Extended adiabatic formalism for computing thermodynamic properties of a quantum system coupled to a nonadiabatic bosonic bath

The solution procedure for computing properties of a quantum system coupled to an environment of harmonic oscillators in the adiabatic (low oscillator frequency) limit is extended into a general formalism capable of treating nonadiabatic effects. Starting from a path integral representation of the quantum propagator, the standard sum over intermediate configurations of the system (which is represented via a discrete set of base states) is replaced by integrations over continuous Gaussian auxiliary variables. In the adiabatic limit only one auxiliary variable is needed; more variables are required as the nonadiabaticity of the oscillator bath increases. We demonstrate numerically that large nonadiabatic effects can be computed with relatively few auxiliary variables. In particular solvation energies and localization probabilities calculated via our Extended Adiabatic prescription for a strongly nonadiabatic (multimode) ‘‘ohmic’’ bath are compared to results obtained via the effective adiabatic approximation method of Carmeli and Chandler [J. Chem. Phys. 82, 3400 (1985)]. Complete agreement is found. Advantages of the extended adiabatic method for more complicated applications are discussed.