Correlation energy Kohn-Sham theory, physical

H. A. Physical interpretation of Kohn-Sham theory exchange-correlation energy functional and its derivative... 

H. A. PHYSICAL INTERPRETATION OF KOHN-SHAM THEORY EXCHANGE-CORRELATION ENERGY FUNCTIONAL AND ITS DERIVATIVE... 

There is, of course, much that remains to be understood with regard to the physical interpretation. For example, the correlation-kinetic-energy field Z, (r) and potential W, (r) need to be investigated further. However, since accurate wavefunctions and the Kohn-Sham theory orbitals derived from the resulting density now exist for light atoms [40] and molecules [54], it is possible to determine, as for the Helium atom, the structure of the fields P(r), < P(r), and Zt (r), and the potentials WjP(r), W (r), W (r), and W (r) derived from them, respectively. A study of these results should lead to insights into the correlation and correlation-kinetic-energy components, and to the numerical determination of the asymptotic power-law structure of these fields and potentials. The analytical determination of the asymptotic structure of either [Z, (r), W, (r)] or [if (r), WP(r)] would then lead to the structure of the other. 

Since the electron-interaction energy functional E [p] of Kohn-Sham theory is representative of Pauli and Coulomb correlations as well as the correlation contribution to the kinetic energy, so is the corresponding local potential v (r) obtained from it through functional differentiation. In the physical interpretation of the potential v (r), however, it is possible to distinguish between the purely quantum-mechanical (Pauli and Coulomb) electron-correlation component Wee(r), and the correlation-kinetic-energy component W, (r). We begin this section with a description of the physical interpretation of Vee (r), and then discuss its components Wee(r) and W, (r) more fully. 

Correlation energy is ultimately a convenient container for all that escapes from first-order coulombic and polarization terms. See Bickelhaupt, F. M. Baerends, E. J. Kohn-Sham density functional theory predicting and understanding chemistry, Reviews in Computational Chemistry, Vol. 15, edited by K. B. Lipkowitz and D. B. Boyd, 2000, Wiley-VCH, New Yorkp.ll Is electron correlation (not defined in a statistical sense, but according to either the quantum chemical or the DFT definition) a true physical phenomenon It is a man-made concept, related to the introduction of a convenient trial wavefunction, that is useful for our communication and understanding. ... 

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