Two-dimensional correlation spectroscopies of localized vibrations

One- and two-dimensional vibrational response functions which may be used in the simulations of molecular fifth-order Raman and second-order infrared techniques are calculated for a set of interacting localized anharmonic vibrations. Employing a vibrational Frenkel exciton model we have accounted for exciton-exciton scattering due to quartic anharmonicities as well as for the creation and annihilation of one vibrational quanta by cubic anharmonicities. Closed expressions for the optical response are given in terms of the one- and two-exciton Green functions, the exciton scattering matrix and the exciton population Green function.