Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region

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1,432

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. Electronic excitation energies are determined using the CAM-B3LYP Coulomb-attenuated functional ͓T. Yanai et al. Chem. Phys. Lett. 393, 51 ͑2004͔͒, together with a standard generalized gradient approximation ͑GGA͒ and hybrid functional. The degree of spatial overlap between the occupied and virtual orbitals involved in an excitation is measured using a quantity ⌳, and the extent to which excitation energy errors correlate with ⌳ is quantified. For a set of 59 excitations of local, Rydberg, and intramolecular charge-transfer character in 18 theoretically challenging main-group molecules, CAM-B3LYP provides by far the best overall performance; no correlation is observed between excitation energy errors and ⌳, reflecting the good quality, balanced description of all three categories of excitation. By contrast, a clear correlation is observed for the GGA and, to a lesser extent, the hybrid functional, allowing a simple diagnostic test to be proposed for judging the reliability of a general excitation from these functionals-when ⌳ falls below a prescribed threshold, excitations are likely to be in very significant error. The study highlights the ambiguous nature of the term "charge transfer," providing insight into the observation that while many charge-transfer excitations are poorly described by GGA and hybrid functionals, others are accurately reproduced.

Section: Molecules Excitations and Computational Detailsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Excitation energies in density functional theory: An evaluation and a diagnostic test

Peach

Benfield

Helgaker

et al. 2008

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1,432

“…This feature is illustrated with Fig. 1 where the xc potentials constructed by statistical averaging of ͑model͒ orbital potentials ͑SAOP͒ 7,9,10 and by gradient-regulated asymptotic connection procedure 8 applied to the GGA Becke-Perdew xc potential 11,12 ͑BP-GRAC͒ are plotted along the main axis of the molecule N 2 . They are compared with the LDA potential and with the uncorrected BP potential.…”

Section: Introductionmentioning

confidence: 99%

“…2, and for a range of response properties including excitation energies in Refs. [3][4][5][6][7][8]. A common feature of the successful new potentials is their effectively more attractive character ͓with respect to the long-range asymptotics v xc (ϱ)͔ in the bulk and outer valence regions compared to the standard potentials of the local density approximation ͑LDA͒ and generalized gradient approximations ͑GGAs͒.…”

Section: Introductionmentioning

confidence: 99%

On the required shape corrections to the local density and generalized gradient approximations to the Kohn–Sham potentials for molecular response calculations of (hyper)polarizabilities and excitation energies

Grüning¹,

Gritsenko²,

Gisbergen³

et al. 2002

121

100

It is well known that shape corrections have to be applied to the local-density ͑LDA͒ and generalized gradient ͑GGA͒ approximations to the Kohn-Sham exchange-correlation potential in order to obtain reliable response properties in time dependent density functional theory calculations. Here we demonstrate that it is an oversimplified view that these shape corrections concern primarily the asymptotic part of the potential, and that they affect only Rydberg type transitions. The performance is assessed of two shape-corrected Kohn-Sham potentials, the gradient-regulated asymptotic connection procedure applied to the Becke-Perdew potential ͑BP-GRAC͒ and the statistical averaging of ͑model͒ orbital potentials ͑SAOP͒, versus LDA and GGA potentials, in molecular response calculations of the static average polarizability ␣, the Cauchy coefficient S Ϫ4 , and the static average hyperpolarizability ␤. The nature of the distortions of the LDA/GGA potentials is highlighted and it is shown that they introduce many spurious excited states at too low energy which may mix with valence excited states, resulting in wrong excited state compositions. They also lead to wrong oscillator strengths and thus to a wrong spectral structure of properties like the polarizability. LDA, Becke-Lee-Yang-Parr ͑BLYP͒, and Becke-Perdew ͑BP͒ characteristically underestimate contributions to ␣ and S Ϫ4 from bound Rydberg-type states and overestimate those from the continuum. Cancellation of the errors in these contributions occasionally produces fortuitously good results. The distortions of the LDA, BLYP, and BP spectra are related to the deficiencies of the LDA/GGA potentials in both the bulk and outer molecular regions. In contrast, both SAOP and BP-GRAC potentials produce high quality polarizabilities for 21 molecules and also reliable Cauchy moments and hyperpolarizabilities for the selected molecules. The analysis for the N 2 molecule shows, that both SAOP and BP-GRAC yield reliable energies i and oscillator strengths f i of individual excitations, so that they reproduce well the spectral structure of ␣ and S Ϫ4 .

“…27͒ potential ͑BP-GRAC-LB͒, see Ref. 28. The BP-GRAC-LB potential shares with the SAOP potential the correct asymptotic behavior, but is in the bulk region an unmodified GGA ͑in the present case BP86͒ potential.…”

Section: Introductionmentioning

confidence: 99%

Nuclear magnetic resonance chemical shifts with the statistical average of orbital-dependent model potentials in Kohn–Sham density functional theory

Poater

Lenthe

Baerends

2003

In this paper, an orbital-dependent Kohn-Sham exchange-correlation potential, the so-called statistical average of ͑model͒ orbital potentials, is applied to the calculation of nuclear magnetic resonance chemical shifts of a series of simple molecules containing H, C, N, O, and F. It is shown that the use of this model potential leads to isotropic chemical shifts which are substantially improved over both local and gradient-corrected functionals, especially for nitrogen and oxygen atoms. This improvement in the chemical shift calculations can be attributed to the increase in the gap between highest occupied and lowest unoccupied orbitals, thus correcting the excessively large paramagnetic contributions, which have been identified to give deficient chemical shifts with both the local-density approximation and with gradient-corrected functionals. This is in keeping with the improvement by the statitical average of orbital model potentials for response properties in general and for excitation energies in particular. The present results are comparable in accuracy to those previously reported with self-interaction corrected functionals by Patchovskii et al., but still inferior to those obtained with accurate Kohn-Sham potentials by Wilson and Tozer. However, the present approach is computationally expedient and routinely applicable to all systems, requiring virtually the same computational effort as local-density and generalized-gradient calculations.