The generalized separated electron pair model. II. An application to NH, NH3, NH, NH2− and N3−

Robb, Michael A.; Csizmadia, Imre G.

doi:10.1002/qua.560050603

Cited by 21 publications

(5 citation statements)

References 25 publications

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“…It is necessary to compare the SPCCI method with other closely related correlation methods 22, 23, 25–38. The generalized valence bond–perfect pairing (GVB‐PP) wave function is a simplified SEP wave function 25.…”

Section: Methodsmentioning

confidence: 99%

“…The generalized valence bond–perfect pairing (GVB‐PP) wave function is a simplified SEP wave function 25. Some earlier approaches 28–31 to extend the SEP theory were essentially traditional MR‐CI methods, although natural orbitals from the SEP wave function were used in constructing configurations. The most successful works are the extended geminal (EG) models introduced by Røeggen in a series of papers 22, 23, 32–36.…”

Section: Methodsmentioning

confidence: 99%

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Pair-correlated configuration interaction method and its approximate version for solving the electron correlation problem in molecules

Jiang

2000

Int. J. Quantum Chem.

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ABSTRACT:The pair-correlated configuration interaction (PCCI) method has been developed in this work to be an alternative to the traditional CI method for solving the correlation problem in closed-shell, ground-state molecules. The PCCI expansion is well defined on the localized molecular orbital description and can be truncated according to how many electron pairs are explicitly correlated (namely, the PCCI-n expansion includes all configurations up to n-pair correlation). However, PCCI-n calculations are formidable for most of chemical systems, and therefore further approximations are required. After the separated electron pair approximation is adopted, the PCCI method reduces to the simplified PCCI (SPCCI) method, which is computationally feasible for moderate molecular systems by using matrix element expressions presented in this work. We have tested the SPCCI-n method by applying it to solve the ground state of the Pariser-Parr-Pople (PPP) Hamiltonian for π-networks of a series of conjugated polyenes. The most significant features of the SPCCI-n method have been brought to light from our test calculations: (1) The SPCCI-n (n = 2, 3) method can recover more than 90% of the total ground-state correlation energy for conjugated polyenes with up to 30 π-electrons. It is far superior to the conventional configuration interaction that includes all singly and doubly excited configurations (CI-SD) method in systems with more than 6 π-electrons. (2) The SPCCI-n method works well in the moderately and strongly correlated regions but less satisfactorily in the weakly correlated domain. Finally, the size consistency error of the general SPCCI-n method is analyzed and a size-consistent coupled-cluster-like approach is proposed.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Pair-correlated configuration interaction method and its approximate version for solving the electron correlation problem in molecules

Jiang

2000

Int. J. Quantum Chem.

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“…Using eq 3, the expression for the average number of pairs in a region (ft) may be expressed so as to incorporate the correlation term to yield Z>2(ft,ft) = f dr, f dr?£>2(r,,r2) = TV(ft)2 + F(ft,ft) Ja Ja (7) where F(ft,ft) = f dr, f dr2Z),(n)Di(r2)/(r,,r2) (8) Q %s F(ft,ft) is a measure of the total correlation which is contained within the region (ft), i.e., a measure of the intraloge correlation. For a Hartree-Fock wave function, which indues only Fermi correlation, the magnitude of F(ft,ft) is a measure of the total (integrated) Fermi hole of the JV(ft) particles that lies within the region (ft).…”

Section: Jwmentioning

confidence: 99%

“…[5][6] Associated with this result is the assumption that in some systems, a large fraction of the correlation energy may be described in terms of just TV/2 strongly intra-correlated pair functions, functions which are considered to be spatially localized and as a result transferrable between systems. This assumption is embodied in the method of "separated electron pairs" [7][8] and in the use of "strongly orthogonal geminals".9-10 The independent electron pair approximation, as recently reviewed by Kutzelnigg,11 is another such approach, but one which may be generalized to include all TV(TV -l)/2 pair interactions. The present work is related to these approaches in a useful way since it details the definition of regions of space which possess pure pair properties and in addition, yields values of the extent of intraand inter-pair correlation over and between well-defined spatial regions.…”

