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The exchange hole of DFT is nearly identical with the Fermi hole commonly studied in quantum chemistry. However, the noninteracting ground state in DFT and the corresponding single-particle orbitals are determined by the Kohn-Sham equation and in principle obtain the density of the exact ground state, while the Fermi hole is usually defined in terms of the Hartree-Fock ground state. Similarly, the correlation hole defined with respect to the full coupling constant exchange-correlation hole is the analog of the Coulomb hole of Ref. [5].
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0342993481
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Note that this argument refers to a perspective complementary to that held elsewhere in this paper and in the literature. One measures the correlation hole at a fixed position in the atom in response to a reference electron somewhere else, and varies the position of the reference electron. The corresponding hole measured at the fixed position should be largest when the reference electron is moved on top of it.
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note
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In principle one should be able to measure the importance of this configuration by a calculation of the overlap between it and the Slater-Jastrow ground state; the significantly different nodal structure of the two states makes a VMC calculation of this quantity unreliable in practice.
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44
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2 will in general not be preserved [C. J. Huang, C. Filippi, and C. J. Umrigar, J. Chem. Phys. 108, 8838 (1998)]. Imposing a spin-independent cusp condition was observed to change the up-spin component of the density noticeably, but preserved fairly closely the degree and anisotropy of spatial separation between spin-components induced by correlations.
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