Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

Sergiy Bubin, Ludwik Adamowicz

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

Original languageEnglish
Article number224317
JournalJournal of Chemical Physics
Volume124
Issue number22
DOIs
Publication statusPublished - Jun 14 2006
Externally publishedYes

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Hamiltonians
matrices
gradients
Differentiation (calculus)
Born approximation
differential calculus
Excited states
Born-Oppenheimer approximation
Ground state
Derivatives
Atoms
formalism
optimization
ground state
energy
excitation
atoms

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters. / Bubin, Sergiy; Adamowicz, Ludwik.

In: Journal of Chemical Physics, Vol. 124, No. 22, 224317, 14.06.2006.

Research output: Contribution to journalArticle

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