Making the random phase approximation to electronic correlation accurate

Grüneis, Andreas; Marsman, Martijn; Harl, Judith; Schimka, Laurids; Kresse, Georg

doi:10.1063/1.3250347

Cited by 245 publications

(285 citation statements)

References 31 publications

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“…(5) and (6) are neglected. 70 While dRPA misses the exchange part of the second order correlation energy (diagram (1b) in Figure 1), it can be obtained if the dRPA amplitudes T dRPA = Y dRPA X −1 dRPA are contracted with antisymmetrised two-electron integrals. The method is termed as second order screened exchange (SO-SEX) and the correlation energy reads 70…”

Section: Correlation Energy In the Random Phase Approximationmentioning

confidence: 99%

“…[63][64][65][66][67][68][69][70][71][72][73][74][75][76] The use of the Kohn-Sham determinant instead of the Hartree-Fock determinant as the reference determinant in RPA methods might be advantageous in order to account implicitly for single excitations that are commonly absent in Hartree-Fock based RPA methods. It has been shown for some small molecules that, depending however on the underlying exchange-correlation potential, Kohn-Sham orbitals are closer to Brueckner orbitals than Hartree-Fock orbitals 77 (see, however, Ref.…”

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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Section: Correlation Energy In the Random Phase Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Third-order corrections to random-phase approximation correlation energies

Heßelmann

2011

The Journal of Chemical Physics

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“…Before exploring another alternative, which consists in an analytical integration according to the interaction strength parameter, the reader must bear in mind the close analogy of dRPA-IIa and the so-called SOSEX (second order screened exchange) approximation [11,44], usually defined in the framework of a drCCD (direct ring coupled cluster doubles) theory. Although the above ACFDT-based expression is not strictly equal to the drCCD-based SOSEX, their difference appears only at the third order of perturbation, as was demonstrated in Ref.…”

Section: B Rpa+sosexmentioning

confidence: 99%

“…with the dRPA polarization propagator being contracted with a list of fully antisymmetrized two-electron integrals [11,14]. We can mention, in this aspect, the SOSEX (second order screened exchange) corrections, which have been formulated originally within the rCCD formalism.…”

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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“…Studies which have explored this aspect for RPA + EXX total-energy calculations have usually focused on the differences between LDA and GGA or on the effect of including Hartree-Fock exchange [22,[34][35][36][37][38]. In most cases, the initial choice of XC potential has been found to play only a minor role; a notable exception is the study of cerium in Ref.…”

Section: Introductionmentioning

confidence: 99%

Hubbard-Ucorrected Hamiltonians for non-self-consistent random-phase approximation total-energy calculations: A study of ZnS,TiO2, and NiO

Patrick

Thygesen

2016

Phys. Rev. B

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In non-self-consistent calculations of the total energy within the random-phase approximation (RPA) for electronic correlation, it is necessary to choose a single-particle Hamiltonian whose solutions are used to construct the electronic density and noninteracting response function. Here we investigate the effect of including a Hubbard-U term in this single-particle Hamiltonian, to better describe the on-site correlation of 3d electrons in the transition metal compounds ZnS, TiO 2 , and NiO. We find that the RPA lattice constants are essentially independent of U , despite large changes in the underlying electronic structure. We further demonstrate that the non-selfconsistent RPA total energies of these materials have minima at nonzero U . Our RPA calculations find the rutile phase of TiO 2 to be more stable than anatase independent of U , a result which is consistent with experiments and qualitatively different from that found from calculations employing U -corrected (semi)local functionals. However we also find that the +U term cannot be used to correct the RPA's poor description of the heat of formation of NiO.

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Making the random phase approximation to electronic correlation accurate

Cited by 245 publications

References 31 publications

Third-order corrections to random-phase approximation correlation energies

Third-order corrections to random-phase approximation correlation energies

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

Hubbard-Ucorrected Hamiltonians for non-self-consistent random-phase approximation total-energy calculations: A study of ZnS,TiO2, and NiO

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