An atomic kinetic energy functional with full Weizsacker correction

Acharya, Prabhat K.; Bartolotti, Libero J.; Sears, Stephen B.; Parr, Robert G.

doi:10.1073/pnas.77.12.6978

Cited by 144 publications

(50 citation statements)

References 13 publications

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“…Similarly, the nondecomposable second derivative approximation introduced by Garcia-Lastra et al 44 seeks to improve the embedding potential close to the nuclei of the frozen subsystem by switching on the full von Weizsäcker term close to the nuclei. Because the von Weizsäcker functional has the correct behavior close to the nuclei ͑i.e., it is able to cancel the nuclear attraction͒, approximate kinetic-energy functional based on the von Weizsäcker functional ͑instead of the Thomas-Fermi functional͒ have a long history 81,82 and might prove useful also for constructing approximations to v T . However, a detailed assessment of these and other approximations to v T is beyond the scope of this work and will be presented elsewhere.…”

Section: Discussionmentioning

confidence: 99%

Accurate frozen-density embedding potentials as a first step towards a subsystem description of covalent bonds

Fux

Jacob

Neugebauer

et al. 2010

The Journal of Chemical Physics

197

278

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Dispersion, static correlation, and delocalisation errors in density functional theory: An electrostatic theorem perspective J. Chem. Phys. 135, 164110 (2011) Evaluation of coupling terms between intra-and intermolecular vibrations in coarse-grained normal-mode analysis: Does a stronger acid make a stiffer hydrogen bond? J. Chem. Phys. 135, 154111 (2011) Calculating dispersion interactions using maximally localized Wannier functions J. Chem. Phys. 135, 154105 (2011) A theoretical study of Ne3 using hyperspherical coordinates and a slow variable discretization approach J. Chem. Phys. 135, 134312 (2011) Additional information on J. Chem. Phys. The frozen-density embedding ͑FDE͒ scheme ͓Wesolowski and Warshel, J. Phys. Chem. 97, 8050 ͑1993͔͒ relies on the use of approximations for the kinetic-energy component v T ͓ 1 , 2 ͔ of the embedding potential. While with approximations derived from generalized-gradient approximation kinetic-energy density functional weak interactions between subsystems such as hydrogen bonds can be described rather accurately, these approximations break down for bonds with a covalent character. Thus, to be able to directly apply the FDE scheme to subsystems connected by covalent bonds, improved approximations to v T are needed. As a first step toward this goal, we have implemented a method for the numerical calculation of accurate references for v T . We present accurate embedding potentials for a selected set of model systems, in which the subsystems are connected by hydrogen bonds of various strength ͑water dimer and F-H-F − ͒, a coordination bond ͑ammonia borane͒, and a prototypical covalent bond ͑ethane͒. These accurate potentials are analyzed and compared to those obtained from popular kinetic-energy density functionals.

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Section: Discussionmentioning

confidence: 99%

Accurate frozen-density embedding potentials as a first step towards a subsystem description of covalent bonds

Fux

Jacob

Neugebauer

et al. 2010

The Journal of Chemical Physics

197

278

View full text Add to dashboard Cite

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“…Employing this approximation as a starting point in the development of some kinetic energy functionals is proposed by an alternative strategy to approximate the kinetic energy functional. 52,53 The non-additive kinetic potential derived from W approximation takes the form…”

Section: Resultsmentioning

confidence: 99%

Exact non-additive kinetic potentials in realistic chemical systems

Silva

Wesołowski

2012

The Journal of Chemical Physics

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In methods based on frozen-density embedding theory or subsystem formulation of density functional theory, the non-additive kinetic potential (v nad t (r)) needs to be approximated. Since v nad t (r) is defined as a bifunctional, the common strategies rely on approximating v nad t [ρ A , ρ B ](r). In this work, the exact potentials (not bifunctionals) are constructed for chemically relevant pairs of electron densities (ρ A and ρ B ) representing: dissociating molecules, two parts of a molecule linked by a covalent bond, or valence and core electrons. The method used is applicable only for particular case, where ρ A is a one-electron or spin-compensated two-electron density, for which the analytic relation between the density and potential exists. The sum ρ A + ρ B is, however, not limited to such restrictions. Kohn-Sham molecular densities are used for this purpose. The constructed potentials are analyzed to identify the properties which must be taken into account when constructing approximations to the corresponding bifunctional. It is comprehensively shown that the full von Weizsäcker component is indispensable in order to approximate adequately the non-additive kinetic potential for such pairs of densities.

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“…It has been recently emphasized by several authors that this term is a natural component of the exact kinetic energy density functional [19][20][21][22][23]25,26]. In fact, this term gives the exact ground-state kinetic energy of a one-electron atom (ion) and of a two-electron Hartree-Fock atom (ion).…”

Section: A Gradient Expansionmentioning

confidence: 97%

Local behavior of the kinetic energy in density functional theory

Zorita

Alonso

Balbás

1985

Int J of Quantum Chemistry

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The local behavior of several approximate kinetic energy functionals is analyzed, for the case of free atoms and ions, by comparison with the local kinetic energy of Hartree-Fock theory. The atomic electron densities used are, in all cases, Hartree-Fock electron densities. The kinetic energy functional obtained by the gradient expansion method (with a small number of terms) is, locally, not very accurate, but its integrated value is fortuitously accurate, due to a strong cancellation of errors. Functionals which have the Weizsacker term t, = (V p)'/S p as a key ingredient are more accurate locally. The explicit incorporation of the shell structure and nonlocal density effects into the kinetic energy functional leads to the best results. The motivation for this work is that only a kinetic energy functional with an accurate local behavior will give good electron densities on solution of the Euler equation derived from it.

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An atomic kinetic energy functional with full Weizsacker correction

Abstract: The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U. S. C. §1734 solely to indicate this fact.

Cited by 144 publications

References 13 publications

Accurate frozen-density embedding potentials as a first step towards a subsystem description of covalent bonds

Accurate frozen-density embedding potentials as a first step towards a subsystem description of covalent bonds

Exact non-additive kinetic potentials in realistic chemical systems

Local behavior of the kinetic energy in density functional theory

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