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It is a common viewpoint thal the GGA exchange and correlation components compensate the deficiencies of each other, providing more accurate approximation for the total exchange-correlation energy than for the exchange and correlation separately. An illustration of this is the PBE correlation potential of He atom which is almost exactly the negative of the exact correlation potential.
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33748685841
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note
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Note that when both q and p are occupied, the terms under the summation change sign with respect to the interchange of q and p, and therefore vanish.
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37
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33748683788
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note
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Note that the definition of the KS potential via the functional derivative is just a consequence of the genuine condition that the model density must reproduce the exact one. Combining the density condition with the fact that the ground-state density minimizes the functional, one obtains the functional derivative definition.
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38
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84859286124
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See EPAPS Document No. E-JCPSA6-125-305625 for derivation of the final expressions for the PT2SC functional and potential. This document can be reached via a direct link in the online article's HTML reference section or via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html).
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39
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33748702311
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a〉 are minimized.
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40
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0003646549
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University of Florida. Integral packages included are J. Almlöf and P. R. Taylor, VMOL; P. Taylor, VPROPS; and T. Helgaker, H. J. A. Jensen, P. Jörgensen, J. Olsen, and P. R. Taylor, ABA-CUS
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J. F. Stanton, J. Gauss, J. D. Watts et al., ACES II, a program product of the Quantum Theory Project, University of Florida. Integral packages included are J. Almlöf and P. R. Taylor, VMOL; P. Taylor, VPROPS; and T. Helgaker, H. J. A. Jensen, P. Jörgensen, J. Olsen, and P. R. Taylor, ABA-CUS.
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ACES II, a Program Product of the Quantum Theory Project
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33748711442
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note
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Note that we did not include the PBE correlation energies in Table II because the absolute values of GGA energies can be quite different from wave function values. However, it is the ab initio nature of the PT2 and PT2SC functionals that allows us to compare the absolute values of the correlation energy. See also Ref. 56.
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