ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

This application provides a fast and easy way to augment the information contained with an easily-obtainable spectral data using multiple analyses common in the field of photochemistry. Though each of the analyses utilized by this application is fairly common, this application represents a significant improvement over previous implementations because of its ease of access and use. We recommend the researchers follow the written procedure and use the spectrum included with the program to familiarize themselves with the technique and software implementation.

The visual demonstration of this method is critical as it orients researchers to the software and demonstrates crucial aspects of the Franck-Condon line shape analysis. To begin, import data by pressing the Import Data button and selecting the type of spectrum being imported. Once a spectrum type is chosen, the MATLAB file explorer will appear.

From this window, select the desired file and press Open. In the Info tab under the sample spectrum press the button corresponding to the desired spectrum to load the desired spectra from nine sample spectra. To load and plot more than one spectrum at a time, go to Settings, select General and Figure Settings.

To activate the checkbox, allow multiple data spectrum on axes. To select a different loaded spectrum than the current active spectrum, press the Select Spectrum to Fit button and then choose the desired spectrum from the list in the Select Spectrum panel. Select a peak by pressing the Select Peak for Normalization button found under the Settings in general tab and following the instructions on screen.

Convert the X-Axises units between wavenumber and wavelength by toggling the slider found under Settings in X-Axis to the desired mode of either wavenumber or wavelength. To manually constrain the X-Axis range, select Manually Adjust X-Axis and fit limits tabs under Settings in the X-Axis. Then use the revealed controls to specify the X-Axis range.

The application will automatically expand and contract to the X-Axis range to fit all loaded data points. From the FIT tab found under Settings, select an alternative Calculation Method for the energy quantity. Change the default method from Full FCSLA fit to another method by selecting the corresponding Radial button and following onscreen instructions.

Plot the fit function with its current parameter values by pressing the Plot Fit Function button. Adjust the parameter values to optimize the fit for the loaded data. With the default setting use the single-mode Franck-Condon line shape analysis formula and if desired, toggle between the single and double mode in Settings in Fit.

If initial parameters are found satisfactory, press the blue Optimized Fit button to run the optimization and then replot the fit function with newly optimized parameter values. To switch between the least squares and simplex methods of optimization, toggle to the desired method in Settings and then Optimization. Use the Setting and Optimization tabs to customize the optimization method.

To fix a parameter's value during optimization, press the checkbox in the edit field corresponding to the desired parameter. Reveal the custom bounding options by activating the Allow Custom Parameter Bounding During Optimization checkbox in Settings and Optimization. Then specify custom Bounds for a parameter's value with the controls revealed by pressing the Custom Bounds button under the edit field.

To custom end triggers for optimization, activate the corresponding checkbox under Settings and Optimization and enter the desired value. If the optimized fitted the data and the associated parameter values are satisfactory, proceed to perform calculations with the Calculate button located at the bottom of the calculations pane. To change the unit, select the desired option from the dropdown list box found under Settings and Calculations.

Change the temperature in the experimental temperature tab. Then, by pressing the pop out button next to the Chromaticity Coordinate text box, display the Chromaticity Diagram with plotted coordinates. Using the third calculation check for the predicted color of the sample.

Then change the illuminate with the desired option from the dropdown menu labeled as White Point. To calculate CIE chromaticity coordinates and color values for multiple loaded spectra, activate the corresponding checkbox found under Settings and Calculations. Press the three-dots button to reveal a panel labeled as Select Spectra.

From this panel select the desired spectra and choose to Export Values as a table and display diagram to reveal the chromaticity diagram with plotted and labeled coordinates. If the fit of loaded data is satisfactory press the Export Data button to export both loaded and calculated data. Use the Figure tab to export the displayed plot as a figure.

Export all parameter values with the Parameter Values tab and export data of the currently selected spectrum with spectrum data points. Export the fit as a series of XY data points by selecting Fit Data Points. Select Color Values to export chromaticity, CIE coordinates, and the predicted color and press Chromaticity Diagram to export the chromaticity diagram with the coordinates.

A typical example of a loosely-structured spectrum is shown in this representative data analysis. At room temperature, emission spectrum and FCLSA fit function was achieved through least-squares optimization and by hand adjustment of parameter values. The resulting coefficient of determination was 0.99947.

The highly-structured spectrum of 9, 10-diphenylanthracene at low temperature was achieved through a simplex optimization with the resulting coefficient of determination calculated as 0.9991. It is imperative to keep in mind that perimeter values returned by the optimization routines are determined on a purely mathematical basis and should be checked for physical relevance.