Improved Feynman propagators on a grid and non-adiabatic corrections within the path integral framework

The idea of using a good representation as the zeroth order description of a problem, which is widely used in perturbation theory and in basis set calculations, is extended to the path integral formulation of quantum mechanics by constructing improved Feynman propagators. The best zeroth order propagators cannot be expressed in closed form in general, and are therefore constructed numerically and stored on one-dimensional grids. Use of improved propagators in discretized path integral calculations involves a trivial modification of Monte Carlo techniques and leads to convergence with fewer time slices. Application of a quasi-adiabatic propagator to a system coupled to a harmonic bath leads to a low-dimensional path integral with a non-local influence functional which incorporates the non-adiabatic corrections to the Born-Oppenheimer approximation and which (with parameters typical of chemical processes) can be evaluated by quadrature, providing an accurate method for investigating the real time quantum dynamics of system-bath Hamiltonians.