Article

# Kohn-Sham calculations combined with an average pair-density functional theory

International Journal of Modern Physics B (Impact Factor: 0.36). 11/2006; DOI:10.1142/S0217979207043804

Source: arXiv

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**ABSTRACT:**The correlation energy in density functional theory can be expressed exactly in terms of the change in the probability of finding two electrons at a given distance r(12) (intracule density) when the electron-electron interaction is multiplied by a real parameter lambda varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is (ideally) kept fixed by a suitable local one-body potential. While an accurate intracule density of the physical system can only be obtained from expensive wavefunction-based calculations, being able to construct good models starting from Kohn-Sham ingredients would highly improve the accuracy of density functional calculations. To this purpose, we investigate the intracule density in the lambda --> infinity limit of the adiabatic connection. This strong-interaction limit of density functional theory turns out to be, like the opposite non-interacting Kohn-Sham limit, mathematically simple and can be entirely constructed from the knowledge of the one-electron density. We develop here the theoretical framework and, using accurate correlated one-electron densities, we calculate the intracule densities in the strong interaction limit for few atoms. Comparison of our results with the corresponding Kohn-Sham and physical quantities provides useful hints for building approximate intracule densities along the adiabatic connection of density functional theory.Physical Chemistry Chemical Physics 07/2008; 10(23):3440-6. · 3.83 Impact Factor - [show abstract] [hide abstract]

**ABSTRACT:**We show that the kinetic energy functional in pair density functional theory is homogeneous of degree 2 with respect to coordinate scaling. Although this result was already derived by Levy and Ziesche using the constrained search method (Levy and Ziesche, J Chem Phys 2001, 115, 9110), we derive our result using the Legendre transform formulation (Ayers et al., J Chem Phys 2006, 124, 054101). The advantage of this approach is that in the Legendre transform functional, the N-representability problem is solved by the functional. By contrast, in the Levy–Ziesche approach, the computationally impracticable N-representability constraints have to be imposed separately. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009International Journal of Quantum Chemistry 02/2009; 109(8):1699 - 1705. · 1.31 Impact Factor - [show abstract] [hide abstract]

**ABSTRACT:**The combination of density-functional theory with other approaches to the many-electron problem through the separation of the electron-electron interaction into a short-range and a long-range contribution (range separation) is a successful strategy, which is raising more and more interest in recent years. We focus here on a range-separated method in which only the short-range correlation energy needs to be approximated, and we model it within the "extended Overhauser approach." We consider the paradigmatic case of the H2 molecule along the dissociation curve, finding encouraging results. By means of very accurate variational wavefunctions, we also study how the effective electron-electron interaction appearing in the Overhauser model should be to yield the exact correlation energy for standard Kohn-Sham density functional theory.International Journal of Quantum Chemistry 01/2009; 109(9):1950-1961. · 1.31 Impact Factor

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