Evaluation of exchange-correlation energy, potential, and stress - art. no. 165110

We describe a method for calculating the exchange and correlation (XC) cont ributions to the total energy, effective potential, and stress tensor in th e generalized gradient approximation. We avoid using the analytical express ions for the functional derivatives of E-xc[rho], which depend on discontin uous second-order derivatives of the electron density rho. Instead, we firs t approximate E-xc by its integral in a real space grid, and then we evalua te its partial derivatives with respect to the density at the grid points. This ensures the exact consistency between the calculated total energy, pot ential, and stress, and it avoids the need of second-order derivatives. We show a few applications of the method, which requires only the value of the (spin) electron density in a grid (possibly nonuniform) and returns a conv entional (local) XC potential.