Trial functions for the two-particle density functional variational method

The N-particle quantum mechanical system in an external field is considered on the basis of two-particle density functions. The main point of the pres ented work is to reveal the advantages of the two-particle density formalis m as compared to the common one-particle density formalism applied to a sim ple example. The two-particle density formalism permits us to take into acc ount the exact two-particle interaction without additional models. The exch ange and correlation effects can be considered by a proper choice of the tr ial function. By using the presented formalism we calculate the density of the electron gas on different metal surfaces. A simple trial function allow ing for correlations gives us a more correct fit to the experimental data o n the metal dipol barriers than corresponding calculations with the one-par ticle density formalism. It is also shown that a pertubation of the externa l potential can be effectively taken into account by a pertubation calculat ion for the trial function.