A Born–Oppenheimer approximation for path integrals with an application to electron solvation in polarizable fluids

The Born–Oppenheimer approximation is introduced into the path integral expression for the canonical partition function. It is difficult to apply this to simulations. We devise a new adiabatic expression which we call the free energy Born–Oppenheimer approximation which is much easier to simulate. It is shown that this approximation deviates from the exact path-integral expression by no more than does the standard Born–Oppenheimer approximation and we apply it to the problem of an excess electron dissolved in a polarizable fluid.