RHOLM Subroutine

public subroutine RHOLM(DEN, DF, GMAT, NSRA, RHO2NS, DRDI, IPAN, IRCUT, PZ, FZ, QZ, SZ, CLEB, ICLEB, IEND, JEND, EKL, IRMD, NCLEB, LMAXD, LMMAXD, LMPOTD)

calculate in the paramagnetic case (nspin=1) : the valence charge density times r2 from the greensfunction calculate in the spin-polarized case (nspin=2) : the valence charge density times r2 and the valence spin density times r**2 from the greensfunction , ( convention spin density := density(spin up)-density(spin down) ) calculate the valence density of states , in the spin-polarized case spin dependent ; splitted into its l-contributions .

in this subroutine an implicit energy-spin integration is done : this subroutine is called for each energy and spin value and n(r,e) times df (the energy weight) is calculated .

recognize that the density of states is always complex also in the case of "real-energy-integation" (ief>0) since in that case the energy integration is done parallel to the real energy axis but not on the real energy axis . in the paramagnetic case only rho2ns(irmd,lmxtsq,natypd,1) is used containing the charge density times r2 . in the spin-polarized case rho2ns(...,1) contains the charge density times r2 and rho2ns(...,2) the spin density times r**2 .

the charge density is expanded in spherical harmonics :

      rho(r) =   { rho(lm,r) * y(r,lm) }       (summed over lm)

   rho(lm,r) =   { do rho(r) * y(r,lm)         (integrated over
                                                  unit sphere)

in the case of spin-polarization : the spin density is developed in spherical harmonics :

     sden(r) =   { sden(lm,r) * y(r,lm) }      (summed over lm)

  sden(lm,r) =   { do sden(r) * y(r,lm)        (integrated over
                                                  unit sphere)

n(r,e) is developed in

 n(r,e) = { y(r,l'm') * n(l'm',lm,r,e) * y(r,lm) }

therefore a faltung of n(l'm',lm,r,e) with the gaunt coeffients has to be used to calculate the lm-contribution of the charge density . (see notes by b.drittler)

attention : the gaunt coeffients are stored in an index array (see subroutine gaunt) the structure part of the greens-function (gmat) is symmetric in its lm-indices , therefore only one half of the matrix is calculated in the subroutine for the back-symmetrisation . the gaunt coeffients are symmetric too (since the are calculated for real spherical harmonics) . that is why the lm2- loop only goes up to lm1 and the summands are multiplied by a factor of 2 in the case of lm1 not equal to lm2 .

                        b.drittler   may 1987
                          changed  dec 1988

For KREL = 1 (relativistic mode) NPOTD = 2 * NATYPD
LMMAXD = 2 * (LMAXD+1)^2
NSPIND = 1

Arguments