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

Sergiy Bubin, Ludwik Adamowicz

Research output: Contribution to journalArticle

29 Scopus citations

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 (US)
Article number224317
JournalJournal of Chemical Physics
Volume124
Issue number22
DOIs
StatePublished - Jun 14 2006
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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