Optimized perturbation approach with a Legendre transformation to a dissipative system: Correlation functions of a Morse oscillator

We apply the optimized perturbation theory (OPT) to study the dynamics of a dimer molecule system in condensed phases described by a Morse potential s ystem coupled to a heat bath. The OPT combines the techniques based on the variational principle and the perturbative expansion. The first-order appro ximation of the OPT agrees with Feynman's variational theory developed for the polaron problem [Statistical Mechanics: A Set of Lectures (Benjamin, Lo ndon, 1972)]. The OPT makes it possible to deal with an anharmonic potentia l system in a nonperturbative way. Combined with the inversion method, whic h is a technique to carry out the Legendre transformation, we take into acc ount the ansymmetry of the potential effectively. We then calculate the abs orption spectrum of the molecule system, which relates to a two-time correl ation function of a nuclear coordinate.