Exchange-correlation energy parameterization

In Eq. [47], epc ( ) and exc (n) are the exchange-correlation energy densities for the nonpolarized (paramagnetic) and fully polarized (ferromagnetic) homogeneous electron gas. The form of both exc(n) and exc(n) has been conveniently parameterized by von Barth and Hedin. Other interpolations have also been proposed24,33 for eKC(n, J ). The results for the homogeneous electron gas can be used to construct an LSDA... 

To further illustrate the importance of coupling the electrostatic and short-ranged repulsion interactions, we consider the example of a dimer of polarizable rare gas atoms, as presented by Jordan et al. In the absence of an external electric field, a PPD model predicts that no induced dipoles exist (see Eq. [12]). But the shell model correctly predicts that the rare gas atoms polarize each other when displaced away from the minimum-energy (force-free) configuration. The dimer will have a positive quadrupole moment at large separations, due to the attraction of each electron cloud for the opposite nucleus, and a negative quadrupole at small separations, due to the exchange-correlation repulsion of the electron clouds. This result is in accord with ab initio quantum calculations on the system, and these calculations can even be used to help parameterize the model. ... 

The first generation is the local density approximation (LDA). This estimation involves the Dirac functional for exchange, which is nothing else than the functional proposed by Dirac [15] in 1927 for the so-called Thomas-Fermi-Dirac model of the atoms. For the correlation energy, some parameterizations have been proposed, and the formula can be considered as the limit of what can be obtained at this level of approximation [16-18], The Xa approximation falls into this category, since a known proportion of the exchange energy approximates the correlation. 

---