Using molecular dynamics simulation and the self-consistent renormalization scheme for liquid-state vibrational spectroscopy developed earlier by us, we have calculated the infrared integrated three-pulse photon echo signal (and in particular, the peak shift) for the OH stretch of dilute HOD in D2O at 300 K. Our results are in reasonable agreement with preliminary experimental results of Tokmakoff and co-workers. We show that the second-cumulant approximation to the integrated three-pulse echo intensity works well when t(1) (the delay time between the first two pulses) is less than 100 fs, even though the frequency fluctuations are not Gaussian. We discuss the reason for, and generality of, this result, and the physical origin of the non-Gaussian fluctuations. Our results indicate that the standard approaches (peak shift, initial slope, and direct determination by nonlinear fitting) for determining the frequency time-correlation function from integrated three-pulse echo data, all of which implicitly assume the validity of this approximation, are useful and adequate. (C) 2003 American Institute of Physics.