Construction of Some Molecular Orbitals to Be Approximately Invariant for Changes from One Molecule to Another

Boys, Samuel Francis

doi:10.1103/revmodphys.32.296

Cited by 1,207 publications

(744 citation statements)

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“…They are also labeled with two quantum numbers: the index ␣ which describes orbital character and position, as well as the direct lattice vector T, indicating the unit cell they belong to. The relation between WFs and Bloch functions can be considered as the generalization to solids of the relation between "Boys orbitals" 48 and localized molecular orbitals for finite systems. It is crucial to realize, that the unitary transformation is not unique.…”

Section: General Framework and Wannier Basicsmentioning

confidence: 99%

Dynamical mean-field theory using Wannier functions: A flexible route to electronic structure calculations of strongly correlated materials

et al. 2006

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A versatile method for combining density functional theory in the local density approximation with dynamical mean-field theory ͑DMFT͒ is presented. Starting from a general basis-independent formulation, we use Wannier functions as an interface between the two theories. These functions are used for the physical purpose of identifying the correlated orbitals in a specific material, and also for the more technical purpose of interfacing DMFT with different kinds of band-structure methods ͑with three different techniques being used in the present work͒. We explore and compare two distinct Wannier schemes, namely the maximally localized Wannier function and the Nth order muffin-tin-orbital methods. Two correlated materials with different degrees of structural and electronic complexity, SrVO 3 and BaVS 3 , are investigated as case studies. SrVO 3 belongs to the canonical class of correlated transition-metal oxides, and is chosen here as a test case in view of its simple structure and physical properties. In contrast, the sulfide BaVS 3 is known for its rich and complex physics, associated with strong correlation effects and low-dimensional characteristics. Insights into the physics associated with the metal-insulator transition of this compound are provided, particularly regarding correlationinduced modifications of its Fermi surface. Additionally, the necessary formalism for implementing selfconsistency over the electronic charge density in a Wannier basis is discussed.

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Section: General Framework and Wannier Basicsmentioning

confidence: 99%

Dynamical mean-field theory using Wannier functions: A flexible route to electronic structure calculations of strongly correlated materials

et al. 2006

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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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“…(9). Established forms of localizing potentials are the one of Edmiston 19,20,21 The functional dependence off + λP 0 on the occupied Wannier orbitals can be disregarded. 32,33 Then, the Fock operator becomes a conventional Hermitian operator and the restriction of the penalty projection operator, to act only on occupied orbitals, can be released, i.e., N ′ in Eq.…”

Section: B Wannier-hartree-fock Equationsmentioning

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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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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Construction of Some Molecular Orbitals to Be Approximately Invariant for Changes from One Molecule to Another

Cited by 1,207 publications

References 1 publication

Dynamical mean-field theory using Wannier functions: A flexible route to electronic structure calculations of strongly correlated materials

Dynamical mean-field theory using Wannier functions: A flexible route to electronic structure calculations of strongly correlated materials

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

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

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