TREATMENT OF ELECTRON-ELECTRON CORRELATIONS IN ELECTRONIC-STRUCTURE CALCULATIONS

A methodology is introduced for the systematic treatment of electron-e lectron correlations in solids and other interacting quantum N-particl e systems. The method is developed within the framework of electronic structure theory (band theory) but, in contrast to conventional approa ches, which are based on the single-particle picture, it is formulated within a many-particle picture in which n particles in d-dimensional phase space are treated as a single particle in a phase space of nd di mensions. In this phase space, interparticle interactions appear as ex ternal potentials allowing the treatment of the system of particles th rough the use of single-particle methods,while at the same time allowi ng a systematic, direct, and nonperturbative treatment of interparticl e interactions. The method makes use of the invariance of the Hamilton ian describing gn interacting-particle system under partitioning into subsystems of n particles. This treatment leads to exact results in th e limit n --> N. Based on such partitioning, we propose a generalizati on of density functional theory and an appropriately defined local den sity approximation to treat the interactions between the n-particle un its in a system of N greater than or equal to n particles. This approa ch yields n-particle correlated densities and n-particle states which can be used in an analysis of the electronic properties of materials, such as total energy, phase stability, electronic transport, and other s. We use the formal construct of multiple-scattering theory to develo p the method for the calculation of the two-particle electronic struct ure of a solid and the corresponding total energy of the ground state. We also illustrate some of the properties of the method in terms of a Hubbard model Hamiltonian on a linear ring. Various features of the m ethod and further possible applications are presented in a discussion section.