  Within the framework of V-T theory of monatomic liquid dynamics, an exact
equation is derived for a general equilibrium time correlation function. The
purely vibrational contribution to such a function expresses the system's
motion in one extended harmonic random valley. This contribution is
analytically tractable and has no adjustable parameters. While this
contribution alone dominates the thermodynamic properties, both vibrations and
transits will make important contributions to time correlation functions. By
way of example, the V-T formulation of time correlation functions is applied to
the dynamic structure factor S(q,w). The vibrational contribution alone is
shown to be in near perfect agreement with low-temperature molecular dynamics
simulations, and a model simulating the transit contribution with three
adjustable parameters achieves equally good agreement with molecular dynamics
results in the liquid regime. The theory indicates that transits will broaden
without shifting the Rayleigh and Brillouin peaks in S(q,w), and this behavior
is confirmed by the MD calculations. We find the vibrational contribution alone
gives the location and much of the width of the liquid-state Brillouin peak. We
also discuss this approach to liquid dynamics compared with potential energy
landscape formalisms and mode coupling theory, drawing attention to the
distinctive features of our approach and to some potential energy landscape
results which support our picture of the liquid state.
