Determining vibrational solvation-correlation functions from three-pulse infrared photon echoes

Vibrational three-pulse photon echo experiments can probe ultrafast dynamics in condensed phase systems. The central objects of interest are vibrational frequency time-correlation functions, otherwise known as vibrational solvation-correlation functions. Established techniques for determining these correlation functions from experimental data include multiparameter nonlinear fits of the entire echo response, or peak-shift methods. In this paper we propose alternative approaches, closely related to those proposed recently for electronic echoes, involving the short-time slope of the echo intensity or amplitude. We explicitly consider the time-integrated intensity, the heterodyned and half-Fourier transformed amplitude, and the frequency-dispersed intensity. We describe approaches that can separately determine the solvation correlation function for the fundamental transition frequency fluctuations, and the cross-correlation function between the fundamental and excited-state frequency fluctuations. We illustrate the approaches with numerical calculations and also comment on the microscopic origin of frequency fluctuation correlations between different transitions.