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! Copyright (C) 2002-2016 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl.
! This file is distributed under the terms of the GNU General Public License.
! See the file COPYING for license details.
!BOP
! !ROUTINE: hmlrad
! !INTERFACE:
subroutine hmlrad
! !USES:
use modmain
use modomp
! !DESCRIPTION:
! Calculates the radial Hamiltonian integrals of the APW and local-orbital
! basis functions. In other words, for atom $\alpha$, it computes integrals of
! the form
! $$ h^{\alpha}_{qq';ll'l''m''}=\begin{cases}
! \int_0^{R_i}u^{\alpha}_{q;l}(r)H u^{\alpha}_{q';l'}(r)r^2dr & l''=0 \\
! \int_0^{R_i}u^{\alpha}_{q;l}(r)V^{\alpha}_{l''m''}(r)
! u^{\alpha}_{q';l'}(r)r^2dr & l''>0 \end{cases} $$
! where $u^{\alpha}_{q;l}$ is the $q$th APW radial function for angular
! momentum $l$; $H$ is the Hamiltonian of the radial Schr\"{o}dinger equation;
! and $V^{\alpha}_{l''m''}$ is the muffin-tin Kohn-Sham potential. Similar
! integrals are calculated for APW-local-orbital and
! local-orbital-local-orbital contributions.
!
! !REVISION HISTORY:
! Created December 2003 (JKD)
! Updated for compressed muffin-tin functions, March 2016 (JKD)
!EOP
!BOC
implicit none
! local variables
integer is,ias,nthd
integer nr,nri,iro,i0,i1
integer l1,l2,l3,lm2
integer io,jo,ilo,jlo
real(8) sm
! begin loops over atoms and species
call holdthd(natmtot,nthd)
!$OMP PARALLEL DO DEFAULT(SHARED) &
!$OMP PRIVATE(is,nr,nri,iro) &
!$OMP PRIVATE(l1,l2,l3,io,jo,sm) &
!$OMP PRIVATE(lm2,i0,i1,ilo,jlo) &
!$OMP SCHEDULE(DYNAMIC) &
!$OMP NUM_THREADS(nthd)
do ias=1,natmtot
is=idxis(ias)
nr=nrmt(is)
nri=nrmti(is)
iro=nri+1
!---------------------------!
! APW-APW integrals !
!---------------------------!
do l1=0,lmaxapw
do io=1,apword(l1,is)
do l3=0,lmaxapw
do jo=1,apword(l3,is)
if (l1 == l3) then
sm=sum((apwfr(1:nr,1,io,l1,ias)*apwfr(1:nr,2,jo,l1,ias) &
+apwfr(1:nr,2,io,l1,ias)*apwfr(1:nr,1,jo,l1,ias)) &
*wr2mt(1:nr,is))
! add kinetic surface term
sm=sm+apwfr(nr,1,io,l1,ias)*apwdfr(jo,l1,ias) &
+apwdfr(io,l1,ias)*apwfr(nr,1,jo,l1,ias)
haa(1,jo,l1,io,l1,ias)=sm*y00i/2.d0
else
haa(1,jo,l3,io,l1,ias)=0.d0
end if
if (l1 >= l3) then
do l2=1,lmaxi
do lm2=l2**2+1,(l2+1)**2
i1=lmmaxi*(nri-1)+lm2
sm=sum(apwfr(1:nri,1,io,l1,ias)*apwfr(1:nri,1,jo,l3,ias) &
*wr2mt(1:nri,is)*vsmt(lm2:i1:lmmaxi,ias))
i0=i1+lmmaxi
i1=lmmaxo*(nr-iro)+i0
sm=sm+sum(apwfr(iro:nr,1,io,l1,ias)*apwfr(iro:nr,1,jo,l3,ias) &
*wr2mt(iro:nr,is)*vsmt(i0:i1:lmmaxo,ias))
haa(lm2,jo,l3,io,l1,ias)=sm
haa(lm2,io,l1,jo,l3,ias)=sm
end do
end do
do l2=lmaxi+1,lmaxo
do lm2=l2**2+1,(l2+1)**2
i0=lmmaxi*nri+lm2
i1=lmmaxo*(nr-iro)+i0
sm=sum(apwfr(iro:nr,1,io,l1,ias)*apwfr(iro:nr,1,jo,l3,ias) &
*wr2mt(iro:nr,is)*vsmt(i0:i1:lmmaxo,ias))
haa(lm2,jo,l3,io,l1,ias)=sm
haa(lm2,io,l1,jo,l3,ias)=sm
end do
end do
end if
end do
end do
end do
end do
!-------------------------------------!
