Self-consistent double-hybrid density-functional theory using the optimized-effective-potential method

Śmiga, Szymon; Franck, Odile; Mussard, Bastien; Buksztel, Adam; Grabowski, Ireneusz; Luppi, E.; Toulouse, Julien

doi:10.1063/1.4964319

Cited by 30 publications

(54 citation statements)

References 93 publications

(115 reference statements)

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“…However, the ground-state energies are not improved for functionals depending on virtual orbitals. 41–43 The reason for this failure is that the orbitals are only optimized in the space of υ -representable densities by a local potential, the OEP, rather than the whole space. In contrast, the orbitals from OO are optimized in the whole space.…”

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confidence: 99%

Generalized Optimized Effective Potential for Orbital Functionals and Self-Consistent Calculation of Random Phase Approximations

Jin

Zhang

Chen

et al. 2017

J. Phys. Chem. Lett.

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A new self-consistent procedure for calculating the total energy with an orbital-dependent density functional approximation (DFA), the generalized optimized effective potential (GOEP), is developed in the present work. The GOEP is a nonlocal Hermitian potential that delivers the sets of occupied and virtual orbitals and minimizes the total energy. The GOEP optimization leads to the same minimum as does the orbital optimization. The GOEP method is promising as an effective optimization approach for orbital-dependent functionals, as demonstrated for the self-consistent calculations of the random phase approximation (RPA) to the correlation functionals in the particle—hole (ph) and particle—particle (pp) channels. The results show that the accuracy in describing the weakly interacting van der Waals systems is significantly improved in the self-consistent calculations. In particular, the important single excitations contribution in non-self-consistent RPA calculations can be captured self-consistently through the GOEP optimization, leading to orbital renormalization, without using the single excitations in the energy functional.

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confidence: 99%

Generalized Optimized Effective Potential for Orbital Functionals and Self-Consistent Calculation of Random Phase Approximations

Jin

Zhang

Chen

et al. 2017

J. Phys. Chem. Lett.

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“…For the m = ∞ case, this is the MP2 method, we should obtain the potential similar in shape to the OEP2-sc method, 172 which slightly overestimates the reference one. The opposite trend is observed when the calculations are performed in the full KS framework 162 , 163 (see Figures S1 and S3 in the Supporting Information 147 ). The fully local potential affect also the unoccupied KS orbitals what in general have a large impact on the functional performance (see the discussion in this context in Sec 4.1. of ref ( 163 )).…”

Section: Resultsmentioning

confidence: 92%

“… 193 All interaction energies have been calculated with counterpoise (CP) corrections to remove the basis set superposition error (BSSE). using the formalism developed in refs ( 162 ). and ( 163 ) we have computed the correlation potentials for the Ne atom and CO molecule (see Section 3.2.3 ).…”

Section: Computational Detailsmentioning

confidence: 99%

Generalizing Double-Hybrid Density Functionals: Impact of Higher-Order Perturbation Terms

Jana

Śmiga

Constantin

et al. 2020

J. Chem. Theory Comput.

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Connections between the Görling–Levy (GL) perturbation theory and the parameters of double-hybrid (DH) density functional are established via adiabatic connection formalism. Moreover, we present a more general DH density functional theory, where the higher-order perturbation terms beyond the second-order GL2 one, such as GL3 and GL4, also contribute. It is shown that a class of DH functionals including previously proposed ones can be formed using the present construction. Based on the proposed formalism, we assess the performance of higher-order DH and long-range corrected DH formed on the Perdew–Burke–Ernzerhof (PBE) semilocal functional and second-order GL2 correlation energy. The underlying construction of DH functionals based on the generalized many-body perturbation approaches is physically appealing in terms of the development of the non-local forms using more accurate and sophisticated semilocal functionals.

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“…The orbitaloptimization is not trivial to implement, but leads to a better description of electron affinities, reaction barrier heights, and radical bond dissociation. [30][31][32][33] We hope to compare UW12 hybrids with orbital-optimized double-hybrids in the future Other disadvantages to using conventional MP2 include the explicit summation over the unoccupied Kohn-Sham orbitals {φ a } in Eqn. 11.…”

Section: Limitations Of Existing Hybrid and Double-hybrid Functionalsmentioning

confidence: 99%

Wavefunction-like Correlation Model for Use in Hybrid Density Functionals

Wiles

Manby

2018

J. Chem. Theory Comput.

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We present Unsöld-W12 (UW12), an approximation to the correlation energy of molecules that is an explicit functional of the single-particle reduced-density matrix. The approximation resembles one part of modern explicitly correlated second-order Møller-Plesset (MP2) theory and is intended as an alternative to MP2 in double-hybrid exchange-correlation functionals. Orbital optimization with UW12 is straightforward, and the UW12 energy is evaluated without a double summation over unoccupied orbitals, leading to a faster basis-set convergence than is seen in double-hybrid functionals. We suggest a one-parameter hybrid exchange-correlation functional XCH-BLYP-UW12. XCH-BLYP-UW12 is similar to double-hybrid functionals, but contains UW12 correlation instead of MP2 correlation. We find that XCH-BLYP-UW12 is more accurate than the existing double-hybrid functional B2-PLYP for small-molecule main-group reaction barrier heights and has roughly the same accuracy as the existing hybrid functional B3LYP for atomization energies.

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Self-consistent double-hybrid density-functional theory using the optimized-effective-potential method

Cited by 30 publications

References 93 publications

Generalized Optimized Effective Potential for Orbital Functionals and Self-Consistent Calculation of Random Phase Approximations

Generalized Optimized Effective Potential for Orbital Functionals and Self-Consistent Calculation of Random Phase Approximations

Generalizing Double-Hybrid Density Functionals: Impact of Higher-Order Perturbation Terms

Wavefunction-like Correlation Model for Use in Hybrid Density Functionals

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