_{ij}^p (\nu_n)|^2 + |r_{ij}^s (\nu_n)|^2 - 2|r_{ij} (\nu_n)|^2_\mathrm{exp} \right]^2 </math><br />
where <math> | r_{ij}^p|^2 </math> and <math> | r_{ij}^s|^2 </math> are the calculated reflectances in the above section. <br />
<math> |r_{ij} (\nu_n)|^2_\mathrm{exp} </math> is the experimental reflectance of unpolarized light at wavenumber <math> \nu_n </math>. The summation of <math> n </math> is taken for all observed wavenumber points in the target vibrational band.<br />
By minimizing the LSR, the parameters of each Lorentz functions, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math>, were obtained. <br />
The minimization is numerically done in the program, thus the initial parameter of <math> l_\text{max} </math>, <math> A_l </math>, <math> \nu_l</math> and <math>\Gamma_l</math> should be determined.<br />
And the initial parameters also have a large effect on whether the minimization can reach the tolerance and how long the minimization procedure is taken. <br />
All of them can be set manually. <br />
In the following, we will introduce a method to automatically determine the initial parameters.<br />
<br />
----<br />
<br />
<div id="Auto Fitting" style="font-size: 200%;"> Automatically determine the initial parameters in fitting procedure </div><br />
<br />
In order to determine the number of Lorentz functions to be used, we first start with only one Lorentz function and represent the complex refractive index as <br />
: <math> n_j (\nu) = n_j^0 + \frac{A_1}{\nu_1 - \nu - i \Gamma_1} </math><br />
The first Lorentz function is used to fit the strongest adsorption band in the target region. <br />
Thus, the initial parameter for <math> \nu_1 </math> is set to the wavenumber of minimum value of reflectance in the experimental data. <br />
The initial parameter for <math> \Gamma_1 </math> and <math> A_1 </math> is set to be 15 <math> \text{cm}^{-1} </math> and 7.5 <math> \text{cm}^{-1} </math>, respectively.<br />
These parameters are estimated from the parameters of very strong adsorption bands of commonly used liquids. <ref name = "ref2" /><br />
<br />
After the first fitting procedure, the strongest adsorption band is expected to be well represented.<br />
Here if the LSR is less than the tolerance, the fitting is finished and no more Lorentz functions are required. <br />
If not, another Lorentz function is added and the complex refractive index become<br />
: <math> n_j (\nu) = n_j^0 + \frac{A_1}{\nu_1 - \nu - i \Gamma_1} + \frac{A_2}{\nu_2 - \nu - i \Gamma_2} </math><br />
The second Lorentz funtion is used to represent major adsorption band in the difference reflectance spectra between the first fitting results and experimental results. <br />
The initial value of <math> \nu_1 </math>, <math> \Gamma_1 </math> and <math> A_1 </math> are set to be the optimized value in the last fitting procedure.<br />
The initial value of <math> \nu_2 </math> is set to the wavenumber of minimum (or maximum) value of difference reflectance spectra. <br />
The initial parameter for <math> \Gamma_2 </math> and <math> A_2 </math> is set to be 15 <math> \text{cm}^{-1} </math> and 3.75 <math> \text{cm}^{-1} </math>, respectively. <br />
A smaller initial value of <math> A_2 </math> suggests that the second Lorentz function is a minor adsorption band in ATR-IR spectra. <br />
Then all parameters are again optimized using the same fitting procedure. <br />
<br />
The number of Lorentz functions keeps increasing and the whole procedure is repeated until the final LSR reaches the set tolerance.<br />
<br />
<br />
<div style="font-size: 200%;"> References </div><br />
<br />
<references><br />
<br />
<ref name = "ref1">"Theory of Sum Frequency Generation Spectroscopy"<br />
Akihiro Morita. Springer Nature Singapore Pte Ltd: 2018 </ref><br />
<ref name = "ref2">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. I Quantitative Spectra"<br />
Ryo Murata, Ken-ichi Inoue, Lin Wang, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9794-9803 (2021).</ref><br />
<br />
