Time-Dependent Hartree—Fock Theory for Molecules

McLachlan, Anton; Ball, Michael

doi:10.1103/revmodphys.36.844

Cited by 444 publications

(287 citation statements)

References 16 publications

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“…It has been shown that the earliest RPA methods, termed in this work NRPA1 (and which is identical to the ring coupled-cluster doubles method) from McLachlan and Ball 43,88 and NRPA2 from Fukuda et al 89 , yield very poor total energies and energy differences, though, among the other "normal" RPA methods presented they are the most complete from the perturbation theory point of view since they contain half of (NRPA1) respectively all (NRPA2) particle-hole (ph) contributions in third order of perturbation theory. The numerical analysis from Sec.…”

Section: Discussionmentioning

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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Section: Discussionmentioning

confidence: 99%

“…43,88 The RPA correlation energy, which will be termed as NRPA1 correlation energy in the following and which is identical to the ring coupledcluster doubles correlation energy (rCCD), 52 is then given by…”

Section: Correlation Energy In the Random Phase Approximationmentioning

confidence: 99%

Third-order corrections to random-phase approximation correlation energies

Heßelmann

2011

The Journal of Chemical Physics

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“…6 Not surprisingly, this eigenvalue problem has the same structure that arises in the time-dependent Hartree-Fock theory, 7,8 and the dimension of the resulting matrix ͑the Liouvillian͒ is twice the product of the number of occupied ͑valence͒ states N v with the number of unoccupied ͑conduction͒ states N c . The calculation of the Liouvillian is by itself a hard task that is often tackled directly in terms of the unperturbed KS eigenpairs.…”

Section: Introductionmentioning

confidence: 99%

Turbo charging time-dependent density-functional theory with Lanczos chains

Rocca

Gebauer

Saad

et al. 2008

The Journal of Chemical Physics

248

309

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We introduce a new implementation of time-dependent density-functional theory which allows the entire spectrum of a molecule or extended system to be computed with a numerical effort comparable to that of a single standard ground-state calculation. This method is particularly well suited for large systems and/or large basis sets, such as plane waves or real-space grids. By using a super-operator formulation of linearized timedependent density-functional theory, we first represent the dynamical polarizability of an interacting-electron system as an off-diagonal matrix element of the resolvent of the Liouvillian super-operator. One-electron operators and density matrices are treated using a representation borrowed from time-independent density-functional perturbation theory, which permits to avoid the calculation of unoccupied Kohn-Sham orbitals. The resolvent of the Liouvillian is evaluated through a newly developed algorithm based on the non-symmetric Lanczos method. Each step of the Lanczos recursion essentially requires twice as many operations as a single step of the iterative diagonalization of the unperturbed Kohn-Sham Hamiltonian. Suitable extrapolation of the Lanczos coefficients allows for a dramatic reduction of the number of Lanczos steps necessary to obtain well converged spectra, bringing such number down to hundreds (or a few thousands, at worst) in typical plane-wave pseudopotential applications. The resulting numerical workload is only a few times larger than that needed by a ground-state Kohn-Sham calculation for a same system. Our method is demonstrated with the calculation of the spectra of benzene, C60 fullerene, and of chlorofyll a.

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“…by taking the contrac-tion of the dRPA response function with non-antisymmetrized two-electron integrals (dRPA-I), or by a full consideration of non-local exchange, when antisymmetrized two-electron integrals are contracted with the RPAx response function matrix elements (RPAx-II). This latter approach has been followed by some early works in quantum chemistry, based on Hartree-Fock orbitals [29,[35][36][37], while dRPA is usually the method of choice in the density functional context, starting from Kohn-Sham orbitals. Partial inclusion/omission of nonlocal exchange leads to "mixed" methodologies, like dRPA-II and RPAx-I.…”

Section: Introductionmentioning

confidence: 99%

Dielectric Matrix Formulation of Correlation Energies in the Random Phase Approximation: Inclusion of Exchange Effects

Mussard¹,

Rocca²,

Jansen

et al. 2016

J. Chem. Theory Comput.

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Starting from the general expression for the ground state correlation energy in the adiabatic connection fluctuation dissipation theorem (ACFDT) framework, it is shown that the dielectric matrix formulation, which is usually applied to calculate the direct random phase approximation (dRPA) correlation energy, can be used for alternative RPA expressions including exchange effects. Within this famework, the ACFDT analog of the second order screened exchange (SOSEX) approximation leads to a logarithmic formula for the correlation energy similar to the direct RPA expression. Alternatively, the contribution of the exchange can be included in the kernel used to evaluate the response functions. In this case the use of an approximate kernel is crucial to simplify the formalism and to obtain a correlation energy in logarithmic form. Technical details of the implementation of these methods are discussed and it is shown that one can take advantage of density fitting or Cholesky decomposition techniques to improve the computational efficiency; a discussion on the numerical quadrature made on the frequency variable is also provided. A series of test calculations on atomic correlation energies and molecular reaction energies shows that exchange effects are instrumental to improve over direct RPA results.

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Time-Dependent Hartree—Fock Theory for Molecules

Cited by 444 publications

References 16 publications

Third-order corrections to random-phase approximation correlation energies

Third-order corrections to random-phase approximation correlation energies

Turbo charging time-dependent density-functional theory with Lanczos chains

Dielectric Matrix Formulation of Correlation Energies in the Random Phase Approximation: Inclusion of Exchange Effects

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