Interaction-site representation of the Smoluchowski–Vlasov equation: The space–time correlation functions in a molecular liquid

A site–site representation of the Smoluchowski–Vlasov equation is proposed based on the generalized Langevin equation, and on the site–site Ornstein–Zernike equation for the molecular liquid. The method is applied for calculating the space–time pair correlation function proposed by van Hove. The results are compared with a molecular dynamics simulation of water. The site–site Smoluchowski–Vlasov equation predicts most of the essential features of the van Hove function for water.