Polarization Propagator Calculations

Oddershede, Jens

doi:10.1016/s0065-3276(08)60240-3

Cited by 359 publications

(142 citation statements)

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“…It has been shown by Oddershede and Jørgensen 47,59 that if the Hartree-Fock wave function is used to solve the RPA Eq.…”

Section: Correlation Energy In the Random Phase Approximationmentioning

confidence: 99%

“…[90][91][92] Namely, the condition that 1 Y 1 X T = − 3 Y 3 X T , which arises from the condition that the wave function is an eigenfunction of the spin-squared operator S 2 with eigenvalue zero, is not fulfilled. 47 Because of this triplet excitation energies, in contrast to singlet excitation energies, within the NRPA (timedependent Hartree-Fock) are often poor [93][94][95][96] and it has been stated by Chambaud et al that in fact triplet instabilities occur in any π -electronic system like ethylene or benzene. 97 While one possibility to overcome this deficiency is to use higher-order RPA approaches 45,47,[55][56][57][58][59][60][61] …”

Section: Correlation Energy In the Random Phase Approximationmentioning

confidence: 99%

“…47,98 Szabo and Ostlund have shown that none of the above given expressions for the RPA correlation energy fulfill the desired criterion that the long-range behaviour of the dispersive part of the interaction energy between two separate closed-shell molecules is described on the coupled HartreeFock level, i.e., the interaction contribution does not reduce to the dispersion energy on the time-dependent Hartree-Fock level for the methods NRPA1, NRPA2, and NRPA3. 46,99 Because of this Szabo and Ostlund proposed the following expression for the RPA correlation energy:…”

Section: Correlation Energy In the Random Phase Approximationmentioning

confidence: 99%

“…II it will be shown that the extraction of the correlation energy from the RPA is by far not unique and a number of RPA methods were developed that are exact in second order of perturbation theory, but differ in third-order. We here refer to these methods as "normal" RPA (NRPA) methods 46,55 in order to point out the difference to so called higher RPA methods 45,47,[55][56][57][58][59][60][61] (like SOPPA, second-order polarisation propagator approximation 47,62 ) in which the wave function that enters the RPA equations also contains double excitations.…”

Section: Introductionmentioning

confidence: 99%

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Third-order corrections to random-phase approximation correlation energies

Heßelmann

2011

The Journal of Chemical Physics

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Several random-phase approximation (RPA) correlation methods were compared in third order of perturbation theory. While all of the considered approaches are exact in second order of perturbation theory, it is found that their corresponding third-order correlation energy contributions strongly differ from the exact third-order correlation energy contribution due to missing interactions of the particle-particle−hole-hole type. Thus a simple correction method is derived which makes the different RPA methods also exact to third-order of perturbation theory. By studying the reaction energies of 16 chemical reactions for 21 small organic molecules and intermolecular interaction energies of 23 intermolecular complexes comprising weakly bound and hydrogen-bridged systems, it is found that the third-order correlation energy correction considerably improves the accuracy of RPA methods if compared to coupled-cluster singles doubles with perturbative triples as a reference.

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“…It has been shown by Oddershede and Jørgensen 47,59 that if the Hartree-Fock wave function is used to solve the RPA Eq.…”

Section: Correlation Energy In the Random Phase Approximationmentioning

confidence: 99%

Section: Correlation Energy In the Random Phase Approximationmentioning

confidence: 99%

Section: Correlation Energy In the Random Phase Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Third-order corrections to random-phase approximation correlation energies

Heßelmann

2011

The Journal of Chemical Physics

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“…See Ref. 1 and references therein for discussion of this point. In order to obtain X and Y once we have T, we can use Eqn.…”

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confidence: 99%

The ground state correlation energy of the random phase approximation from a ring coupled cluster doubles approach

Scuseria¹,

Henderson²,

Sorensen³

2008

The Journal of Chemical Physics

296

336

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We present an analytic proof demonstrating the equivalence between the Random Phase Approximation (RPA) to the ground state correlation energy and a ring-diagram simplification of the Coupled Cluster Doubles (CCD) equations. In the CCD framework, the RPA equations can be solved in O(N 4 ) computational effort, where N is proportional to the number of basis functions.There has recently been a revival of interest in RPA in the quantum chemistry community. The RPA is popular for calculations of excitation energies both in finite systems 1,2 and in solids, 3,4 and is related to time-dependent density functional theory. 5,6,7 As a technique for describing electronic correlations, RPA has significant advantages, particularly for those interested in density functional theory. It describes dispersion and van der Waals interactions correctly, 8,9 and is exact for long-range correlations. 10 Left-right static correlations seem to be properly described by RPA, 11 and RPA fixes the pathologies of nonlocal Hartree-Fock-type exchange in metallic systems. Readers interested in details about RPA for ground state correlation can refer to the recent paper by Furche 12 where he discusses an interesting simplification to reduce the computational cost of RPA correlation and provides ample background information about RPA. Note that his work focuses on direct RPA, in which the exchange terms are neglected; as discussed later in this communication, this is the form of RPA most useful in the context of density functional theory.A connection between the RPA correlation energy and a ring diagram approximation to CCD was first mentioned by Freeman in his 1977 paper. 13 Very recently, A. Grüneis and G. Kresse reproduced this evidence and found numerical proof of the equivalence between these two approaches. 14 Here, we offer an analytic proof that these two problems yield identical correlation energies. To the best of our knowledge, no such formal proof has been given before.As a method for calculating electronic excitation spectra, RPA requires the solution ofThe matrices A, B, X, and Y are all ov × ov, where o and v are respectively the number of occupied and unoccupied spin-orbitals. The eigenvalue problem above can be completed by noting that if Xi Yi is an eigenvector with eigenvalue ω i , then Yi Xi is also an eigenvector, with eigenvalue −ω i . In the (real) canonical spin-orbital basis we use throughout this letter, we haveHere, ǫ p is a diagonal element of the Fock operator. Indices i, j, k, and l indicate occupied spin-orbitals, while a, b, c, d indicate unoccupied spin-orbitals. For arbitrary spin-orbitals p, q, r, and s, the two-electron integral pq rs is defined bywhere x is a combined space and spin electron coordinate. The RPA correlation energy can be obtained by considering two harmonic excitation energy problems: 12,15 RPA and the Tamm-Dancoff approximation (TDA) thereto, which sets B = 0 and thus solvesIn the quantum chemistry community, TDA is also known as configuration interaction singles (CIS). While TDA includes onl...

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Size consistency of an algebraic propagator approach

Schirmer

Mertins

1996

Int J of Quantum Chemistry

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Polarization Propagator Calculations

Cited by 359 publications

References 274 publications

Third-order corrections to random-phase approximation correlation energies

Third-order corrections to random-phase approximation correlation energies

The ground state correlation energy of the random phase approximation from a ring coupled cluster doubles approach

Size consistency of an algebraic propagator approach

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