Abstract
The problem of finding the exact energy of a system given the exact density is well known, though not solved. Here, approximate formulas for calculating the energy from the density are examined using density scaling relations and a functional expansion of the energy. The term that is first order in the functional expansion can be evaluated exactly from the Kohn-Sham effective potential. The term that is second order is evaluated using the Fermi-Amaldi-like correction for the Coulomb energy. An analysis of the approximation of Parr and Ghosh [Phys. Rev. A 51, 3564 (1995)] and of Morrison and Parr [Phys. Rev. A 53, R2918 (1996)] is made using the functional expansion.
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References
P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).
W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
Q. Zhao and R. G. Parr, Phys. Rev. A 46, 2337 (1992).
Q. Zhao and R. G. Parr, J. Chem. Phys. 98, 543 (1993).
Q. Zhao, R. C. Morrison, and R. G. Parr, Phys. Rev. A 50, 2138 (1994).
R. C. Morrison and Q. Zhao, Phys. Rev. A 51, 1980 (1995).
M. Levy, Proc. Natl. Acad. Sci. USA 76, 2062 (1979).
M. Levy and J. P. Perdew, pp. 11-30 in Density Functional Methods in Physics, edited by R. M. Dreizler and J. de Providencia (Plenum, New York, 1985).
F. Aryasetiawan and M. J. Stott, Phys. Rev. B 38, 2974 (1988).
A. Görling, Phys. Rev. A 46, 3753 (1992).
Y. Wang and R. G. Parr, Phys. Rev. A 47, R1591 (1993).
R. van Leeuwen and E. J. Baerends, Phys. Rev. A 49, 2421 (1994).
R. G. Parr and S. K. Ghosh, Phys. Rev. A 51, 3564 (1995).
R. C. Morrison and R. G. Parr, Phys. Rev. A 53, R2918 (1996).
K. Burke, J. P. Perdew, and M. Levy, Phys. Rev. A 53, R2915 (1996).
M. Levy, W. Yang, and R. G. Parr, J. Chem. Phys. 83, 2334 (1985).
F. Averill and G. S. Painter, Phys. Rev. B 24, 6795 (1981).
M. Levy and J. P. Perdew, Phys. Rev. A 32, 2010 (1985).
S. Liu and R. G. Parr, Phys. Rev. A (in press).
R. G. Parr, S. Liu, A. A. Kugler, and Á. Nagy, Phys. Rev. A 52, 969 (1995).
Á. Nagy, Phys. Rev. A 47, 2715 (1993).
E. Fermi and E. Amaldi, Mem. R. Accad. Italia 6, 117 (1934).
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Morrison, R.C., Parr, R.G. (1998). Calculating Electronic Energies from Kohn-Sham Effective Potentials. In: Dobson, J.F., Vignale, G., Das, M.P. (eds) Electronic Density Functional Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0316-7_9
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DOI: https://doi.org/10.1007/978-1-4899-0316-7_9
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