Exact exchange-correlation potential and approximate exchange potential in terms of density matrices

Int J of Quantum Chemistry

2015

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Hartree-Fock (HF) theory makes the prediction that for neutral atoms the chemical potential (l) is equal to minus the ionization potential (I). This has led us to inquire whether this intimate relation is sensitive to electron correlation. We present here therefore some discussion of the predictions for neutral atoms and atomic ions, and some homonuclear diatomic molecules. An account of fairly recent progress in obtaining the HF ionization potentials for the isoelectronic series of He, Be, Ne, Mg, and Ar-like atomic ions is first considered. The 1=Z expansion for total non-relativistic energy of atomic ions evokes that l52I is not very sensitive to the introduction of electron correlation. The connection between l and I for neutral atoms via the Pauli potential (V P ) is then examined. We focus on the relation of V P to more recent advances in density functional theory (DFT) plus low-order density matrix theory. In this context, the example of nonrelativistic Be-like atomic ions is treated. Afterward, we introduce the bosonized equation for the density amplitude ffiffiffi q p , which emphasizes the major role that plays dT W =dq in DFT. For spherical atomic densities, the bosonized potential argument strongly suggests also that l52I remains valid in the presence of electron correlation. Finally, numerical estimates of l and I from natural orbital functional (NOF) theory are presented for neutral atoms ranging from H to Kr. The predicted vertical I by means of the extended Koopmans' theorem are in good agreement with the corresponding experimental data. However, the NOF theory of l lowers the experimental values considerably as we approach to noble gas atoms though oscillatory behavior is in evidence. V C 2015 Wiley Periodicals, Inc. DOI: 10.1002/qua.25039 Ionization Potential and Asymptotic Large r Behavior of Ground-State Density of Spherical AtomsIt seems natural to begin this review relating to advances in density functional theory (DFT) with some account of fairly recent progress in obtaining the ground-state electron density q r ð Þ in some spherical atoms. Then, the nonrelativistic twoelectron He-like series of atomic ions with atomic number Z affords an appropriate starting point.Large r behavior of q r ð Þ in terms of I and Z It is well-known [1] that, in atomic units (a.u.), the ground-state density of rare gas atoms with spherical electron density q r ð Þ falls off at sufficiently large r as where I is the ionization potential. For sufficiently large Z, the expressions for constants n and A were found by March and Pucci [2] based on the early work of Schwartz, [3] namely, n % 2ð3=4ÞZ 21 and A5ð2Z 3 =pÞ½12ð3=4ZÞlnZ1OðZ 21 Þ . However, a more general relationship between n and I for arbitrary atomic number Z can be obtained using the DFT for the He-like series of atomic ions. [4] Consider V(r) is the one-body potential of DFT, then the constant chemical potential equation reads [5] l5 dT s q ½ dq 1V r ð Þwhere T s q ½ is the single-particle kinetic energy functional. While T s is still unknown for gener...

Section: Correlation Aspects As Consequences Of the Pauli Potentialmentioning

confidence: 99%

Section: Differential Virial Theorem In Terms Of Pauli Potential For mentioning

confidence: 99%

“…[34] Their result for the magnitude 2V 0 r ð Þ of the force associated with the one-body potential V(r) of DFT reads, in spherical symmetry,…”

Section: Differential Virial Theorem In Terms Of Pauli Potential For mentioning

confidence: 99%

Section: Future Directionsmentioning

confidence: 99%

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Chemical and ionization potentials: Relation via the Pauli potential and NOF theory

Piris

Int J of Quantum Chemistry

2015

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“…We adopt here the approach via the differential virial theorem (DVT), going back to March and Young [4] for arbitrary level filling in one dimension and generalized first to spherically symmetric systems by Nagy and March [6] then to three dimensions by Holas and March [5]. Their result for the magnitude of ∂V /∂r of the force associated with the one-body potential V (r) of DFT [3] reads, in spherical symmetry…”

mentioning

confidence: 99%

Differential virial theorem in density-functional theory in terms of the Pauli potential for spherically symmetric electron densities: Illustrative example for the family of Be-like atomic ions

Nagy

2008

Phys. Rev. A

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The differential virial theorem relates the force −∂V /∂r associated with the one-body potential V (r) of DFT to the Laplacian ∇ 2 n of the groundstate density n(r) and to a quantity z s (r) involving the kinetic energy density tensor t αβ (r). Having the concept of the Pauli potential V P (r), z s is derived for spherically symmetric ground-state densities n(r) in terms of the von Weizsäcker kinetic energy density and the first derivative of V P (r). z s is related solaly to the gradient kinetic energy density t G (r) for Be-like atomic ions. I. BACKGROUNDIn earlier work with Gál [1], we obtained an explicit differential equation for the nonrelativistic ground-state electron density n(r, Z) for He-like atomic ions in the limit of large nuclear charge Ze, utilizing the work of Schwartz [2]. After a discussion in fairly several terms of some implications of DFT [3] for spherically symmetric ground-state electron densities, our 1

Momentum and position space densities in many-electron systems

1996

Int. J. Quantum Chem.

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rnMotivated by McWeeny's pioneering work on the solution of the Schrodinger equation in momentum space and his early treatment of X-ray scattering factors from the electron distribution p(r) in both isolated and bonded atoms, the relation between momentum space moments ( p") and p(r) is first developed semiclassically, as in the forerunner of density functional theory, the Thomas-Fermi method. The relation between ( p) and the Dirac-Slater exchange energy prompts the treatment of an exact nonlocal relation between kinetic and exchange energies in Hartree-Fock theory. The Hiller-Sucher-Feinberg identity serves then to introduce the differential form of the virial theorem in a many-electron system. Following very recent work of Holas and March, this is used to obtain the exact exchange-correlation potential as a path integral expressed in terms of low-order density matrices.