</references></div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=En/ComplexRI&diff=938En/ComplexRI2022-01-24T09:12:19Z<p>Lwang: </p>
<hr />
<div>__NOTOC__<br />
<br />
<span style="font-size: 100%; color:red;">※Chrome browser is recommend to read this page. </span><br />
<br />
{|class="wikitable"<br />
! Index<br />
|-<br />
|[[#Overview|Overview]]<br />
|-<br />
|[[#Developing History|Developing History]]<br />
|-<br />
|[[#Tutorial|Tutorial]]<br />
|-<br />
|[[#Manual|Manual]]<br />
|-<br />
|[[#Theory|Theory]]<br />
|-<br />
|[[#FAQ|FAQ]]<br />
|}<br />
<br />
== Overview ==<br />
The complex refractive index is a basic property in the study of light-matter interactions and spectroscopy. Especially in the sum frequency generation (SFG) vibrational spectroscopy studies, the analysis of SFG spectra requires detailed information of the Fresnel factors in the typical three-layer interface model. The dispersion of Fresnel factors in SFG spectra originates from the complex refractive index of the liquid. Studies <ref name = "ref1" /> have shown that the dispersion of the Fresnel factor may become significant and seriously change the analysis results of SFG spectra. However, the complex refractive index in the Infrared region is somehow unavailable for most commonly used liquids in SFG studies. Therefore, we have developed ComplexRI software package to obtain the complex refractive index of any liquids by using the ATR-IR spectra. The output of ComplexRI is the complex refractive index in IR region. Users can specify the target vibrational regions.<br />
<br />
==Developing History==<br />
The development of ComplexRI was done by Lin Wang, Ryo Murata, Teppei Kamimura, Akihiro Morita in the lab of computational molecular science at Tohoku University. <br />
<br />
The main code was first developed by Wang in 2019 when he investigated the dispersion of Fresnel factor in electrode/electrolyte interfaces. <ref name = "ref1" /> In 2020, Murata and Wang further extended the code and generated a complex refractive index database with about 20 commonly used liquids in SFG studies. <ref name = "ref2" /> Wang used the database and discussed the general influence of dispersion of Fresnel factor in the SFG spectra analysis. <ref name = "ref3" />. In 2021, the program code was summarized and opened to the website by Kamimura under the supervise of Wang and Morita. The automatic fitting procedure is updated. Kamimura and Wang also created the MediaWiki manual page for ComplexRI. <br />
<br />
Many thanks to the experimental collaborators during the development.<br />
: Dr. Satoshi Nihonyanagi (RIKEN), Dr. Ken-ichi Inoue (Tohoku Univ.), Prof. Shen Ye (Tohoku Univ.), Dr. Tahei Tahara (RIKEN). <br />
<br />
<br />
== Tutorial ==<br />
{|class="wikitable"<br />
! Examples to use ComplexRI<br />
|-<br />
| Tutorial01：[[Tutorial01| Automatic Mode]]<br />
|-<br />
| Tutorial02： [[Tutorial02|Manual Mode]]<br />
|}<br />
<br />
----<br />
<br />
==Manual==<br />
<br />
{|class="wikitable"<br />
! Input of ComplexRI<br />
|-<br />
|[[Input#Information of ATR-IR experiment|Information of ATR-IR experiment]]<br />
|-<br />
|[[Input#Control parameters of ComplexRI fitting|Control parameters of ComplexRI fitting]]<br />
|}<br />
<br />
{|class="wikitable"<br />
! Output of ComplexRI<br />
|-<br />
|[[Output#Stardard output of ComplexRI|Stardard output of ComplexRI]] <br />
|-<br />
|[[Output#Download your results|Download your results]] <br />
|}<br />
<br />
----<br />
<br />
==Theory==<br />
<br />
{|class="wikitable"<br />
|-<br />
|[[Theory#ATR-IR data|Calculated reflectance of ATR-IR from complex refractive index]]<br />
|-<br />
|[[Theory#Fitting procedure| How to Fit the ATR-IR spectra]]<br />
|-<br />
|[[Theory#Auto Fitting|Automatically determine the initial parameters in fitting procedure]]<br />
|}<br />
<br />
----<br />
<br />
==FAQ==<br />
<br />
<div style="font-size: 150%;"> 1. How to cite ComplexRI </div><br />
<br />
: If ComplexRI is helpful, please cite the following references.<br />
<br />
<references><br />
