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A general formulation for the efficient evaluation of n-electron integrals over products of Gaussian charge distributions with Gaussian geminal functions
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10.1063/1.3600745
/content/aip/journal/jcp/134/24/10.1063/1.3600745
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/24/10.1063/1.3600745

Figures

Image of FIG. 1.
FIG. 1.

A diagrammatic representation of an overlap integral between two charge distributions, coupled by a Gaussian geminal factor, σ. Charge distributions are represented by circles, geminal coupling by a solid line.

Image of FIG. 2.
FIG. 2.

A diagrammatic representation of a three-electron overlap integral, where charge distributions are coupled by two Gaussian geminal factors, σ and ρ. Charge distributions are represented by circles, geminal couplings by solid lines.

Image of FIG. 3.
FIG. 3.

A diagrammatic representation of a two-electron repulsion integral, where charge distributions are coupled by a Gaussian geminal factor, σ. Charge distributions are represented by circles, the geminal coupling by a solid lines and the Coulombic repulsion by a dotted line.

Image of FIG. 4.
FIG. 4.

A diagrammatic representation of the most general three-electron repulsion integral. Charge distributions are represented by circles, the geminal couplings by a solid lines, and the Coulombic repulsion by a dotted line.

Image of FIG. 5.
FIG. 5.

A diagrammatic representation of the four-electron repulsion integral. Charge distributions are represented by circles, the geminal couplings by a solid lines, and the Coulombic repulsion by a dotted line.

Image of FIG. 6.
FIG. 6.

A diagrammatic representation of the four-electron repulsion integral. Charge distributions are represented by circles, the geminal couplings by a solid lines, and the Coulombic repulsion by a dotted line.

Image of FIG. 7.
FIG. 7.

A diagrammatic representation of the four-electron repulsion integral. Charge distributions are represented by circles, the geminal couplings by a solid lines, and the Coulombic repulsion by a dotted line.

Image of FIG. 8.
FIG. 8.

A diagrammatic representation of a three-electron repulsion integral with one geminal coupling, which reduces to the two-electron nuclear attraction integral with μ = 1 in the γ → ∞ limit.

Tables

Generic image for table
Table I.

Charge distribution function parameters.

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Table II.

Various quantities that arise in the analysis of electron repulsion integrals, and whether they are or are not invariant with respect to changing electron labels in the Coulomb operator.

Generic image for table
Table III.

matrix elements for the three-electron integral in Eq. (93) .

Generic image for table
Table IV.

Reduced variables for four–particle matrices.

Generic image for table
Table V.

Elements of four–particle and ° matrices.

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/content/aip/journal/jcp/134/24/10.1063/1.3600745
2011-06-29
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A general formulation for the efficient evaluation of n-electron integrals over products of Gaussian charge distributions with Gaussian geminal functions
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/24/10.1063/1.3600745
10.1063/1.3600745
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