Inclusion of nuclear quantum effects for simulations of nonlinear spectroscopy

The computation and interpretation of nonlinear vibrational spectroscopy is of vital importance for understanding a wide range of dynamical processes in molecular systems. Here, we introduce an approach to evaluate multi-time response functions in terms of multi-time double symmetrized Kubo transformed thermal correlation functions. Furthermore, we introduce a multi-time extension of ring polymer molecular dynamics to evaluate these Kubo transforms. Benchmark calculations show that the approximations are useful for short times even for nonlinear operators, providing a consistent improvement over classical simulations of multi-time correlation functions. The introduced methodology thus provides a practical way of including nuclear quantum effects in multi-time response functions of non-linear optical spectroscopy.