<ref name = "ref1">"Effect of Frequency-Dependent Fresnel Factor on the Vibrational Sum Frequency Generation Spectra for Liquid/Solid Interfaces"<br />
Lin Wang, Satoshi Nihonyanagi, Ken-ichi Inoue, Kei Nishikawa, Akihiro Morita, Shen Ye, Tahei Tahara, J. Phys. Chem. C, 123(25) 15665-15673 (2019).</ref><br />
<ref name = "ref2">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. I Quantitative Spectra"<br />
Ryo Murata, Ken-ichi Inoue, Lin Wang, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9794-9803 (2021).</ref><br />
<ref name = "ref3">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. II Implication to Sum Frequency Generation Spectroscopy"<br />
Lin Wang, Ryo Murata, Ken-ichi Inoue, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9804-9810 (2021).</ref><br />
<br />
</references><br />
<br />
[http://comp.chem.tohoku.ac.jp/mediawiki/index.php/en/ComplexRI Top of this page]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=En/ComplexRI&diff=937En/ComplexRI2022-01-24T09:04:13Z<p>Lwang: </p>
<hr />
<div>__NOTOC__<br />
<br />
<span style="font-size: 100%; color:red;">※Chrome browser is recommend to read this page. </span><br />
<br />
{|class="wikitable"<br />
! Index<br />
|-<br />
|[[#Overview|Overview]]<br />
|-<br />
|[[#Developing History|Developing History]]<br />
|-<br />
|[[#Tutorial|Tutorial]]<br />
|-<br />
|[[#Manual|Manual]]<br />
|-<br />
|[[#Theory|Theory]]<br />
|-<br />
|[[#FAQ|FAQ]]<br />
|}<br />
<br />
== Overview ==<br />
The complex refractive index is a basic property in the study of light-matter interactions and spectroscopy. Especially in the sum frequency generation (SFG) vibrational spectroscopy studies, the analysis of SFG spectra requires detailed information of the Fresnel factors in the typical three-layer interface model. The dispersion of Fresnel factors in SFG spectra originates from the complex refractive index of the liquid. Studies <ref name = "ref1" /> have shown that the dispersion of the Fresnel factor may become significant and seriously change the analysis results of SFG spectra. However, the complex refractive index in the Infrared region is somehow unavailable for most commonly used liquids in SFG studies. Therefore, we have developed ComplexRI software package to obtain the complex refractive index of any liquids by using the ATR-IR spectra. The output of ComplexRI is the complex refractive index in IR region. Users can specify the target vibrational regions.<br />
<br />
==Developing History==<br />
The development of ComplexRI was done in the lab of computational molecular science at Tohoku University. <br />
<br />
The main code was first developed by Wang in 2019 when he investigated the dispersion of Fresnel factor in electrode/electrolyte interfaces. <ref name = "ref1" /> In 2020, Murata and Wang further extended the code and generated a complex refractive index database with about 20 commonly used liquids in SFG studies. <ref name = "ref2" /> Wang used the database and discussed the general influence of dispersion of Fresnel factor in the SFG spectra analysis. <ref name = "ref3" />. In 2021, the program code was summarized and opened to the website by Kamimura under the supervise of Wang and Morita. The automatic fitting procedure is updated. Kamimura and Wang also created the MediaWiki manual page for ComplexRI. <br />
<br />
Many thanks to the experimental collaborators during the development.<br />
: Dr. Satoshi Nihonyanagi (RIKEN), Dr. Ken-ichi Inoue (Tohoku Univ.), Prof. Shen Ye (Tohoku Univ.), Dr. Tahei Tahara (RIKEN). <br />
<br />
<br />
== Tutorial ==<br />
{|class="wikitable"<br />
! Examples to use ComplexRI<br />
|-<br />
| Tutorial01：[[Tutorial01| Automatic Mode]]<br />
|-<br />
| Tutorial02： [[Tutorial02|Manual Mode]]<br />
|}<br />
<br />
----<br />
<br />
==Manual==<br />
<br />
{|class="wikitable"<br />
! Input of ComplexRI<br />
|-<br />
|[[Input#Information of ATR-IR experiment|Information of ATR-IR experiment]]<br />
|-<br />
|[[Input#Control parameters of ComplexRI fitting|Control parameters of ComplexRI fitting]]<br />
|}<br />
<br />
{|class="wikitable"<br />
