Time-correlation functions and spectral densities from modified moments

Modified moments provide coefficients in expansions for time-autocorrelation functions (TAF's) and for their spectral densities. The expansions for TAF's are very generally convergent; the expansions for their spectral densities converge when these densities satisfy sufficient continuity or smoothness conditions. Whenever a partial sum to the density is non-negative, the corresponding partial sum to the TAF necessarily lies between the rigorous bounds recently obtained by Platz and Gordon. The accuracy of these expansions is illustrated by an application to the harmonic solid model considered by Platz and Gordon. The expansion for the TAF is consistently one or two orders of magnitude more accurate than the bounds obtained from the same number of moments and accurately represents the TAF to substantially longer times than do the bounds.