Inclusion of frequency shifts in the treatment of N-photon vibronic processes involving uncoupled harmonic surfaces: A simple and exact prescription
Rob D. Coalson · The Journal of Chemical Physics · 1984
An exact prescription is given for averaging an n propagator string involving single mode harmonic oscillator Hamiltonians Ĥ1,Ĥ2,...,Ĥn over a Boltzmann distribution of the eigenstates of Ĥ1. Such averages govern finite temperature multiphoton vibronic spectra, and we calculate the averages relevant to (one photon) electronic absorption and (two photon) Raman scattering in the case where only two electronic surfaces are involved. Our solution is compact and computationally mechanizable. It is valid for arbitrary upper and lower surface frequencies ωu,ω1, and in the ωu=ω1 (‘‘displaced oscillator’’) limit agrees with previous solutions of this special case. An extension to systems moving according to arbitrary quadratic potentials is sketched. A sum rule connecting electronic absorption and Raman spectra of finite temperature samples is given.