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edifwtx.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: edifwtx
!
! !INTERFACE:
subroutine edifwtx(v,omeg,figu,wt)
!
! !DESCRIPTION:
!
! This subroutine calculates the weight on vertex 2 of the small tetrahedron.
! For the case of $sigfreq=3$ when we consider 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,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
!
! !INTRINSIC ROUTINES:
intrinsic datan
intrinsic dlog
! !REVISION HISTORY:
!
! Created 04.11.2004 by XZL.
!
!EOP
!BOC
do i=1,4
do j=1,4
vdif(i,j)=v(i)-v(j)
enddo
enddo
select case(figu)
case(4) ! for the case none of them are equal
aa=2.0d0*vdif(1,2)*(v(2)**2-omeg**2)*vdif(1,3)*vdif(2,3)* &
& vdif(1,4)*vdif(2,4)*vdif(3,4)
aa=aa+2.0d0*omeg*(omeg**2-3.0d0*v(1)**2)*vdif(2,3)**2* &
& vdif(2,4)**2*vdif(3,4)*datan(v(1)/omeg)
dd=omeg**2*(-3.0d0*v(2)**2+2.0d0*v(2)*v(3)+2.0d0* &
& v(2)*v(4)-v(3)*v(4)-v(1)*(-2.0d0*v(2)+v(3)+v(4)))
dd=dd-3.0d0*v(2)*(-v(2)**3-2.0d0*v(1)*v(3)*v(4)+ &
& v(2)*(v(3)*v(4)+v(1)*(v(3)+v(4))))
aa=aa+2.0d0*omeg*vdif(1,3)*vdif(1,4)*vdif(3,4)*dd* &
& datan(v(2)/omeg)
aa=aa-2.0d0*omeg*(omeg**2-3.0d0*v(3)**2)*vdif(1,2)**2* &
& vdif(1,4)*vdif(2,4)**2*datan(v(3)/omeg)
aa=aa+2.0d0*omeg*(omeg**2-3.0d0*v(4)**2)*vdif(1,2)**2* &
& vdif(1,3)*vdif(2,3)**2*datan(v(4)/omeg)
bb=-v(1)*(v(1)**2-3.0d0*omeg**2)*vdif(2,3)**2*vdif(2,4)**2* &
& vdif(3,4)*dlog(v(1)**2+omeg**2)
dd=3.0d0*omeg**2*(v(2)**2*(v(3)+v(4)-2.0d0*v(2))+ &
& v(1)*(v(2)**2-v(3)*v(4)))
dd=dd+v(2)**2*(v(1)*(v(2)**2+3.0d0*v(3)*v(4)-2.0d0* &
& v(2)*(v(3)+v(4)))+v(2)*(v(2)*(v(3)+v(4))-2.0d0* &
& v(3)*v(4)))
bb=bb+vdif(1,3)*vdif(1,4)*vdif(3,4)*dd*dlog(v(2)**2+omeg**2)
bb=bb+v(3)*(v(3)**2-3*omeg**2)*vdif(1,2)**2*vdif(1,4)* &
& vdif(2,4)**2*dlog(v(3)**2+omeg**2)
bb=bb-v(4)*(v(4)**2-3.0d0*omeg**2)*vdif(1,2)**2*vdif(1,3)* &
& vdif(2,3)**2*dlog(v(4)**2+omeg**2)
cc=6.0d0*vdif(1,2)**2*vdif(1,3)*vdif(2,3)**2*vdif(1,4)* &
& vdif(2,4)**2*vdif(3,4)
case(6) ! for the case when v(1)=v(1)
dd=v(2)**3-2.0d0*omeg**2*(v(3)+v(4))-3.0d0*v(2)**2*(v(3)+v(4))+ &
