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! Copyright (C) 2010 Alexey I. Baranov.
! This file is distributed under the terms of the GNU General Public License.
! See the file COPYING for license details.
!BOP
! !ROUTINE: zftrf
! !INTERFACE:
subroutine zftrf(npv,ivp,vpc,rfmt,rfir,zfp)
! !USES:
use modmain
! !INPUT/OUTPUT PARAMETERS:
! npv : number of P-vectors (in,integer)
! ivp : integer coordinates of the P-vectors (in,integer(3,npv))
! vpc : P-vectors in Cartesian coordinates (in,real(3,npv))
! rfmt : real muffin-tin function (in,real(npmtmax,natmtot))
! rfir : real interstitial function (in,real(ngtot))
! zfp : Fourier expansion coefficients of the real-space function
! (out,complex(npv))
! !DESCRIPTION:
! Given a real function periodic in the unit cell, $f({\bf r})$, this routine
! calculates its complex Fourier expansion coefficients:
! $$ f({\bf P})=\frac{1}{\Omega}\int d^3r\,f({\bf r})\tilde{\Theta}({\bf r})
! e^{-i{\bf P}\cdot{\bf r}}
! +\frac{4\pi}{\Omega}\sum_{\alpha}e^{-i{\bf P}\cdot{\bf R}_{\alpha}}
! \sum_{lm}(-i)^l Y_{lm}(\hat{\bf P})
! \int_{0}^{R_{\alpha}}dr\,r^2 j_{l}(|{\bf P}|r)f_{lm}^{\alpha}(r), $$
! where $\tilde{\Theta}$ is the smooth characteristic function of the
! interstitial region, $\Omega$ is the unit cell volume and $R_{\alpha}$ is
! the muffin-tin radius of atom $\alpha$.
!
! !REVISION HISTORY:
! Created July 2010 (Alexey I. Baranov)
! Modified, November 2010 (JKD)
! Optimised, May 2024 (JKD)
!EOP
!BOC
implicit none
! arguments
integer, intent(in) :: npv,ivp(3,npv)
real(8), intent(in) :: vpc(3,npv),rfmt(npmtmax,natmtot),rfir(ngtot)
complex(8), intent(out) :: zfp(npv)
! local variables
integer is,ia,ias,ip,ig,ifg
integer nrc,nrci,irco,irc
integer l,lm,n,i
real(8) p,t0,t1
complex(8) zsm,z1,z2
! automatic arrays
real(8) jl(0:lmaxo,nrcmtmax),rfmt1(npcmtmax)
complex(8) ylm(lmmaxo)
! allocatable arrays
complex(8), allocatable :: zfft(:),zfmt(:,:)
allocate(zfft(ngtot),zfmt(npcmtmax,natmtot))
! zero the coefficients
zfp(1:npv)=0.d0
!---------------------------!
! interstitial part !
!---------------------------!
! Fourier transform to G-space
zfft(1:ngtot)=rfir(1:ngtot)
call zfftifc(3,ngridg,-1,zfft)
! find coefficients for all required input vectors
do ip=1,npv
if ((ivp(1,ip) >= intgv(1,1)).and.(ivp(1,ip) <= intgv(2,1)).and. &
(ivp(2,ip) >= intgv(1,2)).and.(ivp(2,ip) <= intgv(2,2)).and. &
(ivp(3,ip) >= intgv(1,3)).and.(ivp(3,ip) <= intgv(2,3))) then
ig=ivgig(ivp(1,ip),ivp(2,ip),ivp(3,ip))
zfp(ip)=zfft(igfft(ig))
end if
end do
!-------------------------!
! muffin-tin part !
!-------------------------!
