Discontinuous approximate molecular electronic wave‐functions

Stuebing, Edward W.; Weare, John H.; Parr, Robert G.

doi:10.1002/qua.560110108

Cited by 41 publications

(10 citation statements)

References 42 publications

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“…The two discussed in this work are the density fitting ͑DF͒ approximation ͑DF, also called resolution-of-the-identity or RI͒ [39][40][41][42][43][44][45][46] and the Cholesky decomposition ͑CD͒. There are several closely related approaches to approximate twoelectron integrals.…”

Section: Introductionmentioning

confidence: 99%

Density fitting and Cholesky decomposition approximations in symmetry-adapted perturbation theory: Implementation and application to probe the nature of π-π interactions in linear acenes

Hohenstein¹,

Sherrill²

2010

The Journal of Chemical Physics

303

308

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Van der Waals interactions between hydrocarbon molecules and zeolites: Periodic calculations at different levels of theory, from density functional theory to the random phase approximation and Møller-Plesset perturbation theory Density-functional theory-symmetry-adapted intermolecular perturbation theory with density fitting: A new efficient method to study intermolecular interaction energies J. Chem. Phys. 122, 014103 (2005); 10.1063/1.1824898 Symmetry-adapted perturbation theory of three-body nonadditivity of intermolecular interaction energy Density fitting ͑DF͒ approximations have been used to increase the efficiency of several quantum mechanical methods. In this work, we apply DF and a related approach, Cholesky decomposition ͑CD͒, to wave function-based symmetry-adapted perturbation theory ͑SAPT͒. We also test the one-center approximation to the Cholesky decomposition. The DF and CD approximations lead to a dramatic improvement in the overall computational cost of SAPT, while introducing negligible errors. For typical target accuracies, the Cholesky basis needed is noticeably smaller than the DF basis ͑although the cost of constructing the Cholesky vectors is slightly greater than that of constructing the three-index DF integrals͒. The SAPT program developed in this work is applied to the interactions between acenes previously studied by Grimme ͓Angew. Chem., Int. Ed. 47, 3430 ͑2008͔͒, expanding the cases studied by adding the pentacene dimer. The SAPT decomposition of the acene interactions provides a more realistic picture of the interactions than that from the energy decomposition analysis previously reported. The data suggest that parallel-displaced and T-shaped acene dimers both feature a special stabilizinginteraction arising from electron correlation terms which are significantly more stabilizing than expected on the basis of pairwise −C 6 R −6 estimates. These terms are qualitatively the same in T-shaped as in parallel-displaced geometries, although they are roughly a factor of 2 smaller in T-shaped geometries because of the larger distances between the intermolecular pairs of electrons.

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Section: Introductionmentioning

confidence: 99%

Density fitting and Cholesky decomposition approximations in symmetry-adapted perturbation theory: Implementation and application to probe the nature of π-π interactions in linear acenes

Hohenstein¹,

Sherrill²

2010

The Journal of Chemical Physics

303

308

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“…This was proposed by a number of authors 10,11,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39 Among practitioners of APW methods, the prevailing opinion is that discontinuous boundary conditions are legitimate. For example Shaughnessy and coll.…”

Section: Discontinuous Functionsmentioning

confidence: 99%

Boundary conditions for augmented plane-wave methods

Brouder

2005

Phys. Rev. B

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The augmented plane wave method uses the Rayleigh-Ritz principle for basis functions that are continuous but with discontinuous derivatives and the kinetic energy is written as a pair of gradients rather than as a Laplacian. It is shown here that this procedure is fully justified from the mathematical point of view. The domain of the self-adjoint Hamiltonian, which does not contain functions with discontinuous derivatives, is extended to its form domain, which contains them, and this modifies the form of the kinetic energy. Moreover, it is argued that discontinuous basis functions should be avoided.

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“…In some quantum problems, primarily in molecular and solid‐state physics, a relevant configuration space may be divided in a natural way into disjoint regions where an exact eigenfunction is expected to have substantially different behaviors (e.g., being monotonic in one region and highly oscillatory in another). It has been pointed out by a number of investigators 1–18 that in solving such problems it might be advantageous to work with trial functions having discontinuities at interfaces.…”

Section: Introductionmentioning

confidence: 99%

“…To use such functions, one has to replace the simple functional (1.3) by a more general one, differing from (1.3) in the way in which the continuity requirements imposed on exact eigenfunctions are built in it. Several versions of this more general functional may be found in the literature 1–6, 10–18; among them, that proposed in Ref. 4 was devised for the Dirac particle, while others are suitable for the Schrödinger Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%