! local-orbital-APW integrals !
!-------------------------------------!
do ilo=1,nlorb(is)
l1=lorbl(ilo,is)
do l3=0,lmaxapw
do jo=1,apword(l3,is)
if (l1 == l3) then
sm=sum(lofr(1:nr,1,ilo,ias)*apwfr(1:nr,2,jo,l1,ias)*wr2mt(1:nr,is))
hloa(1,jo,l1,ilo,ias)=sm*y00i
else
hloa(1,jo,l3,ilo,ias)=0.d0
end if
do l2=1,lmaxi
do lm2=l2**2+1,(l2+1)**2
i1=lmmaxi*(nri-1)+lm2
sm=sum(lofr(1:nri,1,ilo,ias)*apwfr(1:nri,1,jo,l3,ias) &
*wr2mt(1:nri,is)*vsmt(lm2:i1:lmmaxi,ias))
i0=i1+lmmaxi
i1=lmmaxo*(nr-iro)+i0
sm=sm+sum(lofr(iro:nr,1,ilo,ias)*apwfr(iro:nr,1,jo,l3,ias) &
*wr2mt(iro:nr,is)*vsmt(i0:i1:lmmaxo,ias))
hloa(lm2,jo,l3,ilo,ias)=sm
end do
end do
do l2=lmaxi+1,lmaxo
do lm2=l2**2+1,(l2+1)**2
i0=lmmaxi*nri+lm2
i1=lmmaxo*(nr-iro)+i0
sm=sum(lofr(iro:nr,1,ilo,ias)*apwfr(iro:nr,1,jo,l3,ias) &
*wr2mt(iro:nr,is)*vsmt(i0:i1:lmmaxo,ias))
hloa(lm2,jo,l3,ilo,ias)=sm
end do
end do
end do
end do
end do
!-----------------------------------------------!
! local-orbital-local-orbital integrals !
!-----------------------------------------------!
do ilo=1,nlorb(is)
l1=lorbl(ilo,is)
do jlo=1,nlorb(is)
l3=lorbl(jlo,is)
if (l1 == l3) then
sm=sum(lofr(1:nr,1,ilo,ias)*lofr(1:nr,2,jlo,ias)*wr2mt(1:nr,is))
hlolo(1,jlo,ilo,ias)=sm*y00i
else
hlolo(1,jlo,ilo,ias)=0.d0
end if
do l2=1,lmaxi
do lm2=l2**2+1,(l2+1)**2
i1=lmmaxi*(nri-1)+lm2
sm=sum(lofr(1:nri,1,ilo,ias)*lofr(1:nri,1,jlo,ias)*wr2mt(1:nri,is) &
*vsmt(lm2:i1:lmmaxi,ias))
i0=i1+lmmaxi
i1=lmmaxo*(nr-iro)+i0
sm=sm+sum(lofr(iro:nr,1,ilo,ias)*lofr(iro:nr,1,jlo,ias) &
*wr2mt(iro:nr,is)*vsmt(i0:i1:lmmaxo,ias))
hlolo(lm2,jlo,ilo,ias)=sm
end do
end do
do l2=lmaxi+1,lmaxo
do lm2=l2**2+1,(l2+1)**2
i0=lmmaxi*nri+lm2
i1=lmmaxo*(nr-iro)+i0
sm=sum(lofr(iro:nr,1,ilo,ias)*lofr(iro:nr,1,jlo,ias) &
*wr2mt(iro:nr,is)*vsmt(i0:i1:lmmaxo,ias))
hlolo(lm2,jlo,ilo,ias)=sm
end do
end do
end do
end do
! end loops over atoms and species
end do
!$OMP END PARALLEL DO
call freethd(nthd)
end subroutine
!EOC
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