Uniform Localization of Atomic and Molecular Orbitals. I

Magnasco, Valerio; Perico, Angelo

doi:10.1063/1.1712065

Cited by 188 publications

(64 citation statements)

References 17 publications

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“…on one or two particular atoms in the unit cell). Then, the net atomic Mulliken's [20] population produced by the LMO's in the selected region is maximised [21,19,16]. In this case…”

Section: Mulliken's Net Population (Methods M)mentioning

confidence: 99%

Strongly localized molecular orbitals for -quartz

Danyliv¹,

Kantorovich²

2004

J. Phys.: Condens. Matter

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Abstract. A previously proposed computational procedure for constructing a set of nonorthogonal strongly localised one-electron molecular orbitals (O. Danyliv, L. Kantorovich -Phys. Rev. B, 2004, to be published) is applied to a perfect α-quartz crystal characterised by an intermediate type of chemical bonding. The orbitals are constructed by applying various localisation methods to canonical Hartree-Fock orbitals calculated for a succession of finite molecular clusters of increased size with appropriate boundary conditions. The calculated orbitals span the same occupied Fock space as the canonical HF solutions, but have an advantage of reflecting the true chemical nature of the bonding in the system. The applicability of several localisation techniques as well as of a number of possible choices of localisation regions (structure elements) are discussed for this system in detail.

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“…on one or two particular atoms in the unit cell). Then, the net atomic Mulliken's [20] population produced by the LMO's in the selected region is maximised [21,19,16]. In this case…”

Section: Mulliken's Net Population (Methods M)mentioning

confidence: 99%

Strongly localized molecular orbitals for -quartz

Danyliv¹,

Kantorovich²

2004

J. Phys.: Condens. Matter

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“…These mathematical frameworks for searching a basis set transformation maximizing/minimizing a determined quantity have been widely utilized in procedures of orbital localization, where other tensors different from the 2 D ik jl one have been manipulated. [40][41][42][43][44][45][46][47] In Sec. III, we report results arising from this proposal to be compared with those provided by more conventional molecular orbital basis sets.…”

Section: Minimization Of the Seniority Numbermentioning

confidence: 99%

Seniority number in spin-adapted spaces and compactness of configuration interaction wave functions

Alcoba

Torre

Laín

et al. 2013

The Journal of Chemical Physics

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This work extends the concept of seniority number, which has been widely used for classifying N-electron Slater determinants, to wave functions of N electrons and spin S, as well as to N-electron spin-adapted Hilbert spaces. We propose a spin-free formulation of the seniority number operator and perform a study on the behavior of the expectation values of this operator under transformations of the molecular basis sets. This study leads to propose a quantitative evaluation for the convergence of the expansions of the wave functions in terms of Slater determinants. The non-invariant character of the seniority number operator expectation value of a wave function with respect to a unitary transformation of the molecular orbital basis set, allows us to search for a change of basis which minimizes that expectation value. The results found in the description of wave functions of selected atoms and molecules show that the expansions expressed in these bases exhibit a more rapid convergence than those formulated in the canonical molecular orbital bases and even in the natural orbital ones.

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“…From eq. [ 5 ] one obtains, in a standard manner, that the requirement &Mi = 0 is equivalent to the Hermitian n by n matrix eigenvalue equation for determining the coefficients Aki = a; to be substituted into eq. [4].…”

Section: Equations For Determining the Localized Orbitalsmentioning

confidence: 99%

Orthogonal effective atomic orbitais in the topological theory of atoms

Mayer¹

1996

Can. J. Chem.

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A simple formalism has been developed permitting us to extract, from the molecular wave functions, the effective orthogonal atomic orbitals characterizing the actual state of the atom in the molecule within the framework of Bader's topological theory of atoms. This may give important conceptual connections between the SCF wave functions obtained in the large-scale ab initio calculations, or even at the Hartree-Fock limit, and the traditional atomic orbital picture. The method is based on some partial orthogonality properties of the non-orthogonal localized molecular orbitals constructed by requiring a maximal weight in the given atomic domain, or in another selected molecular fragment. (The use of such localized orbitals may also be of independent interest.)Key words: effective atomic orbitals, atomic orbitals from molecular wave functions, non-orthogonal localized orbitals, topological theory of atoms, Bader's theory of atoms in molecules. RCsurnC

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Uniform Localization of Atomic and Molecular Orbitals. I

Cited by 188 publications

References 17 publications

Strongly localized molecular orbitals for -quartz

Strongly localized molecular orbitals for -quartz

Seniority number in spin-adapted spaces and compactness of configuration interaction wave functions

Orthogonal effective atomic orbitais in the topological theory of atoms

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