Core exchange

Now we go along with an argument offered by Tmhlar et al. [84]. In the evaluation of Eq. (4.33), and consistent with the nonoverlapping core orbitals assumption, we can neglect the core-other core exchange interactions. Because the core charge densities p (r) = 2 < (r)< (r) are spherically symmetric about their... 

The coefficients Ck and exponents 3k are fitted rather than calculated from the corresponding Gaussian AO exponents and contraction coefficients of the atomic core orbitals whose effect they are assumed to represent. By contrast, the core exchange contribution to the pseudopotential is explicitly calculated over the Gaussian AOs and represented by its spectral expansion on the basis of the primitive Gaussians. 

The form of the model potential is much simpler than that of the pseudopotential, and it is relatively easy to implement. The integrals over core projector terms are overlaps, which need no special coding. The core direct potential can be fitted to a linear combination of Gaussian functions. It is the core exchange potential that is the hardest to represent because of its nonlocahty. 

M is the matrix of the combined core exchange and spin-free relativistic operator, given by... 

---