! Output of ComplexRI<br />
|-<br />
|[[Output#Stardard output of ComplexRI|Stardard output of ComplexRI]] <br />
|-<br />
|[[Output#Download your results|Download your results]] <br />
|}<br />
<br />
----<br />
<br />
==Theory==<br />
<br />
{|class="wikitable"<br />
|-<br />
|[[Theory#ATR-IR data|Calculated reflectance of ATR-IR from complex refractive index]]<br />
|-<br />
|[[Theory#Fitting procedure| How to Fit the ATR-IR spectra]]<br />
|-<br />
|[[Theory#Auto Fitting|Automatically determine the initial parameters in fitting procedure]]<br />
|}<br />
<br />
----<br />
<br />
==FAQ==<br />
<br />
<div style="font-size: 150%;"> 1. How to cite ComplexRI </div><br />
<br />
: If ComplexRI is helpful, please cite the following references.<br />
<br />
<references><br />
<ref name = "ref1">"Effect of Frequency-Dependent Fresnel Factor on the Vibrational Sum Frequency Generation Spectra for Liquid/Solid Interfaces"<br />
Lin Wang, Satoshi Nihonyanagi, Ken-ichi Inoue, Kei Nishikawa, Akihiro Morita, Shen Ye, Tahei Tahara, J. Phys. Chem. C, 123(25) 15665-15673 (2019).</ref><br />
<ref name = "ref2">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. I Quantitative Spectra"<br />
Ryo Murata, Ken-ichi Inoue, Lin Wang, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9794-9803 (2021).</ref><br />
<ref name = "ref3">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. II Implication to Sum Frequency Generation Spectroscopy"<br />
Lin Wang, Ryo Murata, Ken-ichi Inoue, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9804-9810 (2021).</ref><br />
<br />
</references><br />
<br />
[http://comp.chem.tohoku.ac.jp/mediawiki/index.php/en/ComplexRI Top of this page]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=En/ComplexRI&diff=936En/ComplexRI2022-01-24T08:54:02Z<p>Lwang: </p>
<hr />
<div>__NOTOC__<br />
<br />
<span style="font-size: 100%; color:red;">※Chrome browser is recommend to read this page. </span><br />
<br />
{|class="wikitable"<br />
! Index<br />
|-<br />
|[[#Overview|Overview]]<br />
|-<br />
|[[#Developing History|Developing History]]<br />
|-<br />
|[[#Tutorial|Tutorial]]<br />
|-<br />
|[[#Manual|Manual]]<br />
|-<br />
|[[#Theory|Theory]]<br />
|-<br />
|[[#FAQ|FAQ]]<br />
|}<br />
<br />
== Overview ==<br />
The complex refractive index is a basic property in the study of light-matter interactions and spectroscopy. Especially in the sum frequency generation (SFG) vibrational spectroscopy studies, the analysis of SFG spectra requires detailed information of the Fresnel factors in the typical three-layer interface model. The dispersion of Fresnel factors in SFG spectra originates from the complex refractive index of the liquid. Studies <ref name = "ref1" /> have shown that the dispersion of the Fresnel factor may become significant and seriously change the analysis results of SFG spectra. However, the complex refractive index in the Infrared region is somehow unavailable for most commonly used liquids in SFG studies. Therefore, we have developed ComplexRI software package to obtain the complex refractive index of any liquids by using the ATR-IR spectra. The output of ComplexRI is the complex refractive index in IR region. Users can specify the target vibrational regions.<br />
<br />
==Developing History==<br />
The development of ComplexRI was done in the lab of computational molecular science at Tohoku University. <br />
<br />
The main code was first developed by Wang in 2019 when he investigated the dispersion of Fresnel factor in electrode/electrolyte interfaces. <ref name = "ref1" /> In 2020, Murata and Wang further extended the code and generated a complex refractive index database with about 20 commonly used liquids in SFG studies. <ref name = "ref2" /> Wang used the database and discussed the general influence of dispersion of Fresnel factor in the SFG spectra analysis. <ref name = "ref3" />. In 2021, the program code was summarized and opened to the website by Kamimura under the supervise of Wang and Morita. The automatic fitting procedure is updated. Kamimura and Wang also created the MediaWiki manual page for ComplexRI. <br />
