Self-consistent Thomas-Fermi-Dirac theory, extended by Gell-Mann and Brueckner correlation, in terms of density n and its two reduced gradients del(2)n and del n

摘要

We prove the following results, relevant for the density functional theory: the Thomas-Fermi-Dirac theory, generalized to include the contribution due to the high electron density result of Gell-Mann and Brueckner for the correlation energy, is shown to lead to a differential equation for the self-consistent ground-state density n(r) in atoms and molecules in the form F(n,(del n)(2), del(2)n) = 1, where the function F is given explicitly. A straightforward extension yields a similar result for the equation determining the Pauli plus exchange-correlation potential and for the divergence of the many-electron force. (C) 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 145-149, 1998. [References: 12]