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

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 H...

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Bibliographic Details
Published inEuropean journal of physics Vol. 31; no. 1; pp. 37 - 46
Main Authors Petersson, T, Hellsing, B
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.01.2010
Institute of Physics Publishing
Institute of Physics
Subjects
Beräkningsfysik
Calculus
Chemistry
Communication, education, history, and philosophy
Computation
Computational physics
Condensed Matter Physics
Den kondenserade materiens fysik
electron structure
Exact sciences and technology
Fysik
Gaussian orbitals
General physics
Kemi
Kvantkemi
matrix elements
Mechanics (Physics)
Molecular Structure
NATURAL SCIENCES
NATURVETENSKAP
Other physics
Physics
Physics literature and publications
Quantum chemistry
Surveys and tutorial papers, resource letters
Teoretisk kemi
Theoretical chemistry
Övrig fysik
Repulsion integral
Higher education
Angular momentum
Hermite polynomials
Orbital elements
Matrix elements
Analytical solution
Physics
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0143-0807
1361-6404
1361-6404
DOI:10.1088/0143-0807/31/1/004