<br />
Many thanks to the experimental collaborators during the development.<br />
: Dr. Satoshi Nihonyanagi (RIKEN), Dr. Ken-ichi Inoue (Tohoku Univ.), Prof. Shen Ye (Tohoku Univ.), Dr. Tahei Tahara (RIKEN). <br />
<br />
<br />
== Tutorial ==<br />
{|class="wikitable"<br />
! Examples to use ComplexRI<br />
|-<br />
| Tutorial01：[[Tutorial01| Automatic Mode]]<br />
|-<br />
| Tutorial02： [[Tutorial02|Manual Mode]]<br />
|}<br />
<br />
----<br />
<br />
==Manual==<br />
<br />
{|class="wikitable"<br />
! Input of ComplexRI<br />
|-<br />
|[[Input#Information of ATR-IR experiment|Information of ATR-IR experiment]]<br />
|-<br />
|[[Input#Control parameters of ComplexRI fitting|Control parameters of ComplexRI fitting]]<br />
|}<br />
<br />
{|class="wikitable"<br />
! Output of ComplexRI<br />
|-<br />
|[[Output#Stardard output of ComplexRI|Stardard output of ComplexRI]] <br />
|-<br />
|[[Output#Download your results|Download your results]] <br />
|}<br />
<br />
----<br />
<br />
==Theory==<br />
<br />
{|class="wikitable"<br />
|-<br />
|[[Theory#ATR-IR data|Calculated reflectance of ATR-IR from complex refractive index]]<br />
|-<br />
|[[Theory#Fitting procedure| How to Fit the ATR-IR spectra]]<br />
|-<br />
|[[Theory#Auto Fitting|Automatically determine the initial parameters in fitting procedure]]<br />
|}<br />
<br />
----<br />
<br />
==FAQ==<br />
<br />
<div style="font-size: 150%;"> 1. How to cite ComplexRI </div><br />
<br />
: If you found ComplexRI is helpful, please cite the following references.<br />
<br />
<references><br />
<ref name = "ref1">"Effect of Frequency-Dependent Fresnel Factor on the Vibrational Sum Frequency Generation Spectra for Liquid/Solid Interfaces"<br />
Lin Wang, Satoshi Nihonyanagi, Ken-ichi Inoue, Kei Nishikawa, Akihiro Morita, Shen Ye, Tahei Tahara, J. Phys. Chem. C, 123(25) 15665-15673 (2019).</ref><br />
<ref name = "ref2">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. I Quantitative Spectra"<br />
Ryo Murata, Ken-ichi Inoue, Lin Wang, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9794-9803 (2021).</ref><br />
<ref name = "ref3">"Dispersion of Complex Refractive Indices for Intense Vibrational Bands. II Implication to Sum Frequency Generation Spectroscopy"<br />
Lin Wang, Ryo Murata, Ken-ichi Inoue, Shen Ye, and Akihiro Morita, J. Phys. Chem. B, 125(34), 9804-9810 (2021).</ref><br />
<br />
</references><br />
<br />
[http://comp.chem.tohoku.ac.jp/mediawiki/index.php/en/ComplexRI Top of this page]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=%E5%87%BA%E5%8A%9B&diff=935出力2022-01-22T02:11:51Z<p>Lwang: </p>
<hr />
<div><div id="標準出力" style="font-size: 150%;"> 標準出力</div><br />
----<br />
[[File:Newoutput.png|750px]]<br />
: 標準出力は上の図のようになる。<br />
: 一行目の(①)はフィッティングが終了したときの残差です。この値が小さいほど、フィッティング結果が実験結果と近いことを意味しています。<br />
: ②の部分はローレンツ関数のフィッティング結果を示しています。それぞれのローレンツ関数に対して<math> A_l, \nu_l, \gamma_l </math> が並んでいます。<br />
: ③の部分はローレンツ関数によって計算された複素屈折率を目標領域でプロットしています。シアン色が実部で、マゼンタ色が虚部になっています。<br />
: ④の部分は反射光の入射光に対する強度比を計算された値とATR-IR実験から得られた値の両方について目標領域でプロットしています。ATR-IR実験から得られた値は赤、計算によって得られた値は緑でプロットされています。青はその差をプロットしています。<br />
<br />
<div id="結果のダウンロード" style="font-size: 150%;">結果のダウンロード </div><br />
----<br />
[[File:DL.png|500px]]<br />
: "Download the output file"をクリックすると、出力ファイルをダウンロードできます。<br />
<br />
: 出力ファイルには、上で述べたような残差の値やローレンツ関数のパラメータ、グラフが出力されています。<br />
<br />
: "Execute another Fitting" をクリックすると、Main packageのページに戻ります。入力は保存されています。</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=%E5%87%BA%E5%8A%9B&diff=934出力2022-01-22T02:11:16Z<p>Lwang: </p>
<hr />
<div><div id="標準出力" style="font-size: 150%;"> 標準出力</div><br />
----<br />
[[File:Newoutput.png|750px]]<br />
: 標準出力は上の図のようになる。<br />
: 一行目の(①)はフィッティングが終了したときの残差です。この値が小さいほど、フィッティング結果が実験結果と近いことを意味しています。この値の計算方法の詳細は <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>で説明しています。<br />
<br />
: ②の部分はローレンツ関数のフィッティング結果を示しています。それぞれのローレンツ関数に対して<math> A_l, \nu_l, \gamma_l </math> が並んでいます。<br />
: ③の部分はローレンツ関数によって計算された複素屈折率を目標領域でプロットしています。シアン色が実部で、マゼンタ色が虚部になっています。<br />
