Basis set methods for describing the quantum mechanics of a "system" interacting with a harmonic bath

The case of a system (e.g., a one-dimensional reaction coordinate) coupled to a "bath" of many harmonic oscillators is treated by quantum mechanical basis set methods. By choosing the basis set for the bath to incorporate the coupling explicitly, it is shown how the bath can then be eliminated to obtain an effective Hamiltonian matrix for only the system. Numerical calculations are carried out which show that, even in the zeroth version of the approach, the effect on the system (e.g., the tunneling splitting in a double-well potential) of coupling to the bath is described well, even when the effect is extremely large.