! convert function from real to complex spherical harmonic expansion on coarse
! radial mesh
do ias=1,natmtot
is=idxis(ias)
nrc=nrcmt(is)
nrci=nrcmti(is)
call rfmtftoc(nrc,nrci,rfmt(:,ias),rfmt1)
call rtozfmt(nrc,nrci,rfmt1,zfmt(:,ias))
end do
! remove continuation of interstitial function into muffin-tin
do ig=1,ngvec
ifg=igfft(ig)
! conjugate spherical harmonics 4π iˡ Yₗₘ(G)*
call genylmv(.true.,lmaxo,vgc(:,ig),ylm)
ylm(1:lmmaxo)=conjg(ylm(1:lmmaxo))
do is=1,nspecies
nrc=nrcmt(is)
nrci=nrcmti(is)
irco=nrci+1
! generate spherical Bessel functions
do irc=1,nrci
t1=gc(ig)*rcmt(irc,is)
call sbessel(lmaxi,t1,jl(:,irc))
end do
do irc=irco,nrc
t1=gc(ig)*rcmt(irc,is)
call sbessel(lmaxo,t1,jl(:,irc))
end do
do ia=1,natoms(is)
ias=idxas(ia,is)
! structure factor
t1=vgc(1,ig)*atposc(1,ia,is) &
+vgc(2,ig)*atposc(2,ia,is) &
+vgc(3,ig)*atposc(3,ia,is)
z1=zfft(ifg)*cmplx(cos(t1),sin(t1),8)
i=1
do irc=1,nrci
do l=0,lmaxi
n=2*l
lm=l**2+1
z2=z1*jl(l,irc)
zfmt(i:i+n,ias)=zfmt(i:i+n,ias)-z2*ylm(lm:lm+n)
i=i+n+1
end do
end do
do irc=irco,nrc
do l=0,lmaxo
n=2*l
lm=l**2+1
z2=z1*jl(l,irc)
zfmt(i:i+n,ias)=zfmt(i:i+n,ias)-z2*ylm(lm:lm+n)
i=i+n+1
end do
end do
end do
end do
end do
t0=1.d0/omega
! loop over input P-vectors
do ip=1,npv
! length of P-vector
p=sqrt(vpc(1,ip)**2+vpc(2,ip)**2+vpc(3,ip)**2)
! spherical harmonics 4π (-i)ˡ Yₗₘ(P)
call genylmv(.true.,lmaxo,vpc(:,ip),ylm)
do is=1,nspecies
nrc=nrcmt(is)
nrci=nrcmti(is)
irco=nrci+1
! generate spherical Bessel functions
do irc=1,nrci
t1=p*rcmt(irc,is)
call sbessel(lmaxi,t1,jl(:,irc))
end do
do irc=irco,nrc
t1=p*rcmt(irc,is)
call sbessel(lmaxo,t1,jl(:,irc))
end do
do ia=1,natoms(is)
ias=idxas(ia,is)
zsm=0.d0
i=1
do irc=1,nrci
z1=jl(0,irc)*zfmt(i,ias)*ylm(1)
i=i+1
do l=1,lmaxi
n=2*l
lm=l**2+1
z1=z1+jl(l,irc)*sum(zfmt(i:i+n,ias)*ylm(lm:lm+n))
i=i+n+1
end do
zsm=zsm+wr2cmt(irc,is)*z1
end do
do irc=irco,nrc
z1=jl(0,irc)*zfmt(i,ias)*ylm(1)
i=i+1
do l=1,lmaxo
n=2*l
lm=l**2+1
z1=z1+jl(l,irc)*sum(zfmt(i:i+n,ias)*ylm(lm:lm+n))
i=i+n+1
end do
zsm=zsm+wr2cmt(irc,is)*z1
end do
! conjugate structure factor
t1=vpc(1,ip)*atposc(1,ia,is) &
+vpc(2,ip)*atposc(2,ia,is) &
+vpc(3,ip)*atposc(3,ia,is)
z1=t0*cmplx(cos(t1),-sin(t1),8)
zfp(ip)=zfp(ip)+z1*zsm
end do
end do
end do
deallocate(zfft,zfmt)
end subroutine
! EOC
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