mirror of https://gitlab.com/QEF/q-e.git
78 lines
2.0 KiB
Fortran
78 lines
2.0 KiB
Fortran
!
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!----------------------------------------------------------------------
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subroutine integrate_inward(e,mesh,ndm,dx,r,r2,sqr,f, &
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y,c,el,ik,nstart)
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!----------------------------------------------------------------------
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!
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! this subroutine integrate inward the schroedinger equation
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! only local potential allowed
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!
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use kinds, only : DP
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implicit none
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integer :: &
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mesh, & ! size of radial mesh
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ndm, & ! maximum radial mesh
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ik ! the matching point
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real(kind=dp) :: &
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e, & ! output eigenvalue
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dx, & ! linear delta x for radial mesh
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r(mesh), & ! radial mesh
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r2(mesh),& ! square of radial mesh
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sqr(mesh),& ! square root of radial mesh
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f(mesh), & ! the function defining the equation
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y(mesh), & ! the output solution
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c(mesh),el(mesh) ! auxiliary space
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real(kind=dp) :: &
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rstart, & ! the starting r of the inward integration
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di, & ! auxiliary for integration
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expn ! exponential for tail of wavefunction
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integer :: &
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nstart, & ! the starting point of inward integration
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n ! counter on mesh points
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!
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! prepare inward integration
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! charlotte froese can j phys 41,1895(1963)
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!
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! start at min( rmax, 10*rmatch )
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!
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nstart=mesh
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rstart=10.0_dp*r(ik)
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if (rstart.lt.r(mesh)) then
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do n=ik,mesh
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nstart=n
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if(r(n).ge.rstart) go to 100
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enddo
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100 if (mod(nstart,2) == 0) nstart=nstart+1
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endif
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!
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! set up a, l, and c vectors
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!
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n=ik+1
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el(n)=10.0_dp*f(n)-12.0_dp
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c(n)=-f(ik)*y(ik)
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do n=ik+2,nstart
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di=10.0_dp*f(n)-12.0_dp
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el(n)=di-f(n)*f(n-1)/el(n-1)
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c(n)=-c(n-1)*f(n-1)/el(n-1)
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enddo
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!
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! start inward integration by the froese's tail procedure
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!
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n=nstart-1
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expn=exp(-sqrt(12.0_dp*abs(1.0_dp-f(n))))
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y(n)=c(n)/(el(n)+f(nstart)*expn)
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y(nstart)=expn*y(n)
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!
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! and integrate inward
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!
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do n=nstart-2,ik+1,-1
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y(n)=(c(n)-f(n+1)*y(n+1))/el(n)
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enddo
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return
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end subroutine integrate_inward
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