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A detailed derivation of Gaussian orbital-based matrix elements in electron structure calculations

T Petersson1 and B Hellsing2

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A detailed derivation of analytic solutions is presented for overlap, kinetic, nuclear attraction and electron repulsion integrals involving Cartesian Gaussian-type orbitals. It is demonstrated how s-type orbitals can be used to evaluate integrals with higher angular momentum via the properties of Hermite polynomials and differentiation with respect to non-integration variables.


PACS

01.50.-i Educational aids

31.15.xr Self-consistent-field methods

Subjects

Atomic and molecular physics

Computational physics

Education and communication

Dates

Issue 1 (January 2010)

Received 2 September 2009, in final form 23 September 2009

Published 4 November 2009



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