From electron densities to Kohn-Sham kinetic energies, orbital energies, exchange-correlation potentials, and exchange-correlation energies

Zhao, Qian; Morrison, Robert C.; Parr, Robert G.

doi:10.1103/physreva.50.2138

Cited by 447 publications

(338 citation statements)

References 12 publications

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“…For the practical evaluation of s ͓ ͔ from a given density ͑r͒, there are different numerical schemes available. 33,41,42 To evaluate the functional derivative ␦T s ͓ ͔ / ␦ , we will consider this KS potential s ͑r͒ as fixed by the given input density; i.e., the functional dependence on ͑r͒ is replaced by a parametrical dependence. For this fixed potential s ͑r͒, the electron density ͑r͒ is the density which minimizes the total-energy functional…”

Section: The Exact Nonadditive Kinetic-energy Potentialmentioning

confidence: 99%

Exact functional derivative of the nonadditive kinetic-energy bifunctional in the long-distance limit

Jacob

Beyhan

Visscher

2007

The Journal of Chemical Physics

104

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We have investigated the functional derivative of the nonadditive kinetic-energy bifunctional, which appears in the embedding potential that is used in the frozen-density embedding formalism, in the limit that the separation of the subsystems is large. We have derived an exact expression for this kinetic-energy component of the embedding potential and have applied this expression to deduce its exact form in this limit. Comparing to the approximations currently in use, we find that while these approximations are correct at the nonfrozen subsystem, they fail completely at the frozen subsystem. Using test calculations on two model systems, a H 2 O¯Li + complex and a cluster of aminocoumarin C151 surrounded by 30 water molecules, we show that this failure leads to a wrong description of unoccupied orbitals, which can lead to convergence problems caused by too low-lying unoccupied orbitals and which can further have serious consequences for the calculation of response properties. Based on our results, a simple correction is proposed, and we show that this correction is able to fix the observed problems for the model systems studied.

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Section: The Exact Nonadditive Kinetic-energy Potentialmentioning

confidence: 99%

Exact functional derivative of the nonadditive kinetic-energy bifunctional in the long-distance limit

Jacob

Beyhan

Visscher

2007

The Journal of Chemical Physics

104

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“…If the value of k is system-independent then the functional is homogeneous of degree k. If the value of k is system-dependent, then the functional is inhomogeneous and in such cases k is termed an 'effective homogeneity'. 32 The degree of system-dependence provides a measure of the degree of inhomogeneity. The exact T s [ρ] is inhomogeneous under density scaling as can be readily seen by evaluating Eqn.…”

Section: Introductionmentioning

confidence: 99%

Molecular Binding in Post-Kohn–Sham Orbital-Free DFT

Borgoo

Green

Tozer

2014

J. Chem. Theory Comput.

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The 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. For a series of 11 molecules, the binding broadly improves as the effective homogeneity improves, although the extent to which it improves is dependent on the accuracy of the non-interacting kinetic energy; optimal binding appears to require both to be accurate simultaneously. The use of a Thomas-Fermi-von Weizsäcker form, augmented with a second gradient correction, goes some way towards achieving this, exhibiting molecular * To whom correspondence should be addressed † Oslo University ‡ Durham University 1 binding on average. The findings are discussed in terms of the non-interacting kinetic potential and the Hellmann-Feynman theorem. The extent to which the functionals can reproduce the system-dependence of the near-exact effective homogeneity is quantified and potential energy curves are presented for selected molecules. The study provides impetus for including density scaling homogeneity considerations in the design of noninteracting kinetic energy functionals.

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“…Finding numerically the potential associated with a given arbitrarily chosen target electron density is a well-known issue in density functional theory [25][26][27] and was even used recently [28] for obtaining the embedding potential in an alternative way to that given in Eq. (1).…”

Section: Introductionmentioning

confidence: 99%

Orbital-Free Embedding Effective Potential in Analytically Solvable Cases

Savin

Wesołowski

2009

Advances in the Theory of Atomic and Molecular Systems

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The effective embedding potential introduced by Wesolowski and Warshel [J. Phys. Chem., 97 (1993) 8050] depends on two electron densities: that of the environment (n B ) and that of the investigated embedded subsystem (n A ). In this work, we analyze this potential for pairs n A and n B , for which it can be obtained analytically. The obtained potentials are used to illustrate the challenges in taking into account the Pauli exclusion principle.

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From electron densities to Kohn-Sham kinetic energies, orbital energies, exchange-correlation potentials, and exchange-correlation energies

Cited by 447 publications

References 12 publications

Exact functional derivative of the nonadditive kinetic-energy bifunctional in the long-distance limit

Exact functional derivative of the nonadditive kinetic-energy bifunctional in the long-distance limit

Molecular Binding in Post-Kohn–Sham Orbital-Free DFT

Orbital-Free Embedding Effective Potential in Analytically Solvable Cases

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