Rotational <i>g</i> Tensors Calculated Using Hybrid Exchange-Correlation Functionals with the Optimized Effective Potential Approach

Teale, Andrew M.; Helgaker, Trygve; Tozer, David J.

doi:10.1021/ct060038n

Cited by 14 publications

(1 citation statement)

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“…While the application of the OEP procedure to standard hybrid functionals including exchange 26,27 and their range-separated analogues 28 is straightforward, the development of correlation functionals compatible with a full complement of OEP exchange has proved more challenging. The most successful forms have resulted from the ab initio DFT approach of Bartlett et al 4,29 In this approach, the OEP method is applied to correlated energy expressions based on many-body and coupled-cluster perturbation theories applied to the KS system.…”

Section: Introductionmentioning

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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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: Introductionmentioning

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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On the use of the exact exchange optimized effective potential method for static response properties

Krykunov¹,

Ziegler²

2009

Int J of Quantum Chemistry

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ABSTRACT:In the present work, we question the notion that the modified Kohn-Sham orbital energies and smaller HOMO-LUMO gaps, produced from the exact exchange optimized effective potential (EXX-OEP) method, might significantly improve the paramagnetic contribution to the NMR chemical shifts compared with the regular Hartree-Fock (HF) scheme. First of all, it is shown analytically that if there is such a local potential that produces the HF energy, and the Kohn-Sham orbitals are obtained as a result of separate rotations of the occupied and virtual HF orbitals, any static magnetic property obtained from the coupled perturbed HF method will be identical to that obtained from the EXX-OEP approach. In fact the EXX-OEP method is equivalent to the improved virtual orbitals (IVO) scheme in which the energies of the virtual orbitals are modified by an effective potential. It is shown that the IVO procedure leaves static response properties unchanged. To test our analysis numerically we have employed several variants of the EXX-OEP method, based on the expansion of the local exchange potential into a linear combination of fit functions. The different EXX-OEP schemes have been used to calculate the NMR chemical shifts for a set of small molecules containing C, H, N, O, and F atoms. Comparison of the deviation between experimental and calculated chemical shifts from the HF, the EXX-OEP, and the common energy denominator approximation (CEDA) approximation to the EXX-OEP methods has shown that for carbon, hydrogen, and fluorine the EXX-OEP methods do not yield any improvement over the HF method. For nitrogen and oxygen we have found that the EXX-OEP performs better than the HF method. However, in the limit of infinite fit basis set and, as a consequence of it, a perfect fit of the HF potential the EXX-OEP and the HF methods would afford the same chemical shifts according to our theoretical analysis. Unfortunately, without a perfect fit the chemical shifts from the EXX-OEP method strongly depend on the fit convergence. In our opinion, the EXX-OEP method should not be used for response properties as it is numerically unstable. Thus, any apparent improvement of the EXX-OEP method over the HF scheme for a finite fit basis set must be considered spurious.

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Hybrid exchange correlation functionals and potentials: Concept elaboration

Arbuznikov

2007

J Struct Chem

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Rotational g Tensors Calculated Using Hybrid Exchange-Correlation Functionals with the Optimized Effective Potential Approach

Cited by 14 publications

References 60 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

On the use of the exact exchange optimized effective potential method for static response properties

Hybrid exchange correlation functionals and potentials: Concept elaboration

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