Exchange Hole Models

Steinmann, S. N., and Corminboeuf, C. (2011). A generalized-gradient approximation exchange hole model for dispersion coefficients,/. Chem. Phys. 134, p. 044117, doi 10.1063/1.3545985. 

Akin-Ojo, O., Bukowski, R.> Szalewicz, K. (2003). Ab initio studies of He-HCCCN interaction. Journal of Chemical Physics, 119, 8379-8396. Angyan, J. G. (2007). On the exchange-hole model of london dispersion forces. Journal of Chemical Physics, 127, 024108-8. 

Becke, A. and M. E. Russel. 1989. Exchange holes in inhomogeneous systems A coordinate-space model. Phys. Rev. A 39, 3761. 

The concept of a spatial correlation is very rich in content, and its content is necessary and sufficient for energy assessment. It is useful to consider the spatial correlation in the approximation of the band model from all the wave functions contained in the Fermi sphere a determinant has to be formed as, also the determinants of weakly excited states a perturbation calculation has to be made with respect to 2e2/ x n — Xjn the reduction to the spatial correlation must be made the energy may be calculated. In fact the pertubation calculation has never been made for metals, while the spatial correlation was only calculated by Wigner and Seitz (1933) in the zero approximation. The result of their calculation is the well-known exchange hole, which may be represented in three-dimensional space if one electron is fixed in the coordinate origin. This may be done if the local space is homogenous i.e., has no... 

The sharp cutoff procedure introduces spurious kinks into the GGA exchange hole of Eq. (107), which complicate the derivation of the P86 and PW91 exchange functionals. In this section, we will consider functionals that are based on smooth analytic hole models normalized from the outset. 

Becke and Roussel [182] constructed a model exchange hole starting with the second-order Taylor expansion of the exact spherically averaged cr-spin hole [183]... 

In view of this interpretation of eqn ( 33.4) we might expect that this normalisation condition is essentially due to the exchange part of the exchange-correlation hole and that it might be useful to divide this density into an exchange hole and a correlation hole . Guided by the product form of the (real) two-particle density for the single-determinant model which involves the density function p and the density matrix pi ... 

Instead of modeling the exchange hole directly, one can use the exact exchange-correlation hole. Alternatively, one can use the pair density (two-density)... 

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