Explicit correlation factors

Cole M. Johnson; So Hirata; Seiichiro Ten-no

doi:10.1016/j.cplett.2017.02.072

Explicit correlation factors

Cole M. Johnson, So Hirata, Seiichiro Ten-no

Research output: Contribution to journal › Article

Abstract

We analyze the performance of 17 different correlation factors in explicitly correlated second-order many-body perturbation calculations for correlation energies. Highly performing correlation factors are found to have near-universal shape and size in the short range of electron-electron distance (0<r₁₂<1.5 a.u.). The long-range behavior (r₁₂>1.5 a.u.) is insignificant insofar as the factor becomes near constant, leaving an orbital expansion to describe decoupled electrons. An analysis based on a low-rank Taylor expansion of the correlation factor seems limited, except that a negative second derivative with the value of around −1.3 a.u. correlates with high performance.

Original language	English (US)
Pages (from-to)	247-252
Number of pages	6
Journal	Chemical Physics Letters
Volume	683
DOIs	https://doi.org/10.1016/j.cplett.2017.02.072
State	Published - Sep 1 2017

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Keywords

Basis set
Correlation energy
Correlation hole
Cusp condition

ASJC Scopus subject areas

Physics and Astronomy(all)
Physical and Theoretical Chemistry

Cite this

Johnson, C. M., Hirata, S., & Ten-no, S. (2017). Explicit correlation factors. Chemical Physics Letters, 683, 247-252. https://doi.org/10.1016/j.cplett.2017.02.072

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abstract = "We analyze the performance of 17 different correlation factors in explicitly correlated second-order many-body perturbation calculations for correlation energies. Highly performing correlation factors are found to have near-universal shape and size in the short range of electron-electron distance (012<1.5 a.u.). The long-range behavior (r12>1.5 a.u.) is insignificant insofar as the factor becomes near constant, leaving an orbital expansion to describe decoupled electrons. An analysis based on a low-rank Taylor expansion of the correlation factor seems limited, except that a negative second derivative with the value of around −1.3 a.u. correlates with high performance.",

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AB - We analyze the performance of 17 different correlation factors in explicitly correlated second-order many-body perturbation calculations for correlation energies. Highly performing correlation factors are found to have near-universal shape and size in the short range of electron-electron distance (012<1.5 a.u.). The long-range behavior (r12>1.5 a.u.) is insignificant insofar as the factor becomes near constant, leaving an orbital expansion to describe decoupled electrons. An analysis based on a low-rank Taylor expansion of the correlation factor seems limited, except that a negative second derivative with the value of around −1.3 a.u. correlates with high performance.

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KW - Cusp condition

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10.1016/j.cplett.2017.02.072