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edifwtz.f90
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! The code was developed at the Fritz Haber Institute, and
! the intellectual properties and copyright of this file
! are with the Max Planck Society. When you use it, please
! cite R. Gomez-Abal, X. Li, C. Ambrosch-Draxl, M. Scheffler,
! Extended linear tetrahedron method for the calculation of q-dependent
! dynamical response functions, to be published in Comp. Phys. Commun. (2010)
!BOP
!
! !ROUTINE: edifwtz
!
! !INTERFACE:
subroutine edifwtz(v,omeg,figu,wt)
!
! !DESCRIPTION:
!
! This subroutine calculates the weight on vertex 4 of the small tetrahedron.
! This is for the case of $sigfreq=3$ when we use the imaginary frequency.
!
! !INPUT PARAMETERS:
implicit none
real(8), intent(in) :: v(4) ! difference of the energy
! in k-mesh tetrahedron vertices and k-q mesh
! tetrahedron vertices.
real(8), intent(in) :: omeg !the frequency omega to be calculated
integer(4), intent(in) :: figu ! If figu=4, it belongs to the none
! equally case. If figu=6, v(1)=v(2).
! If figu=8, v(1)=v(2) and v(3)=v(4).
! If figu=10, v(1)=v(2)=v(3).
! If figu=16, v(1)=v(2)=v(3)=v(4).
! !OUTPUT PARAMETERS:
real(8), intent(out) :: wt ! the weight on vertex 4.
! !LOCAL VARIABLES:
integer(4) :: i,j
real(8) :: aa, bb, cc, dd
real(8) :: bb1,bb2,bb3,bb4
real(8) :: vp
real(8), dimension(4) :: ev
real(8), dimension(4,4) :: vdif
! !DEFINED PARAMETERS:
real(8), parameter :: haier=1.0d-20
!
! !SYSTEM ROUTINES:
intrinsic datan
intrinsic dlog
! !REVISION HISTORY:
!
! Created 04.11.2004 by XZL.
!
!EOP
!BOC
select case(figu)
case(4)
do i=1,4
do j=1,4
vdif(i,j)=v(i)-v(j)
enddo
enddo
aa=2.0d0*vdif(1,2)*vdif(1,3)*vdif(2,3)*vdif(1,4)*vdif(2,4)* &
& vdif(3,4)*(v(4)**2-omeg**2)
aa=aa+2.0d0*omeg*(omeg**2-3.0d0*v(1)**2)*vdif(2,3)* &
& vdif(2,4)**2*vdif(3,4)**2*datan(v(1)/omeg)
aa=aa-2.0d0*omeg*(omeg**2-3.0d0*v(2)**2)*vdif(1,3)* &
& vdif(1,4)**2*vdif(3,4)**2*datan(v(2)/omeg)
aa=aa+2.0d0*omeg*vdif(1,2)*(omeg**2-3.0d0*v(3)**2)* &
& vdif(1,4)**2*vdif(2,4)**2*datan(v(3)/omeg)
dd=omeg**2*(v(2)*v(3)+v(1)*(v(2)+v(3)-2.0d0*v(4))- &
& 2.0d0*v(2)*v(4)-2.0d0*v(3)*v(4)+3.0d0*v(4)**2)
dd=dd+3.0d0*v(4)*(v(2)*v(3)*v(4)-v(4)**3+v(1)*(-2.0d0* &
& v(2)*v(3)+v(2)*v(4)+v(3)*v(4)))
aa=aa-2.0d0*omeg*vdif(1,2)*vdif(1,3)*vdif(2,3)*dd* &
& datan(v(4)/omeg)
bb1=-v(1)*(v(1)**2-3.0d0*omeg**2)*vdif(2,3)*vdif(2,4)**2* &
& vdif(3,4)**2
bb2=v(2)*(v(2)**2-3.0d0*omeg**2)*vdif(1,3)*vdif(1,4)**2* &
& vdif(3,4)**2
bb3=-vdif(1,2)*v(3)*(v(3)**2-3.0d0*omeg**2)*vdif(1,4)**2* &
& vdif(2,4)**2
dd=3.0d0*omeg**2*(v(4)**2*(2.0d0*v(4)-v(3)-v(2))+v(1)* &
& (v(2)*v(3)-v(4)**2))
dd=dd-v(4)**2*(v(4)*(-2.0d0*v(2)*v(3)+v(2)*v(4)+v(3)* &
& v(4))+v(1)*(3.0d0*v(2)*v(3)-2.0d0*v(2)*v(4)-2.0d0* &
& v(3)*v(4)+v(4)**2))
