Some theoretical questions about the <i>G</i>‐particle‐hole hypervirial equation

Valdemoro, C.; Alcoba, Diego R.; Tel, Luis M.; Pérez‐Romero, E.

doi:10.1002/qua.22678

Cited by 13 publications

(21 citation statements)

References 49 publications

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“…This feature makes the ACSE simpler from a computational point of view. Even though the ACSE is not equivalent to the 2‐CSE and it is no longer a sufficient condition to satisfy Equation () [15], it has proven to yield suitable results [13, 14, 16].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…The ACSE turns out to be simpler, since it only depends on the first‐, second‐, and third‐order RDM elements and its computational cost results markedly lower than in the case of its Hermitian counterpart or the primitive 2‐CSE, which depend on up to fourth‐order RDM elements. These features justify the interest aroused by the ACSE based methodology, which has been successfully applied to the study of a great variety of problems [6–19].…”

Section: Introductionmentioning

confidence: 99%

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Exploiting the nearsightedness principle within the framework of the anti‐Hermitian contracted Schrödinger equation

Honore

Ríos

Alcoba

et al. 2021

Int J of Quantum Chemistry

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This work exploits the Kohn nearsightedness principle in the algorithms arising from the anti‐Hermitian contracted Schrödinger equation. The procedure provides the implementation of approximations yielding a considerable saving of computational costs in descriptions of N‐electron molecular systems by means of that technique. We report energies, at correlated level, of linear hydrogen chains designed at different geometries, so that we can analyze the strength of the interactions between first‐, second‐, third‐, fourth‐, and so forth neighbor atoms. Using localized molecular orbital basis sets, we observe rapid decays in the values of the elements of the reduced‐density‐matrix cumulant matrices, beyond a cut‐off radius, which justify the proposed approximations. The results, in terms of energies and reduced density matrices, have been compared with those obtained from the full configuration interaction method, showing the usefulness of the nearsightedness principle in this methodology.

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Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exploiting the nearsightedness principle within the framework of the anti‐Hermitian contracted Schrödinger equation

Honore

Ríos

Alcoba

et al. 2021

Int J of Quantum Chemistry

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“…The accuracy of the results obtained with the GHV method when studying the ground state of molecular systems at equilibrium geometry was excellent when compared with the equivalent Full Configuration Interaction (FCI) quantities [9,[11][12][13]. However, the study of the excited states is still a partially open question [14,15].…”

Section: Introductionmentioning

confidence: 96%

Symmetry-adapted formulation of the combined G-particle-hole hypervirial equation and Hermitian operator method

et al. 2014

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High accuracy energies of low-lying excited states, in molecular systems, have been determined by means of a procedure which combines the G-particle-hole Hypervirial (GHV) equation method [Alcoba et al. Int. J. Quantum Chem. 109:3178 (2009)] and the Hermitian Operator (HO) one [Bouten et al. Nucl. Phys. A 202:127 (1973)]. This paper reports a suitable strategy to introduce the point group symmetry within the framework of the combined GHV-HO method, what leads to an improvement of the computational efficiency. The resulting symmetry-adapted formulation has been applied to illustrate the computer timings and the hardware requirements in selected chemical systems of several geometries.

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“…He applied his methodology to several electronic systems obtaining excellent results. ,,,− The main advantages of this approach are that the ACSE does not depend on the 4-RDM and that the N -representability properties of the 2-RDM are practically preserved during the iterative process. Motivated by this author’s work, some of the authors of this manuscript have recently studied the properties of the hypervirial of the two-body correlation operator or, equivalently, the G -particle−hole hypervirial (GHV) equation. − The particular interest of this approach lies in that satisfying the GHV equation implies that the ACSE is also fulfilled while solving the ACSE does not guarantee that the GHV equation is also satisfied; that is, the GHV equation is a more demanding condition than the ACSE. ,, …”

Section: Introductionmentioning

confidence: 99%

“…53,13,61 Following the ideas reported by Kutzelnigg for the solution of the hypervirials of density operators 32,62,63 and by Mazziotti for the solution of the ACSE, 52-55 a very efficient iterative method for solving the GHV equation has been developed. 53,14,61 The accuracy of the results obtained with this method when studying singlet ground-and excited-states with weak to moderate multiconfigurational character of a set of atoms and molecules was excellent compared to the equivalent full configuration interaction (FCI) quantities. 53,14,61 The purpose of the current work is to investigate the behavior of the GHV methodology in the study of highspin doublet and triplet states occurring in a variety of systems.…”

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confidence: 99%

Optimized Solution Procedure of the G-Particle−Hole Hypervirial Equation for Multiplets: Application to Doublet and Triplet States

et al. 2011

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Highly accurate descriptions of the correlated electronic structure of atoms and molecules in singlet states have recently been directly obtained within the framework of the G-particle-hole hypervirial (GHV) equation method, without any reference to the wave function [Int. J. Quantum Chem. 2009, 109, 3170; ibid. 2011, 111, 245]. Here, the GHV method is optimized and applied to the direct study of doublet and triplet atomic and molecular states. A new set of spin-representability conditions for triplet states has been derived and is also reported here. The results obtained with this optimized version of the GHV method are compared with those yielded by several standard wave function methods. This analysis shows that the GHV energies are more accurate than those obtained with a single-double excitation configuration interaction as well as with a coupled-cluster singles and doubles treatment. Moreover, the resulting 2-body matrices closely satisfy a set of stringent N- and spin-representability conditions.

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Some theoretical questions about the G‐particle‐hole hypervirial equation

Abstract: By applying a matrix contracting mapping, involving the G-particle-hole operator, to the matrix representation of the N-electron density hypervirial equation, one obtains the G-particle-hole hypervirial (GHV) equation (Alcoba, et al., Int J Quant Chem 2009, 109, 3178)

Cited by 13 publications

References 49 publications

Exploiting the nearsightedness principle within the framework of the anti‐Hermitian contracted Schrödinger equation

Exploiting the nearsightedness principle within the framework of the anti‐Hermitian contracted Schrödinger equation

Symmetry-adapted formulation of the combined G-particle-hole hypervirial equation and Hermitian operator method

Optimized Solution Procedure of the G-Particle−Hole Hypervirial Equation for Multiplets: Application to Doublet and Triplet States

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