On the Beebe-Linderberg two-electron integral approximation

Røeggen, I.; Wisløff-Nilssen, E.

doi:10.1016/0009-2614(86)80099-9

Cited by 170 publications

(137 citation statements)

References 15 publications

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“…Density fitting (DF) [30][31][32][33][34][35][36][37] and Cholesky decomposition (CD) [38][39][40][41] were used to reduce computational costs. These approaches reduce disk and memory requirements, and CPU costs in certain terms, by expressing the 4-index two-electron integrals as contractions of 3-index quantities.…”

Section: Theoretical Methodsmentioning

confidence: 99%

Communication: Resolving the three-body contribution to the lattice energy of crystalline benzene: Benchmark results from coupled-cluster theory

Kennedy

McDonald

DePrince

et al. 2014

The Journal of Chemical Physics

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Coupled-cluster theory including single, double, and perturbative triple excitations [CCSD(T)] has been applied to trimers that appear in crystalline benzene in order to resolve discrepancies in the literature about the magnitude of non-additive three-body contributions to the lattice energy. The present results indicate a non-additive three-body contribution of 0.89 kcal mol −1 , or 7.2% of the revised lattice energy of −12.3 kcal mol −1 . For the trimers for which we were able to compute CCSD(T) energies, we obtain a sizeable difference of 0.63 kcal mol −1 between the CCSD(T) and MP2 three-body contributions to the lattice energy, confirming that three-body dispersion dominates over three-body induction. Taking this difference as an estimate of three-body dispersion for the closer trimers, and adding an Axilrod-Teller-Muto estimate of 0.13 kcal mol −1 for long-range contributions yields an overall value of 0.76 kcal mol −1 for three-body dispersion, a significantly smaller value than in several recent studies.

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Section: Theoretical Methodsmentioning

confidence: 99%

Communication: Resolving the three-body contribution to the lattice energy of crystalline benzene: Benchmark results from coupled-cluster theory

Kennedy

McDonald

DePrince

et al. 2014

The Journal of Chemical Physics

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“…Although CD presented some advantages over the DF approximation, strict error control in particular, it did not become popular. [37][38][39] The reasons for this include computational cost, lack of a general implementation, and the lack of an analytic derivative formulation. Since its first general implementation by Koch et al, 40 the CD approximation has been used for efficient ab initio calculations, and the first analytic derivative formulation is now available.…”

Section: Introductionmentioning

confidence: 99%

Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency

Aquilante

Gagliardi

Pedersen

et al. 2009

The Journal of Chemical Physics

225

274

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Cholesky decomposition of the atomic two-electron integral matrix has recently been proposed as a procedure for automated generation of auxiliary basis sets for the density fitting approximation ͓F. Aquilante et al., J. Chem. Phys. 127, 114107 ͑2007͔͒. In order to increase computational performance while maintaining accuracy, we propose here to reduce the number of primitive Gaussian functions of the contracted auxiliary basis functions by means of a second Cholesky decomposition. Test calculations show that this procedure is most beneficial in conjunction with highly contracted atomic orbital basis sets such as atomic natural orbitals, and that the error resulting from the second decomposition is negligible. We also demonstrate theoretically as well as computationally that the locality of the fitting coefficients can be controlled by means of the decomposition threshold even with the long-ranged Coulomb metric. Cholesky decomposition-based auxiliary basis sets are thus ideally suited for local density fitting approximations.

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“…Following its introduction in quantum chemistry by Beebe and Linderberg in 1977 [53] and subsequent investigations in the 1980s, [54][55][56] the CD method was revived by Koch et al in 2003 [57] . CD-based approaches are reviewed in the recent articles by Pedersen et al [46] and Aquilante et al, [47] to which we refer for details.…”

Section: Control Of Integral Accuracy By Cholesky Decompositionmentioning

confidence: 99%

Attractive electron–electron interactions within robust local fitting approximations

et al. 2013

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An analysis of Dunlap's robust fitting approach reveals that the resulting two-electron integral matrix is not manifestly positive semidefinite when local fitting domains or non-Coulomb fitting metrics are used. We present a highly local approximate method for evaluating four-center two-electron integrals based on the resolution-of-the-identity (RI) approximation and apply it to the construction of the Coulomb and exchange contributions to the Fock matrix. In this pair-atomic resolutionof-the-identity (PARI) approach, atomic-orbital (AO) products are expanded in auxiliary functions centered on the two atoms associated with each product. Numerical tests indicate that in 1% or less of all Hartree-Fock and Kohn-Sham calculations, the indefinite integral matrix causes nonconvergence in the self-consistent-field iterations. In these cases, the two-electron contribution to the total energy becomes negative, meaning that the electronic interaction is effectively attractive, and the total energy is dramatically lower than that obtained with exact integrals. In the vast majority of our test cases, however, the indefiniteness does not interfere with convergence. The total energy accuracy is comparable to that of the standard Coulomb-metric RI method. The speed-up compared with conventional algorithms is similar to the RI method for Coulomb contributions; exchange contributions are accelerated by a factor of up to eight with a triple-zeta quality basis set. A positive semidefinite integral matrix is recovered within PARI by introducing local auxiliary basis functions spanning the full AO product space, as may be achieved by using Cholesky-decomposition techniques. Local completion, however, slows down the algorithm to a level comparable with or below conventional calculations.

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On the Beebe-Linderberg two-electron integral approximation

Cited by 170 publications

References 15 publications

Communication: Resolving the three-body contribution to the lattice energy of crystalline benzene: Benchmark results from coupled-cluster theory

Communication: Resolving the three-body contribution to the lattice energy of crystalline benzene: Benchmark results from coupled-cluster theory

Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency

Attractive electron–electron interactions within robust local fitting approximations

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