Treatment of electron-electron correlations in electronic structure calculations

Abstract

A methodology is introduced for the systematic treatment of electron-electron correlations in solids and other interacting quantum N-particle systems. The method is developed within the framework of electronic structure theory (band theory) but, in contrast to conventional approaches, 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 dimensions. In this phase space, interparticle interactions appear as external potentials allowing the treatment of the system of particles through the use of single-particle methods, while at the same time allowing a systematic, direct, and nonperturbative treatment of interparticle interactions. The method makes use of the invariance of the Hamiltonian describing an interacting-particle system under partitioning into subsystems of n particles. This treatment leads to exact results in the limit n{r_arrow}N. Based on such partitioning, we propose a generalization of density functional theory and an appropriately defined local density approximation to treat the interactions between the n-particle units in a system of N{ge}n particles. This approach yields n-particle correlated densities and n-particle states which can be used in an analysis of the electronic properties of materials, such asmore » total energy, phase stability, electronic transport, and others. We use the formal construct of multiple-scattering theory to develop the method for the calculation of the two-particle electronic structure 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 method and further possible applications are presented in a discussion section. {copyright} {ital 1997} {ital The American Physical Society}« less