Factorization of the wave-function coefficients in configuration-interaction expansions

Abstract

A factorization of the wave-function coefficients obtained from configuration-interaction expansions is presented. For this purpose, the system orbitals are partitioned into a set of overlapping domains and a factor is associated with a given electron distribution in each domain. The configuration-interaction coefficient of each Slater determinant is given by the product of all the domain factors that are associated with this determinant. This expansion is asymptotically exact, which means that the exact wave function is recovered in the limit of large domains. Moreover, the number of factors needed to define a wave function has a slow growth as a function of the system size. The idea is illustrated through applications to two model systems, i.e. a collection of non-interacting electron pairs and a Néel-type wave function. A possible strategy for the calculation of the configuration factors is also briefly discussed.