Numerical Evaluation of Exchange-Correlation Integrals

The exchange-correlation functions are sufficiently complicated that the integrals required cannot be carried out analytically. Even the simplest of the family ( E_x^D30) is too complex if Gaussian basis functions are used to represent the density. One way forward is to expand the exchange-correlation potential in terms of auxiliary Gaussian functions [123]. The disadvantage of this scheme is that it is hard to reduce the extent of approximation towards zero. A more popular way is to calculate the integrals numerically using quadrature schemes.