Electron density and density matrix approximations using potential energy error bounds

Publisher Website
Google Scholar
Abstract
The possibility of simplifying expansions of the total electron density, ρ (1), and the first order density matrix, γ (1,1′), derived from a given total wavefunction is considered based on the minimization of positive definite error bound integrals, ε=〈ρ (1)−ρ′ (1) ‖ν12‖ρ (2)−ρ′ (2) 〉 and εγ=〈γ (1,2)−γ′ (1,2) ‖ν12‖γ (1,2) −γ′ (1,2) 〉. Expansions, ρ′ and γ′, are in terms of a subset of the full basis and are designed for iterative use in energy variational calculations. In all of a variety of cases investigated, simple one-center expansions are found to be very accurate for the ρ expansion which determines the total coulombic energy of the system. However, correspondingly simple, one-center γ (1,2), expansions produce significant errors in the exchange, self-energy when the electron distribution is highly delocalized requiring that important two-center distributions be included for accurate calculations. Applications to localized electron distributions and to problems in which a lower level of accuracy is acceptable are discussed.