Efficient spectra from atomistic simulation: a generalized master equation study of the air-water interface

Computing condensed phase spectra from atomistic simulations requires calculating correlation functions from molecular dynamics and can be very expensive. A totally general, data-driven method to reduce cost is to employ an exact rewriting to a generalized master equation characterized by a memory kernel. The decay time of the kernel can be less than the original function, reducing the amount of data required. In this paper we construct the minimal projection operator to predict vibrational sum-frequency generation spectra and apply it to the air-water interface simulated using ab initio molecular dynamics. We are able to obtain a modest reduction in cost of just under 50\%. We explore various avenues to use more of the available data to expand the projector in an attempt to reduce the cost further. Interestingly, we are not able to effect any change by including quadrupoles, inter-molecular couplings, or a depth-dependence. How to strategically go about maximally reducing cost using projection operators remains an open question.