# How to calculate spectral overlap integral using spreadsheets?

I need to calculate the spectral overlap integral for the emission spectrum of coumarin 334 and the absorption spectrum for rhodamine, using spreadsheets (MS Excel).

Following the theory of Fluorescence Resonance Energy Transfer (Förster), I have the definition of the spectral overlap integral:

$$J(\lambda) = \frac{\int_{0}^{\infty}f_\ce{D}(\lambda) \epsilon_\ce{A}(\lambda) \lambda^4\,\mathrm{d}\lambda}{\int_{0}^{\infty}f_\ce{D}(\lambda) \,\mathrm{d}\lambda}$$

I also have the data for emission spectrum of the donor (coumarin 334) and the absorption spectrum of the acceptor (rhodamine). However, I am not sure how to proceed and actually extract the spectral overlap. Since the spectral overlap is a function of wavelength, will I end up with a "spectral overlap spectrum"? And how do I get the absorption coefficient of rhodamine? I have been given the maximum absorption coefficient (at wavelength of maximum absorption), but how do I get the molar absorption spectrum, $$\epsilon_\ce{A}(\lambda)$$?

Should I calculate values at a "per-wavelength" basis, or should I fit functions and integrate those?

• This question would be better asked on Stack Overflow as a question about how to do numerical integration in Excel. I think it would attract better answers. If you are confused about the symbols and nomenclature being used in the Forster equation, then you could revise your question to be about that. – Curt F. Jan 28 '16 at 20:07
• This isn't a pure spreadsheet inquiry. // In general you'd need to do the calculations on a "per-wavelength" basis. Trying to find a function to fit the spectra would be very messy. // You'd need to have both spectra at the same concentration. Not sure how to manipulate spectra (or if they can be) since you haven't provided concentration information. – MaxW Jan 28 '16 at 21:30
• So I ended up normalizing the emission spectrum to 1, and converting wavelength to cm. Because of the linear relationship between absorbance and the molar absorption coefficient, I used the maximum coefficient to find all other coefficients. Then I multiplied, at each wavelength, the normalized emission intensity, the absorption coefficient, and the wavelength^4, and summed all values. I ended up with a very small number, ~2.5E-12, which seems much smaller than I expected. – Yoda Jan 29 '16 at 6:45
• @Yoda the form of this equation doesn't make sense to me. J can't be a function of $\lambda$ if all of the $\lambda$ dependence is integrated out on the right hand side. – Tyberius Apr 25 '19 at 19:01