: ④の部分は反射光の入射光に対する強度比を計算された値とATR-IR実験から得られた値の両方について目標領域でプロットしています。ATR-IR実験から得られた値は赤、計算によって得られた値は緑でプロットされています。青はその差をプロットしています。<br />
<br />
<div id="結果のダウンロード" style="font-size: 150%;">結果のダウンロード </div><br />
----<br />
[[File:DL.png|500px]]<br />
: "Download the output file"をクリックすると、出力ファイルをダウンロードできます。<br />
<br />
: 出力ファイルには、上で述べたような残差の値やローレンツ関数のパラメータ、グラフが出力されています。<br />
<br />
: "Execute another Fitting" をクリックすると、Main packageのページに戻ります。入力は保存されています。</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=%E5%87%BA%E5%8A%9B&diff=933出力2022-01-22T02:10:17Z<p>Lwang: </p>
<hr />
<div><div id="標準出力" style="font-size: 150%;"> 標準出力</div><br />
----<br />
[[File:Newoutput.png|750px]]<br />
: 標準出力は上の図のようになる。<br />
: 一行目の(①)はフィッティングが終了したときの残差です。この値が小さいほど、フィッティング結果が実験結果と近いことを意味しています。この値の計算方法の詳細は<u> [[En/ComplexRI#理論|理論]]</u>の<u> [[理論#Fitting procedure| How to Fit the ATR-IR spectra]] </u>で説明しています。<br />
<br />
: ②の部分はローレンツ関数のフィッティング結果を示しています。それぞれのローレンツ関数に対して<math> A_l, \nu_l, \gamma_l </math> が並んでいます。<br />
: ③の部分はローレンツ関数によって計算された複素屈折率を目標領域でプロットしています。シアン色が実部で、マゼンタ色が虚部になっています。<br />
: ④の部分は反射光の入射光に対する強度比を計算された値とATR-IR実験から得られた値の両方について目標領域でプロットしています。ATR-IR実験から得られた値は赤、計算によって得られた値は緑でプロットされています。青はその差をプロットしています。<br />
<br />
<div id="結果のダウンロード" style="font-size: 150%;">結果のダウンロード </div><br />
----<br />
[[File:DL.png|500px]]<br />
: "Download the output file"をクリックすると、出力ファイルをダウンロードできます。<br />
<br />
: 出力ファイルには、上で述べたような残差の値やローレンツ関数のパラメータ、グラフが出力されています。<br />
<br />
: "Execute another Fitting" をクリックすると、Main packageのページに戻ります。入力は保存されています。</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=Input&diff=932Input2022-01-22T02:07:27Z<p>Lwang: </p>
<hr />
<div><br />
<br />
: [[File:Newtoppage.png|1000px]]<br />
: This is the typical snapshot of the input of ComplexRI. <br />
: The input of Complex contains two parts. The left part is the information of ATR-IR experimental data. The right part is the control parameters of the complex refractive index fitting procedure. Each part will be explained in the following. <br />
<br />
----<br />
<div id="Information of ATR-IR experiment" style="font-size: 200%;"> Information of ATR-IR experiment </div><br />
<br />
----<br />
<div id="Input01" style="font-size: 150%;"> ①ATR-IR File </div><br />
: Please upload the ATR-IR experimental data in this part. The inside should be like the following.<br />
: [[File:NewFILE01.png|200px]]<br />
: There are two rules for the format of input file.<br />
: (1). The format of input file must be txt.<br />
: (2). The columns are separated by the space.<br />
<br />
----<br />
<div id="Input02" style="font-size: 150%;"> ②The order of data </div><br />
: Please select the sort order of your data.<br />
:: Ascending order: The wavenumbers in the input file are in ascending order (left picture). (Default)<br />
:: Descending order: The wavenumbers in the input file are in descending order (right picture). <br />
:[[File:NewFILE01.png|200px]][[File:NewFILE04.png|220px]]<br />
<br />
----<br />
<div id="Input03" style="font-size: 150%;"> ③Reflectance or Absorptance? </div><br />
: Please select the type of your ATR-IR data.<br />
:: Reflectance(%): The Reflectance of ATR-IR spectra in the value of percentage. (Default)<br />
:: Reflectance: The Reflectance of ATR-IR spectra. <br />
:: Absorptance: The Absorptance of ATR-IR spectra.<br />
: The relationships between each data are<br />
:: <math> Reflectance(%)=Reflectance*100 </math><br />
:: <math> Absorptance=-\log_{10}(Reflectance) </math><br />
<br />
----<br />
<div id="Input04" style="font-size: 150%;"> ④The Substrate in ATR-IR </div><br />
: Please select the substrate you used in the ATR-IR experiment. Here, we prepare the three substrates that often used <br />
:: Diamond(Refractive Index = 2.38). (Default)<br />
:: Zinc selenide(Refractive Index = 2.40).<br />
:: Germanium(Refractive Index = 4.0).<br />
: You can also input the refractive index of your substrate by selecting Others in the list.<br />
:[[File:4_other.png|500px]]<br />
<br />
----<br />
<div id="Input05" style="font-size: 150%;"> ⑤Incident angle in ATR-IR </div><br />
