Investigations of the Stokes and anti-Stokes resonance Raman scattering of cytochrome c

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Abstract
We present the first Stokes and anti‐Stokes Raman intensity measurements of a molecular system using laser excitation throughout a resonant electronic transition. Experiments on oxidized and reduced cytochrome c at both room and cryogenic temperatures are reported. We employ a Kramers–Kronig transform method in our analysis and use the absorption and Raman cross sections on an absolute scale in order to find the linear Franck–Condon coupling strengths of the observed low frequency modes. A general expression for the Boltzmann factor is also derived in terms of the resonant Stokes and anti‐Stokes scattering intensities. This expression is appropriate for the determination of temperatures in absorbing media. The traditional Stokes/anti‐Stokes ratio used for this purpose is shown to fail both experimentally and theoretically when the laser excitation is in resonance with an electronic transition of the material under study. Finally, we discuss the frequency domain approximations necessary for application of the transform method at finite temperature and quantitatively treat the dispersion of the coupling strength across the Raman spectrum of cytochrome c. This latter phenomenon leads naturally to the concept of a coupling strength ‘‘spectrum.’’ This spectrum is calculated and subsequently used to estimate a parameter of interest (the Stokes shift, Δ) in recent theories of vibrationaly assisted electron transport.