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confidence: 99%

Spatial localization of the electronic pair and number distributions in molecules

Bader¹,

Stephens²

1975

J. Am. Chem. Soc.

721

709

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It is shown that the quantum mechanical requirement for the spatial localization of an electron in a many-electron system is that the Fermi correlation hole for the electron be totally contained within the same spatial region. Correspondingly, the extent to which this requirement is not met provides a quantitative measure of its delocalization over the remaining space of the system. The localizability of the Fermi hole is a property of the pair density and the total localization of some number of electrons N ( Q ) in a region (Q) of real spacejs obtEined only when the exclusion principle acts so as to reduce the average pair population of (a) to its limiting value of N ( R ) ( N ( Q ) -I). It is shown that the partitioning of a system which most closely approaches the limit of spatially localized subsets of electrons may be determined by demanding that the fluctuation in the average population of each of the spatial regions be a minimum. The extent to which the (Hartree-Fock) charge distributions of LiH, BeH2, BH3, BH4-, CH4, NH3,OHz. FH, Ne, N2, and Fz may be regarded as arising from the localization of individual a,@ pairs of electrons in distinct spatial regions is determined. The model of spatially localized pairs is appropriate for LiH, BeH2, BH3, and BH4-, it is borderline for CH4, but in the remaining systems, the motions of the valence electrons are so strongly inter-correlated, the localized pair model ceases to afford a suitable description. For example, the properties of the charge and pair densities of H2O provide no physical basis for the view that there are two separately localized pairs of nonbonded electrons in this system. The same analysis indicates that a wave function constructed from N / 2 intra-correlated pair functions would fail to recover the major fraction of the correlation energy in this latter set of molecules.In this paper we investigate the extent to which the electronic charge distribution of a molecular system may be regarded as arising from the localization of individual pairs of electrons in well-defined and nonoverlapping regions of space. W e do this in the following way. We determine the average number of pairs in a given region of space by integration of the quantum mechanical expression for the pair density over that region. W e next show that this average number of pairs is dependent upon the correlative interactions between the electrons and in particular, that the decomposition of a total system which most closely approaches the limit of spatially localized pairs of electrons is attained by maximizing the extent to which the integrated Fermi correlation hole of each electron in a given pair is localized within the same spatial domain. Finally, we show that this latter condition is attained by demanding that the fluctuation in the average population of each of the spatial regions be a minimum.Daudel and co-workers'%2 have reasoned that there should be some "best" decomposition of the physical space of a system into a number of mutually exclusive spaces called loges. The "...

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“…[2][3][4][5][6][7] Sometimes this model is referred to as separated electron pair ͑SEP͒ theory. [8][9][10][11][12] Most prior studies focused on the total amount of correlation energy recovered by the product of strongly orthogonal geminals. It was generally concluded that the model has its limitations, primarily attributable to either lack of intergeminal correlation, 5 strong orthogonality approximation, 13 or both.…”

Section: Introductionmentioning

confidence: 99%

Geminal model chemistry II. Perturbative corrections

Rassolov

Garashchuk

2004

The Journal of Chemical Physics

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We introduce and investigate a chemical model based on perturbative corrections to the product of singlet-type strongly orthogonal geminals wave function. Two specific points are addressed ͑i͒ Overall chemical accuracy of such a model with perturbative corrections at a leading order; ͑ii͒ Quality of strong orthogonality approximation of geminals in diverse chemical systems. We use the Epstein-Nesbet form of perturbation theory and show that its known shortcomings disappear when it is used with the reference Hamiltonian based on strongly orthogonal geminals. Application of this model to various chemical systems reveals that strongly orthogonal geminals are well suited for chemical models, with dispersion interactions between the geminals being the dominant effect missing in the reference wave functions.

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The generalized separated electron pair model. II. An application to NH, NH₃, NH, NH²⁻ and N³⁻

Cited by 21 publications

References 25 publications

Pair-correlated configuration interaction method and its approximate version for solving the electron correlation problem in molecules

Pair-correlated configuration interaction method and its approximate version for solving the electron correlation problem in molecules

Spatial localization of the electronic pair and number distributions in molecules

Geminal model chemistry II. Perturbative corrections

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