Quantum theory of chemical valence concepts

Roby, Keith R.

doi:10.1080/00268977400100071

Cited by 299 publications

(92 citation statements)

References 31 publications

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“…Fukui's frontier orbital theory 4 and the WoodwardHoffmann rules 5 are notable examples of the power of this model. The role that minimal basis sets can play in understanding ab initio wave functions has been examined from various points of view by Mulliken, 6 Adams, 7 Davidson, 8 Anderson, 9 Roby, 10 Ahlrichs and co-workers, 11 Weinhold and co-workers, 12 Sanchez-Portal, 13 Mayer, 14 Cioslowski, 15 and others.…”

Section: Introductionmentioning

confidence: 99%

A comprehensive analysis of molecule-intrinsic quasi-atomic, bonding, and correlating orbitals. I. Hartree-Fock wave functions

West

Schmidt

Gordon

et al. 2013

The Journal of Chemical Physics

203

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Through a basis-set-independent web of localizing orbital-transformations, the electronic wave function of a molecule is expressed in terms of a set of orbitals that reveal the atomic structure and the bonding pattern of a molecule. The analysis is based on resolving the valence orbital space in terms of an internal space, which has minimal basis set dimensions, and an external space. In the internal space, oriented quasi-atomic orbitals and split-localized molecular orbitals are determined by new, fast localization methods. The density matrix between the oriented quasi-atomic orbitals as well as the locations of the split-localized orbitals exhibit atomic populations and inter-atomic bonding patterns. A correlation-adapted quasi-atomic basis is determined in the external orbital space. The general formulations are specified in detail for Hartree-Fock wave functions. Applications to specific molecules exemplify the general scheme. Through a basis-set-independent web of localizing orbital-transformations, the electronic wave function of a molecule is expressed in terms of a set of orbitals that reveal the atomic structure and the bonding pattern of a molecule. The analysis is based on resolving the valence orbital space in terms of an internal space, which has minimal basis set dimensions, and an external space. In the internal space, oriented quasi-atomic orbitals and split-localized molecular orbitals are determined by new, fast localization methods. The density matrix between the oriented quasi-atomic orbitals as well as the locations of the split-localized orbitals exhibit atomic populations and interatomic bonding patterns. A correlation-adapted quasi-atomic basis is determined in the external orbital space. The general formulations are specified in detail for Hartree-Fock wave functions. Applications to specific molecules exemplify the general scheme. © 2013 AIP Publishing LLC.

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Section: Introductionmentioning

confidence: 99%

A comprehensive analysis of molecule-intrinsic quasi-atomic, bonding, and correlating orbitals. I. Hartree-Fock wave functions

West

Schmidt

Gordon

et al. 2013

The Journal of Chemical Physics

203

View full text Add to dashboard Cite

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“…The Roby's population maximization [42] gives LMOs for which the projection on the subspace spanned by the basis orbitals centered within the selected region is a maximum, or is at least stationary [39]. In this method the localization operator Ω A in Eq.…”

Section: The Projection On the Atomic Subspace (Methods P)mentioning

confidence: 99%

Comparison of localization procedures for applications in crystal embedding

Danyliv

Kantorovich

2004

Phys. Rev. B

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With the aim of future applications in quantum mechanical embedding in extended systems such as crystals, we suggest a simple and computationally efficient method which enables construction of a set of nonorthogonal highly localized one-electron orbitals for periodic nonmetallic crystals which reflect their chemical nature. The orbitals are also used to build up the Hartree-Fock (HF) electron density of the entire crystals. The simplicity of the method stems from the fact that it does not require usage and/or modification of periodic electronic structure codes, and is instead based on the HF calculation of a sequence of finite clusters with subsequent application of a localization procedure to transform the HF canonical molecular orbitals. Two extreme cases of chemical bonding, ionic (MgO crystal) and covalent (Si crystal), are considered for which a number of known localization schemes are applied and compared. With some modifications our method can also be applied to nonperiodic nonmetallic systems as well.

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“…A related approach is the use of small adaptive basis sets. The idea of encoding chemical environment information into atomic/quasiatomic basis functions to understand chemical bonding dates back to early tools [67][68][69][70][71][72] , as well as more contemporary methods [73][74][75][76][77][78] . Apart from interpretive purposes, the merits of utilizing small adaptive bases in KS-DFT calculations have been recognized with the development of fast (especially linear-scaling) SCF algorithms, leading to renewed interest in the concept of "polarized atomic orbitals" (PAOs), first put forward by Adams in the 1960s 79,80 .…”

Section: Kohn-sham Density Functional Theorymentioning

confidence: 99%

Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: Formulation, proof of concept, and a pilot implementation

Mao

Horn

Mardirossian

et al. 2016

The Journal of Chemical Physics

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Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large basis sets are used. To approach the basis set limit with potentially lower costs, a new SCF scheme with minimal adaptive basis (MAB) functions variationally optimized on each atomic site is presented, and the desired accuracy can be obtained by applying a perturbative correction (PC). Compared to exact SCF results, using this MAB-SCF (PC) approach with the same target basis set produces < 0.15 kcal/mol RMS errors for most of the tested TC datasets, and < 0.1 kcal/mol for most of the NCs. The performance of density functionals near the basis set limit can be well reproduced with slight discrepancies. With further improvement to its implementation, MAB-SCF (PC) could be a promising substitute for its conventional counterpart to viably approach the basis set limit of modern density functionals.

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Quantum theory of chemical valence concepts

Cited by 299 publications

References 31 publications

A comprehensive analysis of molecule-intrinsic quasi-atomic, bonding, and correlating orbitals. I. Hartree-Fock wave functions

A comprehensive analysis of molecule-intrinsic quasi-atomic, bonding, and correlating orbitals. I. Hartree-Fock wave functions

Comparison of localization procedures for applications in crystal embedding

Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: Formulation, proof of concept, and a pilot implementation

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