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Cholesky decomposition within local multireference singles and doubles configuration interaction
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10.1063/1.3315419
/content/aip/journal/jcp/132/7/10.1063/1.3315419
http://aip.metastore.ingenta.com/content/aip/journal/jcp/132/7/10.1063/1.3315419

Figures

Image of FIG. 1.
FIG. 1.

CPU time (minutes) for constructing components of the vector that utilize three different representative integral classes, in local SDCI (open symbols) compared to nonlocal (conventional) SDCI (filled symbols). {, , , and } and {, , , and } refer to internal (occupied) and external (virtual) orbitals, respectively. The test cases here are linear alkanes, , within a basis set.

Image of FIG. 2.
FIG. 2.

Total number and maximum rank of Cholesky vectors for using a basis set. The CD threshold was set to 1.0d-7 while the screening threshold for the diagonal elements was set to 1.0d-9.

Image of FIG. 3.
FIG. 3.

Total CPU time for CD of the AO two-electron integrals and transformation of the Cholesky vectors to an MO basis for linear alkanes within a basis set.

Image of FIG. 4.
FIG. 4.

CPU time for assembling two-electron integrals in the MO basis from transformed Cholesky vectors and subsequent construction of the vector, for linear alkanes within a basis set.

Image of FIG. 5.
FIG. 5.

Total CPU time (seconds) for our previous nonorthogonal PAO-based linear scaling LSDCI and the current implementation of LSDCI using Cholesky vectors, a CSF-driven scheme for the integrals, along with localized orthogonal virtual orbitals. The test set again is linear alkanes within a basis set.

Tables

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Table I.

Savings in storage of data elements in the ERI matrix when using a Cholesky vector representation for the two-electron integrals within a basis set. a denotes the total number of data elements in the Cholesky-decomposed integral matrix using a CD threshold of 1.0d-7. b denotes the total number of unique two-electron integrals–approximated as , where N is defined as and bf refers to the number of contracted Gaussian basis functions. c denotes the percentage of stored data elements in (a) with respect to unique two-electron integrals.

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Table II.

Total energies (hartrees) for at different CD thresholds using a basis set.

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Table III.

Total energies (hartrees) for linear alkanes using a basis set.

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Table IV.

Total energies (hartrees) for hex-3-ene, hex-3-yne, cytosine, 1,1,1-trifluorobutane, phenol, and trans-6-dodecene using a basis set.

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/content/aip/journal/jcp/132/7/10.1063/1.3315419
2010-02-16
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Cholesky decomposition within local multireference singles and doubles configuration interaction
http://aip.metastore.ingenta.com/content/aip/journal/jcp/132/7/10.1063/1.3315419
10.1063/1.3315419
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