I am working on a Luminescent Solar Concentrators (LSC) using dyes such as Coumarin 1, Coumarin 153, and Perylene Green Ph-probe 720-5.5. I need to calculate the Mean-free-path (MFP) for the above-mentioned dyes. For the calculation of MFP, I need the optical cross-section value which indeed requires the values of Absorption co-efficient or Absorbance for a range wavelength.
I am aware that these values (Absorption co-efficient, Absorbance, Optical cross-section) are determined through the experimental procedure. Since I cannot carry out the experiment, I am trying to determine one of these values (Absorption co-efficient, Absorbance, Optical cross-section ) theoretically. Is there any method to calculate them?
Thank you.
It is possible to calculate oscillator strength (f) using a variety of computational methods, which can then be converted to an absorption extinction coefficient if one assumes that the absorption band is of a uniform shape. Oscillator strength f relates to the area under an absorption curve, so calculating an extinction coefficient from a value of f depends on the width of the band and its shape. Calculations relating to electronic transitions, such as predicting f, in organic molecules require specialist software and a capable computer; some of the higher end calculations require supercomputing time. However, even if one obtains oscillator strength figures, the vibronic transitions of a dye often mean that absorption bands are not a perfect Gaussian shape and also may overlap with other band(s), which interferes with such a conversion of f to extinction coefficient. In addition, the assumptions in modern computational methods mean that predicted oscillator strength values f can be unreliable. Other factors can influence real-world absorption data that is difficult to accurately model computationally, e.g. environmental effects. It is usually the case that computational methods can give a rough idea of relative intensity in absorption between different general chromophoric types. However, comparisons between experimental and calculated data for similar derivatives may not hold up well. (Please see attached paper for details.) However, I am not sure whether you've searched for experimentally determined extinction coefficients for Coumarin 1 and 153: these might be available in the literature as they are well known compounds.
Please look at the following below links which may help you in your analysis:
http://www1.lasalle.edu/~prushan/Particle%20in%20a%20box.pdf
https://www.lakeheadu.ca/sites/default/files/uploads/31/CHEM_3451_lab_manual_F2013_UV-Vis.pdf
https://aslopubs.onlinelibrary.wiley.com/doi/pdf/10.4319/lo.2002.47.4.1261
Thanks
In addition to the anwser of Andy Towns , you also have to take into account that absorption cross sections and absorption coefficients are actually no specific quantities. They are influenced e.g. by the solvent and the concentration. The Beer-Lambert law on which these quantities are based is nothing more than an ideal absorption law with strong limitations very much like the ideal gas law. See e.g. Article The Bouguer-Beer-Lambert Law: Shining Light on the Obscure
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