Resolutions of the Coulomb operator: IV. the spherical bessel quasi-resolution

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

doi:10.1021/ct200115t

Resolutions of the Coulomb operator: IV. the spherical bessel quasi-resolution

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

^*Corresponding author for this work

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

11 Citations (Scopus)

Abstract

We show that the Coulomb operator can be resolved as r12^-1 = Σ_nlm φ_nlm(r₁) φ _nlm(r₂) where φ_nlm(r) is proportional to the product of a spherical Bessel function and a spherical harmonic, provided that r₁ + r₂ < 2π. The resolution reduces Coulomb matrix elements to Cholesky-like sums of products of auxiliary integrals. We find that these sums converge rapidly for four prototypical electron densities. To demonstrate its viability in large-scale quantum chemical calculations, we also use a truncated resolution to calculate the Coulomb energy of the nanodiamond crystallite C₈₄H₆₄.

Original language	English
Pages (from-to)	830-833
Number of pages	4
Journal	Journal of Chemical Theory and Computation
Volume	7
Issue number	4
DOIs	https://doi.org/10.1021/ct200115t
Publication status	Published - 12 Apr 2011

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abstract = "We show that the Coulomb operator can be resolved as r12-1 = Σnlm φnlm(r1) φ nlm(r2) where φnlm(r) is proportional to the product of a spherical Bessel function and a spherical harmonic, provided that r1 + r2 < 2π. The resolution reduces Coulomb matrix elements to Cholesky-like sums of products of auxiliary integrals. We find that these sums converge rapidly for four prototypical electron densities. To demonstrate its viability in large-scale quantum chemical calculations, we also use a truncated resolution to calculate the Coulomb energy of the nanodiamond crystallite C84H64.",

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

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T2 - IV. the spherical bessel quasi-resolution

AU - Limpanuparb, Taweetham

AU - Gilbert, Andrew T.B.

AU - Gill, Peter M.W.

PY - 2011/4/12

Y1 - 2011/4/12

N2 - We show that the Coulomb operator can be resolved as r12-1 = Σnlm φnlm(r1) φ nlm(r2) where φnlm(r) is proportional to the product of a spherical Bessel function and a spherical harmonic, provided that r1 + r2 < 2π. The resolution reduces Coulomb matrix elements to Cholesky-like sums of products of auxiliary integrals. We find that these sums converge rapidly for four prototypical electron densities. To demonstrate its viability in large-scale quantum chemical calculations, we also use a truncated resolution to calculate the Coulomb energy of the nanodiamond crystallite C84H64.

AB - We show that the Coulomb operator can be resolved as r12-1 = Σnlm φnlm(r1) φ nlm(r2) where φnlm(r) is proportional to the product of a spherical Bessel function and a spherical harmonic, provided that r1 + r2 < 2π. The resolution reduces Coulomb matrix elements to Cholesky-like sums of products of auxiliary integrals. We find that these sums converge rapidly for four prototypical electron densities. To demonstrate its viability in large-scale quantum chemical calculations, we also use a truncated resolution to calculate the Coulomb energy of the nanodiamond crystallite C84H64.

UR - https://www.scopus.com/pages/publications/79954462623

U2 - 10.1021/ct200115t

DO - 10.1021/ct200115t

M3 - Article

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SP - 830

EP - 833

JO - Journal of Chemical Theory and Computation

JF - Journal of Chemical Theory and Computation

IS - 4

ER -

Resolutions of the Coulomb operator: IV. the spherical bessel quasi-resolution

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