& v(2)*(4.0d0*omeg**2+5.0d0*v(3)*v(4))
aa=vdif(3,2)*vdif(2,4)*vdif(3,4)*dd
dd=-omeg**2*(3.0d0*v(2)**2+v(3)**2+v(3)*v(4)+v(4)**2-3.0d0*v(2)*&
& (v(3)+v(4)))+3.0d0*(-3.0d0*v(2)**2*v(3)*v(4)+v(3)**2*v(4)**2+&
& v(2)**3*(v(3)+v(4)))
aa=aa-2.0d0*omeg*vdif(3,4)*dd*datan(v(2)/omeg)
aa=aa-2.0d0*omeg*(omeg**2-3.0d0*v(3)**2)*vdif(2,4)**3* &
& datan(v(3)/omeg)
aa=aa+2.0d0*omeg*vdif(2,3)**3*(omeg**2-3.0d0*v(4)**2)* &
& datan(v(4)/omeg)
dd=-3.0d0*omeg**2*v(3)*v(4)*(v(3)+v(4))-3.0d0*v(2)**2*v(3)* &
& v(4)*(v(3)+v(4))+3.0d0*v(2)*v(3)*v(4)*(3.0d0*omeg**2+v(3)* &
& v(4))+v(2)**3*(-3.0d0*omeg**2+v(3)**2+v(3)*v(4)+v(4)**2)
bb1=-vdif(3,4)*dd
bb3=v(3)*vdif(2,4)**3*(v(3)**2-3.0d0*omeg**2)
bb4=-v(4)*vdif(2,3)**3*(v(4)**2-3.0d0*omeg**2)
bb=bb1*dlog((v(2)**2+omeg**2))+ &
& bb3*dlog((v(3)**2+omeg**2))+ &
& bb4*dlog(v(4)**2+omeg**2)
cc=6.0d0*vdif(2,3)**3*vdif(2,4)**3*vdif(3,4)
case(8) !for the case when v(1)=v(2) and v(3)=v(4)
vp=(v(3)+v(4))*0.5d0
ev(1)=v(1)
ev(2)=v(2)
ev(3)=vp
ev(4)=vp
do i=1,4
do j=1,4
vdif(i,j)=ev(i)-ev(j)
enddo
enddo
dd=6.0d0*omeg**2+ev(2)**2-5.0d0*ev(2)*ev(3)-2.0d0*ev(3)**2
aa=vdif(3,2)*dd
dd=6.0d0*omeg*(omeg**2-ev(3)*(ev(3)+2.0d0*ev(2)))
aa=aa+dd*(datan(ev(2)/omeg)-datan(ev(3)/omeg))
bb=-3.0d0*(ev(2)*ev(3)**2-(ev(2)+2.0d0*ev(3))*omeg**2)
bb=bb*(dlog(ev(2)**2+omeg**2)-dlog(ev(3)**2+omeg**2))
cc=6.0d0*vdif(2,3)**4
case(10) ! for the case when v(1)=v(2)=v(3)
aa=vdif(2,4)*(6.0d0*omeg**2-2.0d0*v(2)**2+7.0d0*v(2)*v(4)- &
& 11.0d0*v(4)**2)
dd=6.0d0*omeg*(omeg**2-3.0d0*v(4)**2)
aa=aa-dd*(datan(v(2)/omeg)-datan(v(4)/omeg))
dd=3.0d0*v(4)*(v(4)**2-3.0d0*omeg**2)
bb=dd*dlog((v(2)**2+omeg**2)/(v(4)**2+omeg**2))
cc=18.0d0*vdif(2,4)**4
case(16)
aa=-v(2)
bb=0.0d0
cc=12.0d0*(omeg**2+v(2)**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,aa+bb,cc
! stop
endif
1 format('warning: weightx =',g18.10,' case:',i4,/,'omeg =',g18.10,/,'v =',4g18.10, &
& /,'vdif = ',/,4(4g18.10,/),' aa =',g18.10,' bb =',g18.10, &
& ' aa+bb =',g18.10,' cc =',g18.10)
return
end subroutine edifwtx
!EOC