Vibrational energy relaxation (VER) of a CD stretching mode in cytochrome c

We first review how to determine the rate of vibrational energy relaxation (VER) using perturbation theory. We then apply those theoretical results to the problem of VER of a CD stretching mode in the protein cytochrome c. We model cytochrome c in vacuum as a normal mode system with the lowest-order anharmonic coupling elements. We find that, for the “lifetime” width parameter γ = 3 ∼ 30 cm, the VER time is 0.2 ∼ 0.3 ps, which agrees rather well with the previous classical calculation using the quantum correction factor method, and is consistent with spectroscopic experiments by Romesberg’s group. We decompose the VER rate into separate contributions from two modes, and find that the most significant contribution, which depends on the “lifetime” width parameter, comes from those modes most resonant with the CD vibrational mode.