A Model of Vibrational Relaxation and Dephasing

It has been found that the short-range interaction model can be applied to study the vibrational relaxation of molecules in condensed phases. This model is applied to treat vibrational relaxation and pure dephasing in condensed phases. For this purpose, the secular approximation is employed to Eq. (129). This assumption allows one to focus on several important system-heat bath induced processes such as the vibrational population transition processes, the vibrational coherence transfer processes, and the vibronic processes. 

Employing V — b)F bQ exp(— J2j xj9j) b as the system-heat bath interaction, where qj denotes the vibrational coordinate of theyth heat bath mode, the vibrational population decay rate constant is obtained as 

y 0 represents the vibrational relaxation rate constant for the transition v — 1 - v — 0 and is given by 

With the same interaction model used in Eq. (130), the vibrational relaxation rate constants associated with the vibrational population transitions bv + 1 -+bv and bv bv— 1 are given by 

The rate constants of the vibrational coherence dynamics such as vibrational coherence transfer can be derived by using the same interaction model used in Eq. (130). For example, the rate constants of the vibrational coherence transfer processes from bv + 1 - bv + 1 to bv -+bi/ and from bv —l 1 to bv - bv are, respectively, given by 

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