bb4=-vdif(1,2)*vdif(1,3)*vdif(2,3)*dd
bb=bb1*dlog((v(1)**2+omeg**2)/(v(4)**2+omeg**2))+ &
& bb2*dlog((v(2)**2+omeg**2)/(v(4)**2+omeg**2))+ &
& bb3*dlog((v(3)**2+omeg**2)/(v(4)**2+omeg**2))+ &
& (bb1+bb2+bb3+bb4)*dlog(v(4)**2+omeg**2)
cc=6.0d0*vdif(1,2)*vdif(1,3)*vdif(2,3)*vdif(1,4)**2* &
& vdif(2,4)**2*vdif(3,4)**2
case(6)
vp=(v(1)+v(2))*0.5d0
ev(1)=vp
ev(2)=vp
ev(3)=v(3)
ev(4)=v(4)
do i=1,4
do j=1,4
vdif(i,j)=ev(i)-ev(j)
enddo
enddo
dd=omeg**2*ev(4)+ev(1)*(omeg**2-ev(4)**2)+ev(3)*(ev(4)**2- &
& 2.0d0*omeg**2)+ev(1)**2*vdif(3,4)
aa=-2.0d0*dd*vdif(1,3)*vdif(1,4)*vdif(3,4)
dd=3.0d0*ev(1)**3+3.0d0*ev(1)**2*ev(4)+omeg**2*(2.0d0*ev(3)+ &
& ev(4))-3.0d0*ev(1)*(omeg**2+2.0d0*ev(3)*ev(4))
aa=aa+2.0d0*omeg*dd*vdif(3,4)**2*datan(ev(1)/omeg)
aa=aa+2.0d0*omeg*(omeg**2-3.0d0*ev(3)**2)*vdif(1,4)**3* &
& datan(ev(3)/omeg)
dd=-2.0d0*omeg**2*ev(3)+3.0d0*omeg**2*ev(4)-3.0d0*ev(4)**3-ev(1)* &
& (omeg**2-6.0d0*ev(3)*ev(4)+3.0d0*ev(4)**2)
aa=aa+2.0d0*omeg*vdif(1,3)**2*dd*datan(ev(4)/omeg)
dd=3.0d0*omeg**2*ev(1)*ev(3)+3.0d0*omeg**2*ev(3)*ev(4)+ev(1)**3* &
& (ev(3)+2.0d0*ev(4))-3.0d0*ev(1)**2*(2.0d0*omeg**2+ev(3)*ev(4))
bb1=vdif(3,4)**2*dd
bb3=-ev(3)*(ev(3)**2-3.0d0*omeg**2)*vdif(1,4)**3
dd=-ev(4)**2*(-3.0d0*ev(1)*ev(3)+2.0d0*ev(1)*ev(4)+ev(3)*ev(4))- &
& 3.0d0*omeg**2*(ev(1)*ev(3)+(ev(3)-2.0d0*ev(4))*ev(4))
bb4=vdif(1,3)**2*dd
bb=bb1*dlog(ev(1)**2+omeg**2)+bb3*dlog(ev(3)**2+omeg**2)+ &
& bb4*dlog(ev(4)**2+omeg**2)
cc=6.0d0*vdif(1,3)**2*vdif(1,4)**3*vdif(3,4)**2
case(8) ! for the case when v(1)=v(2) and v(3)=v(4)
vp=(v(1)+v(2))*0.5d0
ev(1)=vp
ev(2)=vp
ev(3)=v(3)
ev(4)=v(4)
do i=1,4
do j=1,4
vdif(i,j)=ev(i)-ev(j)
enddo
enddo
dd=6.0d0*omeg**2-2.0d0*ev(1)**2-5.0d0*ev(1)*ev(4)+ev(4)**2
aa=vdif(1,4)*dd
dd=6.0d0*omeg*(ev(1)**2+2.0d0*ev(1)*ev(4)-omeg**2)
aa=aa+dd*(datan(ev(1)/omeg)-datan(ev(4)/omeg))
dd=3.0d0*(ev(1)**2*ev(4)-(2.0d0*ev(1)+ev(4))*omeg**2)
bb=dd*dlog((ev(1)**2+omeg**2)/(ev(4)**2+omeg**2))
cc=6.0d0*vdif(1,4)**4
case(10)
vp=(v(1)+v(2)+v(3))/3.0d0
ev(1)=vp
ev(2)=vp
ev(3)=vp
ev(4)=v(4)
do i=1,4
do j=1,4
vdif(i,j)=ev(i)-ev(j)
enddo
enddo
dd=6.0d0*omeg**2+ev(1)**2-5.0d0*ev(1)*ev(4)-2.0d0*ev(4)**2
aa=vdif(4,1)*dd
dd=6.0d0*omeg*(omeg**2-ev(4)**2-2.0d0*ev(1)*ev(4))
aa=aa+dd*(datan(ev(1)/omeg)-datan(ev(4)/omeg))
dd=-3.0d0*ev(1)*ev(4)**2+3.0d0*omeg**2*(ev(1)+2.0d0*ev(4))
bb=dd*dlog((ev(1)**2+omeg**2)/(ev(4)**2+omeg**2))
cc=6.0d0*vdif(1,4)**4
case(16)
aa=-v(4)
bb=0.0d0
cc=12.0d0*(omeg**2+v(4)**2)
end select
! wt=0.0d0
! if((dabs(cc)*1.0d+2).gt.dabs(aa+bb)) then
wt=(aa+bb)/cc
! endif
if(abs(wt).gt.1.0d+1)then
write(*,1)wt,figu,omeg,v,vdif,aa,bb,cc
! stop
endif
1 format('warning: weightz =',g18.10,' case:',i4,/,'omeg =',g18.10,/,'v =',4g18.10, &
& /,'vdif = ',/,4(4g18.10,/),' aa =',g18.10,' bb =',g18.10, &
& ' cc =',g18.10)
return
end subroutine edifwtz
!EOC