An Introduction to the Theory of Geminals

Śurján, Péter R.

doi:10.1007/3-540-48972-x_4

Cited by 147 publications

(91 citation statements)

References 115 publications

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“…1 They are based on the ansatz of antisymmetrized product of twoelectron functions called geminals. The resulting optimization problem is, in general, involved unless geminals are restricted to be strongly orthogonal that leads to the antisymmetrized product of strongly orthogonal geminal (APSG) theory.…”

Section: Introductionmentioning

confidence: 99%

How accurate is the strongly orthogonal geminal theory in predicting excitation energies? Comparison of the extended random phase approximation and the linear response theory approaches

Pernal

Chatterjee

Kowalski

2014

The Journal of Chemical Physics

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Articles you may be interested inPerformance of the antisymmetrized product of strongly orthogonal geminal (APSG) ansatz in describing ground states of molecules has been extensively explored in the recent years. Not much is known, however, about possibilities of obtaining excitation energies from methods that would rely on the APSG ansatz. In the paper we investigate the recently proposed extended random phase approximations, ERPA and ERPA2, that employ APSG reduced density matrices. We also propose a time-dependent linear response APSG method (TD-APSG). Its relation to the recently proposed phase including natural orbital theory is elucidated. The methods are applied to Li 2 , BH, H 2 O, and CH 2 O molecules at equilibrium geometries and in the dissociating limits. It is shown that ERPA2 and TD-APSG perform better in describing double excitations than ERPA due to inclusion of the so-called diagonal double elements. Analysis of the potential energy curves of Li 2 , BH, and H 2 O reveals that ERPA2 and TD-APSG describe correctly excitation energies of dissociating molecules if orbitals involved in breaking bonds are involved. For single excitations of molecules at equilibrium geometries the accuracy of the APSG-based methods approaches that of the time-dependent Hartree-Fock method with the increase of the system size. A possibility of improving the accuracy of the TD-APSG method for single excitations by splitting the electron-electron interaction operator into the long-and short-range terms and employing density functionals to treat the latter is presented.

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Section: Introductionmentioning

confidence: 99%

How accurate is the strongly orthogonal geminal theory in predicting excitation energies? Comparison of the extended random phase approximation and the linear response theory approaches

Pernal

Chatterjee

Kowalski

2014

The Journal of Chemical Physics

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“…1 The simplest variant of such a model represents wavefunctions as a single antisymmetrized product of strongly orthogonal geminals ͑APSG͒. [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.…”

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 third order CMX correction, however, is not zero, and it often represents a considerable improvement. This is illustrated on the example of the symmetric dissociation curve of the water molecule in 6-31G basis set, where the CMX correction is shown as applied to the Hartree-Fock (HF) and the antisymmetrized product of strongly orthogonal geminal [164] (APSG) approximations.…”

Section: Optimized Unsøld Approximation: Cmx2mentioning

confidence: 99%

“…The pioneering work in this direction by Dyall [155] was followed in Malrieu's [76,156] and Mukherjee's [157,158] laboratories. In our group, we have developed [159][160][161][162][163] a specific PT to perturb the antisymmetrized product of strongly orthogonal geminal [164] (APSG) wave function, where the geminals are eigenfunctions of an effective two-body Hamiltonian. Inclusion of explicit two-body terms is conceptually an appealing feature, but complicates the formalism significantly.…”

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confidence: 99%

Appendix to “Studies in Perturbation Theory”: The Problem of Partitioning

Śurján

Szabados

2004

Fundamental World of Quantum Chemistry

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The problem of partitioning in perturbation theory is reviewed starting from the classical works by Epstein and Nesbet or by Møller and Plesset, up to optimized partitionings introduced recently. Equations for optimal sets of level shift parameters are presented. Attention is paid to the specific problems appearing if the zero order solution is not a single Slater determinant. A special formalism for multi-configurational perturbation theories is outlined. It is shown that divergent perturbation series, like that of an anharmonic oscillator, can be converted to a convergent series by an appropriate redefinition of the zero order Hamiltonian via level shifts. The possible use of effective one-particle energies in many-body perturbation theory is also discussed. Partitioning optimization in a constant denominator perturbation theory leads to second order correction familiar from connected moment expansion techniques. Ionization potentials, computed perturbatively, are found sensitive to the choice of partitioning, and ordinary approximations are improved upon level shift optimization.

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An Introduction to the Theory of Geminals

Cited by 147 publications

References 115 publications

How accurate is the strongly orthogonal geminal theory in predicting excitation energies? Comparison of the extended random phase approximation and the linear response theory approaches

How accurate is the strongly orthogonal geminal theory in predicting excitation energies? Comparison of the extended random phase approximation and the linear response theory approaches

Geminal model chemistry II. Perturbative corrections

Appendix to “Studies in Perturbation Theory”: The Problem of Partitioning

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