On finite basis set implementation of the exchange-only optimized effective potential method

Glushkov, V. N.; Fesenko, S. I.; Polatoglou, Hariton Μ.

doi:10.1007/s00214-009-0624-y

Cited by 18 publications

(12 citation statements)

References 47 publications

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“…Some computational difficulties have been encountered in the application of the LCAO OEP calculations both to the exchange-only energy functional 25,58,[68][69][70][71][72][73][74][75][76] and with correlation included, 7,8,35 which is a manifestation of the wellknown instability associated with numerical solutions of Fredholm integral equations of the first kind. In order to obtain numerical solutions of reasonable accuracy for this class of equations, a careful choice of Gaussian basis sets is required.…”

Section: Computational Detailsmentioning

confidence: 99%

“…4,8,9,25,67 These issues have been discussed extensively in the literature and several schemes have been proposed for managing this problem. 7,58,59,[68][69][70][71][72][73][74][75][76] In addition, for correlated OEP calculations, such as those considered in this work, we must take care to ensure that the basis sets used are suitable for the description of correlation effects, akin to those employed in standard wave function based calculations. To accommodate these considerations at reasonable computational cost, an even tempered 20s10p2d basis was employed for He atom and the uncontracted ROOS-ATZP (Ref.…”

Section: Computational Detailsmentioning

confidence: 99%

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Comparing ab initio density-functional and wave function theories: The impact of correlation on the electronic density and the role of the correlation potential

Grabowski

Teale²,

Śmiga³

et al. 2011

The Journal of Chemical Physics

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The framework of ab initio density-functional theory (DFT) has been introduced as a way to provide a seamless connection between the Kohn-Sham (KS) formulation of DFT and wave-function based ab initio approaches [R. J. Bartlett, I. Grabowski, S. Hirata, and S. Ivanov, J. Chem. Phys. 122, 034104 (2005)]. Recently, an analysis of the impact of dynamical correlation effects on the density of the neon atom was presented [K. Jankowski, K. Nowakowski, I. Grabowski, and J. Wasilewski, J. Chem. Phys. 130, 164102 (2009)], contrasting the behaviour for a variety of standard density functionals with that of ab initio approaches based on second-order Møller-Plesset (MP2) and coupled cluster theories at the singles-doubles (CCSD) and singles-doubles perturbative triples [CCSD(T)] levels. In the present work, we consider ab initio density functionals based on second-order many-body perturbation theory and coupled cluster perturbation theory in a similar manner, for a range of small atomic and molecular systems. For comparison, we also consider results obtained from MP2, CCSD, and CCSD(T) calculations. In addition to this density based analysis, we determine the KS correlation potentials corresponding to these densities and compare them with those obtained for a range of ab initio density functionals via the optimized effective potential method. The correlation energies, densities, and potentials calculated using ab initio DFT display a similar systematic behaviour to those derived from electronic densities calculated using ab initio wave function theories. In contrast, typical explicit density functionals for the correlation energy, such as VWN5 and LYP, do not show behaviour consistent with this picture of dynamical correlation, although they may provide some degree of correction for already erroneous explicitly density-dependent exchange-only functionals. The results presented here using orbital dependent ab initio density functionals show that they provide a treatment of exchange and correlation contributions within the KS framework that is more consistent with traditional ab initio wave function based methods.

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Section: Computational Detailsmentioning

confidence: 99%

Section: Computational Detailsmentioning

confidence: 99%

Comparing ab initio density-functional and wave function theories: The impact of correlation on the electronic density and the role of the correlation potential

Grabowski

Teale²,

Śmiga³

et al. 2011

The Journal of Chemical Physics

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show abstract

“…21,22 Unfortunately, the structure of the OEP equation is such that it is not well-suited for solving in finite (Gaussian) basis sets. [23][24][25][26][27][28][29][30][31][32][33] There are two pragmatic alternatives to the OEP method in basis-set calculations with orbital-dependent functionals. One is to use OEP approximations such as the Krieger-Li-Iafrate 34 (KLI) potential, the Becke-Johnson potential, 35 and others.…”

Section: Introductionmentioning

confidence: 99%

Hierarchy of model Kohn–Sham potentials for orbital-dependent functionals: A practical alternative to the optimized effective potential method

Kohut

Ryabinkin

Staroverov

2014

The Journal of Chemical Physics

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We describe a method for constructing a hierarchy of model potentials approximating the functional derivative of a given orbital-dependent exchange-correlation functional with respect to electron density. Each model is derived by assuming a particular relationship between the self-consistent solutions of Kohn-Sham (KS) and generalized Kohn-Sham (GKS) equations for the same functional. In the KS scheme, the functional is differentiated with respect to density, in the GKS scheme--with respect to orbitals. The lowest-level approximation is the orbital-averaged effective potential (OAEP) built with the GKS orbitals. The second-level approximation, termed the orbital-consistent effective potential (OCEP), is based on the assumption that the KS and GKS orbitals are the same. It has the form of the OAEP plus a correction term. The highest-level approximation is the density-consistent effective potential (DCEP), derived under the assumption that the KS and GKS electron densities are equal. The analytic expression for a DCEP is the OCEP formula augmented with kinetic-energy-density-dependent terms. In the case of exact-exchange functional, the OAEP is the Slater potential, the OCEP is roughly equivalent to the localized Hartree-Fock approximation and related models, and the DCEP is practically indistinguishable from the true optimized effective potential for exact exchange. All three levels of the proposed hierarchy require solutions of the GKS equations as input and have the same affordable computational cost.

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“…Several attempts have been made to overcome these issues [13][14][15][16][17][18][19][20] but with limited success so far. As a result and despite promise, interest in OEP has diminished.…”

Section: Introductionmentioning

confidence: 99%

Nonanalyticity of the optimized effective potential with finite basis sets

Gidopoulos

Lathiotakis

2012

Phys. Rev. A

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On finite basis set implementation of the exchange-only optimized effective potential method

Cited by 18 publications

References 47 publications

Comparing ab initio density-functional and wave function theories: The impact of correlation on the electronic density and the role of the correlation potential

Comparing ab initio density-functional and wave function theories: The impact of correlation on the electronic density and the role of the correlation potential

Hierarchy of model Kohn–Sham potentials for orbital-dependent functionals: A practical alternative to the optimized effective potential method

Nonanalyticity of the optimized effective potential with finite basis sets

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