Nonempirical methods in solid state theory

Reznik, I. M.; Tolpygo, K. B.

doi:10.1007/bf00748111

Cited by 3 publications

(11 citation statements)

References 66 publications

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“…A similar approach can also be applied to another important class of systems which consists of two electronic bonds in covalent materials (geminals) [30,31]. The main simplification which arises for such systems [48] is twofold: (1) the diagrammatic expansion is largely cut off and (2) the RDMs of only up to the second order are needed, simplifying the parametrization substantially (in fact, in this case the RDMs can be made exactly Nrepresentable).…”

Section: Discussionmentioning

confidence: 98%

“…As a rule, parameters introduced are fitted to a number of observed crystal properties. Already by the fifties Tolpygo [29] (see also [30,31]) suggested a model which was based on a microscopic quantum mechanical consideration reminiscent of second-order perturbation theory. Instead of shells in the shell model, polarization effects were treated by considering dipole and quadrupole moments induced on atoms (or bonds in covalent materials).…”

Section: Introductionmentioning

confidence: 99%

“…Instead of shells in the shell model, polarization effects were treated by considering dipole and quadrupole moments induced on atoms (or bonds in covalent materials). It was assumed in the theory that the crystal can be divided into nonoverlapping structure elements (SEs) consisting of electronic groups (EGs) and certain nuclei and that the total wavefunction of the whole system is given by an antisymmetrized product of wavefunctions A of the individual groups A (group functions, GFs) which comprise the whole system [30,31]. The approach due to Tolpygo corresponds to the socalled strong orthogonality approximation within the group-function theory (GFT) which was developed in detail by McWeeny [32].…”

Section: Introductionmentioning

confidence: 99%

“…According to the original method [29,31,49], the minimization with respect to the coefficients C Aµ is performed in two stages. In the first stage, we vary the energy, keeping all the multipole moments Q A fixed.…”

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confidence: 99%

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Derivation of atomistic models for lattices consisting of weakly overlapping structural elements

Kantorovich

2000

Int. J. Quantum Chem.

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ABSTRACT:A theoretical approach based on the arrow diagram technique within the group function theory is applied to an infinite crystal consisting of weakly overlapping structural elements (SE: ions, atoms, and molecules). A perturbation method is used to derive the lattice energy in terms of two-body, three-body, etc. types of interactions accompanied by electronic polarization of SEs for the system which is slightly away from some reference configuration. It is demonstrated how an atomistic model for the particular material can be derived from the general theory. A general approach to obtain a parametrization scheme is suggested which is based on a representation of transition and ground-state reduced density matrices (RDM) of various orders via a finite set of basis functions. Using group theory and necessary conditions for N-representability of the RDMs, the representation containing the least possible number of the fitting parameters is worked out. The method is illustrated on a special case of spherical SEs (e.g., atoms/ions in atomic/ionic solids) and it is discussed whether existing models are in accord with the ideas developed.

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Section: Discussionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Derivation of atomistic models for lattices consisting of weakly overlapping structural elements

Kantorovich

2000

Int. J. Quantum Chem.

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“…[1][2][3][4][5][6][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] Valence electrons of an atom or a molecule [11][12][13] and electrons of an embedded molecular cluster in a solid 6,[14][15][16][17][18][19][20]23,24 present two examples of active electron subsystems. The active part is subject to a quantum-mechanical treatment which can be less or more complete, depending on one's need and possibilities.…”

Section: Introductionmentioning

confidence: 99%

Gauge transformations of electron group functions

Zapol

1996

The Journal of Chemical Physics

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Ab initio electronic structure of PtH+, PtH, Pt2, and Pt2H from a oneelectron pseudopotential approach Within the scope of the electron group functions ͑EGF͒ theory, the concept of gauge transformations ͑GT͒ of EGFs is introduced as such transformations that leave the state of the entire system invariant. The variational equations for EGFs should contain additional terms representing the Pauli repulsion part of the pseudopotential and being consistent with the choice of EGFs ͑the requirement of gauge consistency͒. The GTs present a natural way of ab initio defining the generalized many-electron pseudopotentials produced by an internally correlated subsystem. Some specific, but rather general forms of GTs are proposed. One of the form is defined using properties of group functions with odd number of electrons. The GTs belonging to another class are defined using properties of antisymmetrically annulling ͑ASA͒ functions introduced in our earlier work and studied further in the present work. In particular, we introduce the ASA kernel basis set for a given group function and show that any function ASA the given group function can be expanded in terms of this set. The algebraic properties of GTs and of their sets are studied, both general ones and specific for the mentioned forms. In general case, the proposed GTs depend on a set of parameters which are functions rather than numbers, that can provide improved transferability of pseudopotentials. The linear transformations of one-electron functions of a determinant as well as the procedures of strong orthogonalization of a group function to a determinant ͑by Fock, Veselov, and Petrashen', and by Szasz͒ are shown to be special cases of the GTs considered.

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Application of the group function theory to infinite systems

Kantorovich

2000

Int. J. Quant. Chem.

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ABSTRACT:We consider application of the group function theory to an arbitrary infinite system consisting of weakly overlapping structural elements which may be atoms, ions, molecules, bonds, etc. We demonstrate that the arrow diagram (AD) expansion developed previously is ill-defined for such a system resulting in divergences in any physical quantity associated with the entire system such as, for example, the energy and charge density. A "linked-AD" theorem is then formulated and proven, which results in a diagrammatic expansion that scales correctly with the system size. Coulomb systems with long-range interactions between structure elements are also considered and the diagrammatic expansion is rearranged in such a way as to also give the correct (linear) scaling. We give an explicit expression for the total energy up to the third order with respect to overlap. Finally, we discuss the problem of choosing structure elements (SE) in a general insulating system and propose a variational method based on a configuration interaction (CI) type expansion within the Fock subspace associated with every SE.

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Nonempirical methods in solid state theory

Cited by 3 publications

References 66 publications

Derivation of atomistic models for lattices consisting of weakly overlapping structural elements

Derivation of atomistic models for lattices consisting of weakly overlapping structural elements

Gauge transformations of electron group functions

Application of the group function theory to infinite systems

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