Energy and energy gradient matrix elements with N -particle explicitly correlated complex Gaussian basis functions with L=1

Sergiy Bubin, Ludwik Adamowicz

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N -particle system with the L=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

Original languageEnglish
Article number114107
JournalJournal of Chemical Physics
Volume128
Issue number11
DOIs
Publication statusPublished - 2008
Externally publishedYes

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gradients
matrices
Potential energy
Kinetic energy
kinetic energy
potential energy
differential calculus
energy
Differentiation (calculus)
positronium
Beryllium
beryllium
Angular momentum
Wave functions
parity
Coulomb interactions
derivation
angular momentum
wave functions
formalism

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Energy and energy gradient matrix elements with N -particle explicitly correlated complex Gaussian basis functions with L=1. / Bubin, Sergiy; Adamowicz, Ludwik.

In: Journal of Chemical Physics, Vol. 128, No. 11, 114107, 2008.

Research output: Contribution to journalArticle

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