Long-range-corrected hybrids including random phase approximation correlation

Janesko, Benjamin G.; Henderson, Thomas M.; Scuseria, Gustavo E.

doi:10.1063/1.3090814

Cited by 175 publications

(212 citation statements)

References 46 publications

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“…This has been repeatedly observed in calculations using Dunning correlationconsistent basis sets [35] for second-order perturbation * odile.franck@etu.upmc.fr † bastien.mussard@upmc.fr ‡ eleonora.luppi@upmc.fr § julien.toulouse@upmc.fr theory [4,6,10,15,16], coupled-cluster theory [17] and random-phase approximations [22,23,25,27,31]. The physical reason for this reduced sensitivity to the basis is easy to understand.…”

Section: Introductionmentioning

confidence: 95%

“…The long-range correlation energy can also be approximated beyond second-order perturbation theory by coupledcluster [17] or random-phase [22,23,[28][29][30] approximations. Beyond perturbation theory approaches, Eq.…”

Section: Range-separated Density-functional Theorymentioning

confidence: 99%

“…The strategy of range-separated DFT consists in separating the Coulomb electron-electron interaction into long-range and shortrange components, and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. In particular, for describing systems with van der Waals dispersion interactions, it is appropriate to use methods based on many-body perturbation theory for the longrange part such as second-order perturbation theory [4][5][6][7][8][9][10][11][12][13][14][15][16], coupled-cluster theory [17][18][19][20][21], or random-phase approximations [22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

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Basis convergence of range-separated density-functional theory

Franck

Mussard

Luppi

et al. 2015

The Journal of Chemical Physics

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Range-separated density-functional theory is an alternative approach to Kohn-Sham densityfunctional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components, and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the oneelectron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with the cardinal number X of the Dunning basis sets cc-p(C)VXZ, and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.

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Section: Introductionmentioning

confidence: 95%

Section: Range-separated Density-functional Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Basis convergence of range-separated density-functional theory

Franck

Mussard

Luppi

et al. 2015

The Journal of Chemical Physics

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“…In the literature we can find several studies of H 2 dissociation in the context of RPA. The influence of the reference orbitals has often been studied [6,21,54]. The use of unrestricted Kohn-Sham orbitals is thought to allow for some inclusion of static correlation in the description of the dissociation [6,54].…”

Section: Application To Reaction Energiesmentioning

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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“…Some examples of such functionals are already appearing in the literature. [81][82][83][84][85][86][87][88] Throughout our analysis, we excluded the O 3 molecule due to its multireference nature. As may be expected, its Table II. FIG.…”

Section: -7mentioning

confidence: 99%

Benchmarking density-functional-theory calculations of rotational g tensors and magnetizabilities using accurate coupled-cluster calculations

Lutnæs

Teale

Helgaker

et al. 2009

The Journal of Chemical Physics

121

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'Benchmarking density-functional-theory calculations of rotational g tensors and magnetizabilities using accurate coupled-cluster calculations. ', Journal of chemical physics., 131 (14 ). p. 144104.Further information on publisher's website: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. An accurate set of benchmark rotational g tensors and magnetizabilities are calculated using coupled-cluster singles-doubles ͑CCSD͒ theory and coupled-cluster single-doubles-perturbative-triples ͓CCSD͑T͔͒ theory, in a variety of basis sets consisting of ͑rotational͒ London atomic orbitals. The accuracy of the results obtained is established for the rotational g tensors by careful comparison with experimental data, taking into account zero-point vibrational corrections. After an analysis of the basis sets employed, extrapolation techniques are used to provide estimates of the basis-set-limit quantities, thereby establishing an accurate benchmark data set. The utility of the data set is demonstrated by examining a wide variety of density functionals for the calculation of these properties. None of the density-functional methods are competitive with the CCSD or CCSD͑T͒ methods. The need for a careful consideration of vibrational effects is clearly illustrated. Finally, the pure coupled-cluster results are compared with the results of density-functional calculations constrained to give the same electronic density. The importance of current dependence in exchange-correlation functionals is discussed in light of this comparison.

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Long-range-corrected hybrids including random phase approximation correlation

Cited by 175 publications

References 46 publications

Basis convergence of range-separated density-functional theory

Basis convergence of range-separated density-functional theory

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

Benchmarking density-functional-theory calculations of rotational g tensors and magnetizabilities using accurate coupled-cluster calculations

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