mod_vxcgga Module

Add the exchange-correlation-potential in the GGA approach to the given potential and if total energies should be calculated (kte=1) the exchange-correlation-energies are calculated . Use as input the charge density times $r^2$ (rho2ns(...,1)) and in the spin-polarized case (nspin=2) the spin density times $r^2$ (rho2ns(...,2)) . The density times $4\pi$ is generated at an angular mesh. the exchange-correlation potential and the exchange-correlation energy are calculated at those mesh points with a subroutine. In the non-spin-polarized case the spin-density is set equal zero. After that the exchange-correlation potential and in the case of total energies (kte=1) the exchange-correlation energy are expanded into spherical harmonics. The ex.-cor. potential is added to the given potential. The expansion into spherical harmonics uses the orthogonality of these harmonics. Therefore a gauss-legendre integration for $\theta$ and a gauss-tschebyscheff integration for $\phi$ is used. All needed values for the angular mesh and angular integration are generate in the subroutine sphere. The ex.-cor. potential is extrapolated to the origin only for the lm=1 value .