Calculation of the two-dimensional vibrational response function

We present a complete analytical expression of the two-dimensional (2D) vib rational response function without invoking the factorization approximation s based on the Wick's theorem that have been used in most previously report ed theories. Since the harmonic approximation to the vibrational degrees of freedom is not required in this new formulation, the vibrational-level dep endencies of the transition frequencies and the vibrational relaxation rate s are fully incorporated in the obtained formula for the 2D vibrational res ponse function. Furthermore, the non-Markovian nature of the vibrational de phasing process in condensed phases is also fully taken into account by car rying out the resummation of the associated diagrams with the linked diagra m theory. It is found that there exists an additional contribution to the 2 D vibrational response function, which was completely ignored due to the ap proximations based on the Wick's theorem. (C) 2000 American Institute of Ph ysics. [S0021-9606(00)51641-9].