Localized Atomic and Molecular Orbitals

Edmiston, C.; Ruedenberg, Klaus

doi:10.1103/revmodphys.35.457

Cited by 1,577 publications

(945 citation statements)

References 15 publications

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“…Alternatively, the potential of Edmiston and Ruedenberg can be used as a localizing potential. 22 This study is based on the Hartree-Fock theory. However, the extension of the ideas to density-functional theory 40,41,42 is straightforward.…”

Section: Discussionmentioning

confidence: 99%

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A prioriWannier functions from modified Hartree-Fock and Kohn-Sham equations

Buth

2007

Phys. Rev. B

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The Hartree-Fock equations are modified to directly yield Wannier functions following a proposal of Shukla et al. [Chem. Phys. Lett. 262, 213-218 (1996)]. This approach circumvents the a posteriori application of the Wannier transformation to Bloch functions. I give a novel and rigorous derivation of the relevant equations by introducing an orthogonalizing potential to ensure the orthogonality among the resulting functions. The properties of these, so-called a priori Wannier functions, are analyzed and the relation of the modified Hartree-Fock equations to the conventional, Bloch-function-based equations is elucidated. It is pointed out that the modified equations offer a different route to maximally localized Wannier functions. Their computational solution is found to involve an effort that is comparable to the effort for the solution of the conventional equations. Above all, I show how a priori Wannier functions can be obtained by a modification of the Kohn-Sham equations of density-functional theory.

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Section: Discussionmentioning

confidence: 99%

“…Marzari and Vanderbilt 6 and Zicovich-Wilson et al 7 advocate the FosterBoys functional. 19,20,21 However, there are a number of other localization criteria such as the method of Edmiston and Ruedenberg 22 or the recipe of Pipek and Mezey 23 which can be used, too.…”

Section: Introductionmentioning

confidence: 99%

A prioriWannier functions from modified Hartree-Fock and Kohn-Sham equations

Buth

2007

Phys. Rev. B

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“…Three orbital localization functions have been exceedingly popular and widely used for localizing the occupied orbital space. These are the localization functions of Boys (as modified by Edmiston and Ruedenberg), [6][7][8] Edmiston and Ruedenberg, 8,9 and Pipek and Mezey. 15 The Boys localization minimizes the sum of the orbitals' second central moments, the Pipek-Mezey localization scheme minimizes the number of atomic centers over which an orbital extends, and the Edmiston-Rudenberg localization function maximizes the sum of orbital self-repulsion energies.…”

Section: Localization Functionsmentioning

confidence: 99%

Characterization and Generation of Local Occupied and Virtual Hartree–Fock Orbitals

2016

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The scope of this review article is to discuss the locality of occupied and virtual orthogonal Hartree-Fock orbitals generated by localization function optimization. Locality is discussed from the stand that an orbital is local if it is confined to a small region in space. Focusing on locality measures that reflects the spatial extent of the bulk of an orbital and the thickness of orbital tails, we discuss, with numerical illustrations, how the locality may be reported for individual orbitals as well as for sets of orbitals. Traditional and more recent orbital localization functions are reviewed, and the locality measures are used to compare the locality of the orbitals generated by the different localization functions, both for occupied and virtual orbitals. Numerical illustrations are given also for large molecular systems and for cases where diffuse functions are included in the atomic orbital basis. In addition, we have included a discussion on the physical and mathematical limitations on orbital locality.

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“…However, localization can be ensured e.g. by applying any of the well-known localization criteria [77][78][79][80][81][82].…”

Section: Epstein-nesbet Partitioningmentioning

confidence: 99%

Appendix to “Studies in Perturbation Theory”: The Problem of Partitioning

Śurján

Szabados

2004

Fundamental World of Quantum Chemistry

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The problem of partitioning in perturbation theory is reviewed starting from the classical works by Epstein and Nesbet or by Møller and Plesset, up to optimized partitionings introduced recently. Equations for optimal sets of level shift parameters are presented. Attention is paid to the specific problems appearing if the zero order solution is not a single Slater determinant. A special formalism for multi-configurational perturbation theories is outlined. It is shown that divergent perturbation series, like that of an anharmonic oscillator, can be converted to a convergent series by an appropriate redefinition of the zero order Hamiltonian via level shifts. The possible use of effective one-particle energies in many-body perturbation theory is also discussed. Partitioning optimization in a constant denominator perturbation theory leads to second order correction familiar from connected moment expansion techniques. Ionization potentials, computed perturbatively, are found sensitive to the choice of partitioning, and ordinary approximations are improved upon level shift optimization.

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Localized Atomic and Molecular Orbitals

Cited by 1,577 publications

References 15 publications

A prioriWannier functions from modified Hartree-Fock and Kohn-Sham equations

A prioriWannier functions from modified Hartree-Fock and Kohn-Sham equations

Characterization and Generation of Local Occupied and Virtual Hartree–Fock Orbitals

Appendix to “Studies in Perturbation Theory”: The Problem of Partitioning

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