Electron density of periodic systems derived from non-orthogonal localized orbitals

Kantorovich, Lev; Danyliv, O.D.

doi:10.1088/0953-8984/16/15/009

Cited by 7 publications

(6 citation statements)

References 35 publications

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“…Because P ∞ /σ < 1 for any 0 σ < 1 2 , we obtain that both (P ∞ /σ ) N −3 and σ N /G Chain N −1 tend to zero when N → ∞. Hence, χ N has a zero limit and disappears in the ratios (17) and (18). Consequently, ξ N → 0 too (see equation ( 19)), so that the third term in the right-hand side of equation ( 14) also does not contribute when the limit of an infinite ring is taken.…”

Section: Infinite Ringmentioning

confidence: 77%

“…It is obtained (see, e.g. [18]) by representing the overlap matrix S as S = 1 + ∆ and then expanding S −1 = (1 + ∆) −1 with respect to the matrix ∆; the latter contains only overlap between different groups and zeros along the diagonal. The method developed in section 4.2 generalizes this expansion method for the case when group functions are linear combinations of Slater determinants, i.e.…”

Section: Discussionmentioning

confidence: 99%

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Arrow diagram approach to nonorthogonal electron group functions in extended systems

Wang¹,

Kantorovich²

2005

J. Phys.: Condens. Matter

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For nonorthogonal electron group functions, the arrow diagram (AD) method (Kantorovich and Zapol 1992 J. Chem. Phys. 96 8420; 1992 J. Chem. Phys. 96 8427) provides a convenient procedure for calculating matrix elements| O | of arbitrary symmetrical operators O. The total wavefunction of the system = A I I is represented as an antisymmetrized product of nonorthogonal many-electron group functions I of each group I in the system. For extended (e.g. infinite) systems the calculation of the mean value of an operator is ill defined, however, as it requires that each term of the diagram expansion be divided by the normalization integral S = | which is given by an AD expansion as well. In this work, we cast the mean value of a symmetrical operator in a form of an AD expansion which is a linear combination of linked ADs. By analysing an exactly solvable one-dimensional Hartree-Fock problem, we find that pre-factors, attached to every linked AD in the linear combination, can be expanded in a power series with respect to overlap. A general method of calculating these pre-factors in a form of a power series expansion with respect to overlap is suggested. This advance makes the AD theory applicable to extended systems, and allows one to calculate the mean value of an arbitrary symmetrical operator correct up to the desired order of overlap within the group function theory. In particular, we derive the effective Hamiltonian of a quantum cluster surrounded by overlapping group functions (e.g. bonds) in the environment region which is correct up to the second order with respect to overlap (an embedding problem).

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Section: Infinite Ringmentioning

confidence: 77%

Section: Discussionmentioning

confidence: 99%

Arrow diagram approach to nonorthogonal electron group functions in extended systems

Wang¹,

Kantorovich²

2005

J. Phys.: Condens. Matter

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“…The localization of one‐electron states is an important characteristic both for a system as well as for a method. A method that gives highly localized states has a potential advantage because these states (in the assumption of their transferability) can be used for constructing the electron density of large molecular systems and even solids 33. We therefore study the local properties of variationally optimized one‐electron states on the example of terminal (corresponding to a pair of atoms on the end of a chain) local bonding and antibonding orbitals for chains of types (a) and (b).…”

Section: Resultsmentioning

confidence: 99%

“…In addition, product functions serve as a solid basis for constructing schemes that can be applied to extended systems 29–31. Their application seems to be very natural for problems of crystal embedding,32, 33 which are in close relationship with the general problem of constructing hybrid schemes 20…”

Section: Introductionmentioning

confidence: 99%

Electron group functions for the analysis of the electronic structures of molecules

Tokmachev

Dronskowski

2005

J Comput Chem

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The electronic structure of a vast majority of molecular systems can be understood in terms of electron groups and their wave functions. They serve as a natural basis for bringing intuitive chemical and physical concepts into quantum chemical calculations. This article considers the general electron group functions formalism as well as its simple geminal version. We try to characterize the wave function with the group structure and its capabilities in actual calculations. For this purpose we implement a variational method based on the wave function in the form of an antisymmetrized product of strongly orthogonal group functions and perform a series of electronic structure calculations for small molecules and model systems. The most important point studied is the relation between the choice of electron groups and the results obtained. We consider energetic characteristics as well as optimal geometry parameters. In view of practical importance, the structure of variationally optimized local one-electron states is considered in detail as well as intuitive characteristics of chemical bonds.

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“…We concentrate here on threedimensional periodic systems as the localized MOs of the perfect bulk crystal are required anyway to represent the environment region in the embedding scheme based on group functions. We have shown previously 20,21,25 that by lifting the orthogonality condition, highly localized molecular orbitals ͑LMOs͒ may be obtained that can span the whole occupied Fock space, and thus are capable of representing correctly the system total electron density. 25 Our method, which is similar in spirit to some existing one-electron methods, [26][27][28] is based on the partitioning of the entire periodic system into overlapping electronic groups ͑EGs͒ corresponding to atoms, ions, bonds, or molecules comprising the entire system.…”

Section: Introductionmentioning

confidence: 99%

Treating periodic systems using embedding: Adams-Gilbert approach

2007

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A direct-space electronic structure method for electronic structure calculations of periodic systems, based on highly localized ͑noncanonical͒ molecular orbitals ͑MOs͒ and the quantum cluster embedding, is suggested. The method utilizes a modified Adams-Gilbert approach that allows one to find self-consistently ͑for the given geometry͒ the system energy and the corresponding localized MOs which give the correct total electron density. The approach suggested here can also be considered as an exact derivation of embedded quantum cluster models. We illustrate this method on a Hartree-Fock calculation of a model periodic He system and the MgO crystal, and the results are compared with a conventional approach based on canonical Bloch-like orbitals as implemented in the CRYSTAL code. Our method, which scales linearly with the system size, can also be used to solve the Kohn-Sham equations of density-functional theory.

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Electron density of periodic systems derived from non-orthogonal localized orbitals

Cited by 7 publications

References 35 publications

Arrow diagram approach to nonorthogonal electron group functions in extended systems

Arrow diagram approach to nonorthogonal electron group functions in extended systems

Electron group functions for the analysis of the electronic structures of molecules

Treating periodic systems using embedding: Adams-Gilbert approach

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