Convergence enhancement in the iterative solution of the second‐order contracted Schrödinger equation

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

doi:10.1002/qua.20441

Cited by 37 publications

(39 citation statements)

References 60 publications

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“…This process is referred to in the following as dynamical purification. Several types of purifications have been discussed in literature and are used primarily for the iterative solution of the second order contracted Schrödinger equation to find a self-consistent N -representable solution for the ground state of molecules [52,53].…”

Section: Contraction-consistent Reconstruction Of the 3-rdmmentioning

confidence: 99%

Propagating two-particle reduced density matrices without wave functions

et al. 2015

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Describing time-dependent many-body systems where correlation effects play an important role remains a major theoretical challenge. In this paper we develop a time-dependent many-body theory that is based on the two-particle reduced density matrix (2-RDM). We develop a closed equation of motion for the 2-RDM employing a novel reconstruction functional for the three-particle reduced density matrix (3-RDM) that preserves norm, energy, and spin symmetries during time propagation. We show that approximately enforcing N -representability during time evolution is essential for achieving stable solutions. As a prototypical test case which features long-range Coulomb interactions we employ the one-dimensional model for lithium hydride (LiH) in strong infrared laser fields. We probe both one-particle observables such as the time-dependent dipole moment and two-particle observables such as the pair density and mean electron-electron interaction energy. Our results are in very good agreement with numerically exact solutions for the N -electron wavefunction obtained from the multiconfigurational time-dependent Hartree-Fock method.

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Section: Contraction-consistent Reconstruction Of the 3-rdmmentioning

confidence: 99%

Propagating two-particle reduced density matrices without wave functions

et al. 2015

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“…It permitted Colmenero and Valdemoro to report in 1994 21 the first iterative solution of the 2‐CSE. This started a successful line of work which was mainly developed by the groups lead by Nakatsuji, Valdemoro, Mazziotti, Harriman, and Kutzelnigg 22–42.…”

Section: Introductionmentioning

confidence: 99%

The correlation contracted Schrödinger equation: An accurate solution of the G‐particle‐hole hypervirial

Alcoba

Valdemoro

Tel

et al. 2009

Int J of Quantum Chemistry

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“…This important property is counterbalanced by the fact that it depends on the 4-CM. On the other hand, it is far more convenient to solve this 3-order GHV equation than the CCSE/2-CSE since, as will be seen below, the iterative procedure for solving this hypervirial equation preserves the N-representability of the resulting solutions, which is not the case in the CCSE/2-CSE methods where an N-representability purification procedure must be combined with the iterative process [21,27,31,33,43,48,[63][64][65]. As mentioned earlier, although a similar theorem has not yet been demonstrated for the (2-order) GHV equation, the results it yielded have proved to be highly accurate, which is why in what follows we will focus on this second-order equation.…”

Section: The Anti-hermitian Part Of the 3-order Ccsementioning

confidence: 97%

“…Until now, and as a provisional solution, the 3-CM elements were evaluated indirectly [38] in terms of an approximated 3-order cumulant [28,[31][32][33][34]37]. At present, to improve both the method accuracy as well as its performance rate, we deem necessary-although we realize that it is a complex and difficult task-to change the strategy used previously for constructing the different GHV terms and to attempt to evaluate directly the 3-CM in terms of the 2-CM.…”

Section: Introductionmentioning

confidence: 99%

Theoretical and applicative properties of the correlation and G‐particle‐hole matrices

Valdemoro

Alcoba

Tel

et al. 2009

Int J of Quantum Chemistry

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We have recently (Valdemoro et al., Sixth International Congress of theInternational Society for Theoretical Chemical Physics, 2008; Alcoba et al., Int J Quantum Chem, in press) reported the form of the G-particle-hole hypervirial equation, which can be identified with the anti-Hermitian part of the correlation contracted Schrödinger equation (Alcoba, Phys Rev A, 2002, 65, 032519), as a tool to obtain the second-order reduced density matrix of an N-electron system without previous knowledge of the wave-function. The results which have been obtained when solving the G-particle-hole hypervirial equation with an iterative method also described in (Valdemoro et al., Sixth International Congress of the International Society for Theoretical Chemical Physics, 2008; Alcoba et al., Int J Quantum Chem, in press) have been highly accurate. The convergence of these test calculations has been very smooth, though rather slow. One of the factors which determines the performance of the method is the accuracy with which the 3-order correlation matrices (3-CM) involved in the calculations are approximated. It is, therefore, necessary to optimize to the utmost the construction algorithms of these 3-order matrices in terms of the 2-CM. In this article, the main theoretical features of the p-CM are described. Also, some aspects of the correlation contracted Schrödinger equation and of the G-particle-hole hypervirial equation are revisited. A new theorem, concerning the sufficiency of the hypervirial of the 3-order correlation operator to guarantee a correspondence between its solution and that of the Schrödinger equation, and some preliminary results concerning the constructing algorithms of the 3-CM in terms of the 2-CM, are reported in the second part of this article.

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Convergence enhancement in the iterative solution of the second‐order contracted Schrödinger equation

Cited by 37 publications

References 60 publications

Propagating two-particle reduced density matrices without wave functions

Propagating two-particle reduced density matrices without wave functions

The correlation contracted Schrödinger equation: An accurate solution of the G‐particle‐hole hypervirial

Theoretical and applicative properties of the correlation and G‐particle‐hole matrices

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