Resolutions of the Coulomb operator: II. The Laguerre generator

Peter M.W. Gill; Andrew T.B. Gilbert

doi:10.1016/j.chemphys.2008.10.047

Resolutions of the Coulomb operator: II. The Laguerre generator

Peter M.W. Gill^*, Andrew T.B. Gilbert

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

34 Citations (Scopus)

Abstract

We discuss a resolution of the Coulomb operator, r₁₂^{- 1} = | φ{symbol}_i 〉〈 φ{symbol}_i |, into a one-particle basis. We show that the Laguerre polynomials generate a resolution with attractive computational properties and we apply it to the calculation of Coulomb and exchange energies in hydrogenic ions, the H₂ molecule, and the Be atom. Rapid convergence is observed in all cases and a theoretical reason for this is discussed.

Original language	English
Pages (from-to)	86-90
Number of pages	5
Journal	Chemical Physics
Volume	356
Issue number	1-3
DOIs	https://doi.org/10.1016/j.chemphys.2008.10.047
Publication status	Published - 17 Feb 2009

Access to Document

10.1016/j.chemphys.2008.10.047

Cite this

@article{3e3139082eed46d7b64e38109a15d3e9,

title = "Resolutions of the Coulomb operator: II. The Laguerre generator",

abstract = "We discuss a resolution of the Coulomb operator, r12- 1 = | φ\{symbol\}i 〉〈 φ\{symbol\}i |, into a one-particle basis. We show that the Laguerre polynomials generate a resolution with attractive computational properties and we apply it to the calculation of Coulomb and exchange energies in hydrogenic ions, the H2 molecule, and the Be atom. Rapid convergence is observed in all cases and a theoretical reason for this is discussed.",

keywords = "Auxiliary basis sets, Cholesky decomposition, Coulomb operator, Density fitting, Kronecker product approximation, Resolution of the identity",

author = "Gill, \{Peter M.W.\} and Gilbert, \{Andrew T.B.\}",

year = "2009",

month = feb,

day = "17",

doi = "10.1016/j.chemphys.2008.10.047",

language = "English",

volume = "356",

pages = "86--90",

journal = "Chemical Physics",

issn = "0301-0104",

publisher = "Elsevier B.V.",

number = "1-3",

}

TY - JOUR

T1 - Resolutions of the Coulomb operator

T2 - II. The Laguerre generator

AU - Gill, Peter M.W.

AU - Gilbert, Andrew T.B.

PY - 2009/2/17

Y1 - 2009/2/17

N2 - We discuss a resolution of the Coulomb operator, r12- 1 = | φ{symbol}i 〉〈 φ{symbol}i |, into a one-particle basis. We show that the Laguerre polynomials generate a resolution with attractive computational properties and we apply it to the calculation of Coulomb and exchange energies in hydrogenic ions, the H2 molecule, and the Be atom. Rapid convergence is observed in all cases and a theoretical reason for this is discussed.

AB - We discuss a resolution of the Coulomb operator, r12- 1 = | φ{symbol}i 〉〈 φ{symbol}i |, into a one-particle basis. We show that the Laguerre polynomials generate a resolution with attractive computational properties and we apply it to the calculation of Coulomb and exchange energies in hydrogenic ions, the H2 molecule, and the Be atom. Rapid convergence is observed in all cases and a theoretical reason for this is discussed.

KW - Auxiliary basis sets

KW - Cholesky decomposition

KW - Coulomb operator

KW - Density fitting

KW - Kronecker product approximation

KW - Resolution of the identity

UR - https://www.scopus.com/pages/publications/59349095918

U2 - 10.1016/j.chemphys.2008.10.047

DO - 10.1016/j.chemphys.2008.10.047

M3 - Article

SN - 0301-0104

VL - 356

SP - 86

EP - 90

JO - Chemical Physics

JF - Chemical Physics

IS - 1-3

ER -

Resolutions of the Coulomb operator: II. The Laguerre generator

Abstract

Access to Document

Other files and links

Fingerprint

Cite this