: Please input the incident angle in your ATR-IR experiment. (Default=45 degree)<br />
<br />
----<br />
<div id="Input06" style="font-size: 150%;"> ⑥Select the column of your data </div><br />
: Please input the column number of the data that you want to analyze in your ATR-IR file. <br />
:: Wavenumber: The column number of wavenumber in your input file. (Default: 1)<br />
:: ATR-IR data: The column number of ATR-IR data in your input file. (Default: 2)<br />
<br />
: For example, an input file like following can be uploaded and column 1 and column 5 can be selected for analyzing. <br />
: [[File:NewFILE03.png|500px]]<br />
: [[File:6_15.png|300px]]<br />
<br />
----<br />
<br />
<div id="Control parameters of ComplexRI fitting" style="font-size: 200%;">Control parameters of ComplexRI fitting </div><br />
<br />
----<br />
<div id="Input07" style="font-size: 150%;"> ⑦Title of your job </div><br />
: Please input the title of your job (alphabet). The output results of ComplexRI will be saved in the excel format with the name @Title.xlsx<br />
<br />
----<br />
<div id="Input08" style="font-size: 150%;"> ⑧Input the fitting range </div><br />
: Please input the frequency range (in wavenumber) inside which you want to perform the fitting. ComplexRI will only fit the data inside the range you input here.<br />
:: Minimum wavenumber: The lower boundary of wavenumber. (Default: 1636)<br />
:: Maximum wavenumber: The upper boundary of wavenumber. (Default: 1863)<br />
<br />
---- <br />
<div id="Input09" style="font-size: 150%;"> ⑨Refractive index of target sample in non-resonance region (<math> n_j^0 </math>) </div><br />
: Please input the refractive index of the target sample (<math> n_j^0 </math>) in non-resonance region. (Default=1.360)<br />
: The determination of <math> n_j^0 </math> and some comments about it can be found in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>. <br />
<br />
----<br />
<div id="Input10" style="font-size: 150%;"> ⑩The tolerance of fitting </div><br />
: Please input the tolerance of fitting procedure. (default: 0.02)<br />
: The fitting will be finished when the calculated residual is less than this value. <br />
: The details are described in <u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>.<br />
:<span style color="red">Notice!! Fitting can not finish if this value is too small. </span><br />
<br />
----<br />
<div id="Input11" style="font-size: 150%;"> ⑪ Manually set the initial parameters </div><br />
: Please select whether to set the initial fitting parameters by yourself. <br />
:: No: Automatically done by the algorithm (Default)<br />
:: Yes: Manually set the initial parameters by users. <br />
: In the fitting, we use a set of Lorentz functions to represent the complex refractive index <br />
:: <math>n_j=n_j^0+\sum_{l=1}^{l_{max}} \frac{A_l}{\nu_l-\nu-i\gamma_l}</math><br />
: where <math> n_j^0 </math> is input in ⑨. The number of Lorentz functions <math> l_{max} </math>, and the corresponding initial parameters <math> A_l, \nu_l, \gamma_l </math> should be determined.<br />
: By selecting <math> No </math>, it means the initial parameters are automatically guessed by the algorithm explained in <u> [[Theory#Auto Fitting| Automatically determine the initial parameters in fitting procedure]] </u>. <br />
: By selecting <math> Yes </math>, you can manually set <math> l_{max} </math> and <math> A_l, \nu_l, \gamma_l </math> for each Lorentz function by yourself. The units of <math> A_l, \nu_l, \gamma_l </math> are all wavenumber. <math> l_{max} </math> is up to 5. <br />
: [[File:11yes.png|500px]]</div>Lwanghttp://comp.chem.tohoku.ac.jp/mediawiki/index.php?title=%E5%85%A5%E5%8A%9B&diff=931入力2022-01-22T02:01:53Z<p>Lwang: </p>
<hr />
<div><br />
<br />
: [[File:Newtoppage.png|1000px]]<br />
: これはComplexRIの標準入力のスナップショットです。<br />
: ComplexRIの入力は大きく二つに分類されます。左の部分は、ATR-IR実験の情報に関する部分、右の部分は複素屈折率のフィッティングのパラメータを調整する部分です。以下では、それぞれについて説明します。<br />
<br />
----<br />
<div id="Information of ATR-IR experiment" style="font-size: 200%;"> Information of ATR-IR experiment </div><br />
