Exchange—correlation potential basis

In words, the integral of equation (7-33) for the exchange-correlation potential is approximated by a sum of P terms. Each of these is computed as the product of the numerical values of the basis functions and rp, with the exchange-correlation potential Vxc at each point rp on the grid. Each product is further weighted by the factor Wp, whose value depends on the actual numerical technique used. 

LCAO expansion of the MOs [15]. In the DV-Xa MO method based on the Hartree-Fock-Slater approach, the exchange-correlation potential is approximated by the simple Slater form [16] Vxc(r) = —3a 3p(r)/47i 1/3, where the coefficient a is a scaling parameter (fixed at 0.7 in the present study) and p(r) is the local electron density at a position r. The basis functions for the MO calculation consisted of atomic orbital wave eigenfunctions obtained in numerical form, which included the ls-6s, ls-5s, ls-6p, ls-4p, and ls-2p orbitals for Ba, Sr, Pb, Ti, and O ions, respectively... 

Here a and b stand for orbital basis functions and c denotes Gaussian functions used in the fitting of the electron density or the exchange-correlation potential. Most of the time is spent in the computation of I. We can rewrite the original Obara and Saika formula (15) in a form suitable for computation of three-index integrals ... 

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