Characteristic times in the nanometer-picosecond translational collective dynamics of molecular liquids.

Molecular-dynamics calculations of the translational dynamic structure factor in liquid CO2 and CD4 are analyzed by means of the generalized Langevin equation for the intermediate scattering function in the second-order memory function approximation. We give a rigorous general relation among the decay times of the memory and the lifetimes of the modes of the density-density correlation function. The comparison of the various characteristic times among them and with the collision time, carried out as a function of the wave vector, reveals strong relationships between the memory relaxation and the density-density correlation modes, some of which have purely "collisional" and other "collective" character. We show that essential information about the life time of structural properties in a molecular liquid at nanometer dimensions can be obtained if the time behavior of the correlation function is considered in addition to that of the memory function.