<br />
----<br />
<div id="Input01" style="font-size: 150%;"> ①ATR-IR File </div><br />
: ここでは、ATR-IRの実験データをアップロードしてください。中身は以下のようになっている必要があります。<br />
: [[File:NewFILE01.png|200px]]<br />
: ファイル形式には二つのルールがあります。<br />
: (1). テキスト形式になっている。<br />
: (2). 各列は空白で区切られている。<br />
<br />
----<br />
<div id="Input02" style="font-size: 150%;"> ②The order of data </div><br />
: データの並び方を入力してください。<br />
:: Ascending order: 波数が昇順 (下の図の左側)。(デフォルト)<br />
:: Descending order:波数が降順 (下の図の右側)。 <br />
:[[File:NewFILE01.png|200px]][[File:NewFILE04.png|220px]]<br />
<br />
----<br />
<div id="Input03" style="font-size: 150%;"> ③Reflectance or Absorptance? </div><br />
: ATR-IRのデータの種類を選択してください。<br />
:: Reflectance(%): 反射率のスペクトル。単位は(%)。(デフォルト)<br />
:: Reflectance: 反射率のスペクトル。<br />
:: Absorptance: 吸光度スペクトル。<br />
: それぞれのデータは以下の関係を持っています。<br />
:: <math> Reflectance(%)=Reflectance*100 </math><br />
:: <math> Absorptance=-\log_{10}(Reflectance) </math><br />
<br />
----<br />
<div id="Input04" style="font-size: 150%;"> ④The Substrate in ATR-IR </div><br />
: ATR-IR実験で使用した基板の屈折率を入力してください。ここには、よく使われる３つの基板は選択として用意します。<br />
:: Diamond(Refractive Index = 2.38) (デフォルト)<br />
:: Zinc selenide(Refractive Index = 2.40)<br />
:: Germanium(Refractive Index = 4.0).<br />
:Othersを使うことで基板の屈折率の値を入力することもできます。<br />
:[[File:4_other.png|500px]]<br />
<br />
----<br />
<div id="Input05" style="font-size: 150%;"> ⑤Incident angle in ATR-IR </div><br />
: ATR-IR実験のIR光の入射角を入力してください。(Default=45°)<br />
<br />
----<br />
<div id="Input06" style="font-size: 150%;"> ⑥Select the column of your data </div><br />
: 入力ファイルの中で解析したいデータの列番号を入力してください。<br />
:: Wavenumber: 波数の列番号。 (デフォルト: 1)<br />
:: ATR-IR data: 反射率もしくは吸光度の列番号。(デフォルト: 2)<br />
<br />
: 例えば、以下のようなファイルをアップロードした場合は、１列目と５列目を選んで解析に用いることができる。 <br />
: [[File:NewFILE03.png|500px]]<br />
: [[File:6_15.png|300px]]<br />
<br />
----<br />
<br />
<div id="Control parameters of ComplexRI fitting" style="font-size: 200%;">Control parameters of ComplexRI fitting </div><br />
<br />
----<br />
<div id="Input07" style="font-size: 150%;"> ⑦Title of your job </div><br />
: 今回の解析に名前を付けてください。<span color=”red”>(※半角入力)</span>。 結果は@Title.xlsxという名前のエクセルファイルに保存されます。<br />
<br />
----<br />
<div id="Input08" style="font-size: 150%;"> ⑧Input the fitting range </div><br />
: フィッティングを行う範囲を波数単位で入力してください。ComplexRIはこの範囲でのみ解析を行います。<br />
:: Minimum wavenumber: 波数の下限。 (デフォルト: 1636)<br />
:: Maximum wavenumber: 波数の上限。 (デフォルト: 1863)<br />
<br />
---- <br />
<div id="Input09" style="font-size: 150%;"> ⑨Refractive index of target sample in non-resonance region (<math> n_j^0 </math>) </div><br />
: 目標分子の非共鳴領域における屈折率(<math> n_j^0 </math>)を入力してください。(デフォルト＝1.360)<br />
: 詳細は<u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>で説明しています。<br />
<br />
----<br />
<div id="Input10" style="font-size: 150%;"> ⑩The tolerance of fitting </div><br />
: フィッティングの収束判定のしきい値を指定してください。(デフォルト: 0.02)<br />
: 最小二乗法の残差は与えられた値よりも小さくなったらフィッティングが終了します。<br />
: 詳細は<u> [[Theory#Fitting procedure| How to Fit the ATR-IR spectra]] </u>で説明しています。<br />
:<span style color="red">注意!! この入力値が小さすぎると解析が終わらないことがあります。 </span><br />
<br />
----<br />
<div id="Input11" style="font-size: 150%;"> ⑪ Manually set the initial parameters </div><br />
: フィッティング関数のパラメータの初期値を自分で設定するかを選択してください。<br />
:: No: 内部で自動的に設定されます。(デフォルト)<br />
:: Yes: ユーザーが入力します。<br />
: フィッティングにおいて、複素屈折率はローレンツ関数を用いて複素屈折率表しています。<br />
:: <math>n_j=n_j^0+\sum_{l=1}^{l_{max}} \frac{A_l}{\nu_l-\nu-i\gamma_l}</math><br />
: <math> n_j^0 </math> ⑨での入力になっています。ローレンツ関数の本数<math> l_{max} </math>とそれに対応するパラメータ <math> A_l, \nu_l, \gamma_l </math> 初期値を決定する必要があります。<br />
: <math> No </math>を選んだ場合、パラメータの初期値は<u> [[Theory#Auto Fitting| Automatically determine the initial parameters in fitting procedure]] </u>で説明されているようなアルゴリズムで自動的に決定されます。<br />
: <math> Yes </math>を選んだ場合、<math> l_{max} </math> と それぞれのローレンツ関数に対する<math> A_l, \nu_l, \gamma_l </math>の初期値を自分で設定することが可能です。<math> A_l, \nu_l, \gamma_l </math> の単位は<math>cm^{-1}</math>で<math> l_{max} </math>の最大値は５になっています。<br />
: [[File:11yes.png|500px]]</div>Lwang