Correlations in the Motion of Atoms in Liquid Argon

A system of 864 particles interacting with a Lennard-Jones potential and obeying classical equations of motion has been studied on a digital computer (CDC 3600) to simulate molecular dynamics in liquid argon at 94.4\ifmmode^\circ\else\textdegree\fi{}K and a density of 1.374 g ${\mathrm{cm}}^{\ensuremath{-}3}$. The pair-correlation function and the constant of self-diffusion are found to agree well with experiment; the latter is 15% lower than the experimental value. The spectrum of the velocity autocorrelation function shows a broad maximum in the frequency region $\ensuremath{\omega}=0.25(\frac{{k}_{B}T}{\ensuremath{\hbar}})$. The shape of the Van Hove function ${G}_{s}(r, t)$ attains a maximum departure from a Gaussian at about $t=3.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ sec and becomes a Gaussian again at about ${10}^{\ensuremath{-}11}$ sec. The Van Hove function ${G}_{d}(r, t)$ has been compared with the convolution approximation of Vineyard, showing that this approximation gives a too rapid decay of ${G}_{d}(r, t)$ with time. A delayed-convolution approximation has been suggested which gives a better fit with ${G}_{d}(r, t)$; this delayed convolution makes ${G}_{d}(r, t)$ decay as ${t}^{4}$ at short times and as $t$ at long times.