Electron transfer and protein transfer reactions in salvation and protein environments

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We employ various statistical mechanical models, such as a quantum Brownian oscillator system with nonlinear system-bath interactions and a quantum dissipative rotator to study dynamics of molecules in condensed phases and we demonstrate how the differences of models reveal on two-dimensional spectroscopy as profiles of signals. Calculations of multi-time correlation functions of molecular coordinate, which are the observables of two-dimensional spectroscopy, are based on newly developed path-integral and quantum Fokker-Planck formalisms. For nonlinear system-bath coupling model, we calculate the three and four-time correlation functions, which corresponds to fifth-order Raman and infrared photon echo measurements, by solving Gaussian-Markovian Fokker-Planck equation and show an interesting change of signal profiles corresponding to the homogeneous and inhomogeneous distribution of system oscillators which are set by a noise correlation time. For damped rotator case, we obtained analytical solution of multi-time correlation functions by using analytical expression of generating functional and show that quantum effects play a minor role in two-time correlation functions, but play a major role In four-time correlation functions.Our results in three years (1998-2001) are published as nine scientific papers of JCP and CPL, etc.