Mixed quantum-classical statistical mechanics is employed to calculate dipole moment correlation function and linear absorption spectra.A quantum two-level subsystem interacting with quantum vibrations (primary oscillators) which in turn are coupled to a classical bath composed of infinite set of harmonic oscillators is used as a dissipative system.Starting with mixed quantum-classical Liouville equation for the evaluation of the mixed quantum-classical dipole moment correlation function and using coherent states and the inverse of Baker-Campbell-Hausdorf formula to evaluate the trace over the primary oscillators,whereby,a closed analytical expression for the electronic dipole moment correlation function is obtained.Illustrations of several absorption spectra at different temperatures are provided.An approximate optical four-point correlation is obtained in the high temperature limit.A strategy for deriving an exact optical four-point correlation is suggested.
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