2020-03-19 10:21:18 +01:00
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subroutine evGF3(maxSCF,thresh,max_diis,renormalization,nBas,nC,nO,nV,nR,V,e0)
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2019-03-19 10:13:33 +01:00
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! Perform third-order Green function calculation in diagonal approximation
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implicit none
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include 'parameters.h'
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! Input variables
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double precision,intent(in) :: thresh
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integer,intent(in) :: maxSCF,max_diis,renormalization
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integer,intent(in) :: nBas,nC,nO,nV,nR
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double precision,intent(in) :: e0(nBas),V(nBas,nBas,nBas,nBas)
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! Local variables
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2019-04-24 15:33:04 +02:00
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integer :: nSCF
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integer :: n_diis
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2019-03-19 10:13:33 +01:00
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double precision :: eps,eps1,eps2,Conv
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2019-04-24 15:33:04 +02:00
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double precision :: rcond
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2019-03-19 10:13:33 +01:00
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double precision,allocatable :: Sig2(:),SigInf(:),Sig3(:),eGF3(:),eOld(:)
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double precision,allocatable :: App(:,:),Bpp(:,:),Cpp(:,:),Dpp(:,:)
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double precision,allocatable :: Z(:),X2h1p(:),X1h2p(:),Sig2h1p(:),Sig1h2p(:)
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double precision,allocatable :: error_diis(:,:),e_diis(:,:)
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integer :: i,j,k,l,a,b,c,d,p
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! Hello world
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write(*,*)
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write(*,*)'************************************************'
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write(*,*)'| Third-order Green function calculation |'
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write(*,*)'************************************************'
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write(*,*)
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! Memory allocation
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allocate(eGF3(nBas),eOld(nBas), &
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Sig2(nBas),SigInf(nBas),Sig3(nBas), &
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App(nBas,6),Bpp(nBas,2),Cpp(nBas,6),Dpp(nBas,6), &
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Z(nBas),X2h1p(nBas),X1h2p(nBas),Sig2h1p(nBas),Sig1h2p(nBas), &
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error_diis(nBas,max_diis),e_diis(nBas,max_diis))
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!------------------------------------------------------------------------
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! Compute third-order frequency-independent contribution
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!------------------------------------------------------------------------
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App(:,:) = 0d0
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do p=nC+1,nBas-nR
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do i=nC+1,nO
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do j=nC+1,nO
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do k=nC+1,nO
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do a=nO+1,nBas-nR
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do b=nO+1,nBas-nR
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eps1 = e0(j) + e0(i) - e0(a) - e0(b)
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eps2 = e0(k) + e0(i) - e0(a) - e0(b)
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App(p,1) = App(p,1) &
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- (2d0*V(p,k,p,j) - V(p,k,j,p))*(2d0*V(j,i,a,b) - V(j,i,b,a))*V(a,b,k,i)/(eps1*eps2)
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enddo
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enddo
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enddo
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enddo
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enddo
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enddo
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do p=nC+1,nBas-nR
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do i=nC+1,nO
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do j=nC+1,nO
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do a=nO+1,nBas-nR
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do b=nO+1,nBas-nR
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do c=nO+1,nBas-nR
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eps1 = e0(j) + e0(i) - e0(a) - e0(b)
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eps2 = e0(j) + e0(i) - e0(a) - e0(c)
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App(p,2) = App(p,2) &
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+ (2d0*V(p,c,p,b) - V(p,c,b,p))*(2d0*V(j,i,a,b) - V(j,i,b,a))*V(j,i,c,a)/(eps1*eps2)
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enddo
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enddo
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enddo
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enddo
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enddo
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enddo
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do p=nC+1,nBas-nR
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do i=nC+1,nO
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do j=nC+1,nO
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do a=nO+1,nBas-nR
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do b=nO+1,nBas-nR
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do c=nO+1,nBas-nR
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eps1 = e0(j) + e0(i) - e0(a) - e0(b)
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eps2 = e0(j) - e0(c)
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App(p,3) = App(p,3) &
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+ (2d0*V(p,c,p,j) - V(p,c,j,p))*(2d0*V(j,i,a,b) - V(j,i,b,a))*V(a,b,c,i)/(eps1*eps2)
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enddo
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enddo
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enddo
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enddo
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enddo
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enddo
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App(:,4) = App(:,3)
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do p=nC+1,nBas-nR
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do i=nC+1,nO
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do j=nC+1,nO
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do k=nC+1,nO
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do a=nO+1,nBas-nR
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do b=nO+1,nBas-nR
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eps1 = e0(j) + e0(i) - e0(a) - e0(b)
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eps2 = e0(k) - e0(b)
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App(p,5) = App(p,5) &
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- (2d0*V(p,b,p,k) - V(p,b,k,p))*(2d0*V(j,i,a,b) - V(j,i,b,a))*V(i,j,k,a)/(eps1*eps2)
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enddo
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enddo
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enddo
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enddo
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enddo
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enddo
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App(:,6) = App(:,5)
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! Frequency-independent part of the third-order self-energy
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SigInf(:) = App(:,1) + App(:,2) + App(:,3) + App(:,4) + App(:,5) + App(:,6)
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!------------------------------------------------------------------------
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! Main SCF loop
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!------------------------------------------------------------------------
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nSCF = 0
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n_diis = 0
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Conv = 1d0
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Sig2(:) = 0d0
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Sig3(:) = 0d0
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e_diis(:,:) = 0d0
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error_diis(:,:) = 0d0
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eGF3(:) = e0(:)
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eOld(:) = e0(:)
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do while(Conv > thresh .and. nSCF < maxSCF)
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! Frequency-dependent second-order contribution
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Bpp(:,:) = 0d0
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do p=nC+1,nBas-nR
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do i=nC+1,nO
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do j=nC+1,nO
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do a=nO+1,nBas-nR
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eps = eGF3(p) + e0(a) - e0(i) - e0(j)
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Bpp(p,1) = Bpp(p,1) &
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+ (2d0*V(p,a,i,j) - V(p,a,j,i))*V(p,a,i,j)/eps
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enddo
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enddo
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enddo
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enddo
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do p=nC+1,nBas-nR
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do i=nC+1,nO
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do a=nO+1,nBas-nR
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do b=nO+1,nBas-nR
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eps = eGF3(p) + e0(i) - e0(a) - e0(b)
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Bpp(p,2) = Bpp(p,2) &
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+ (2d0*V(p,i,a,b) - V(p,i,b,a))*V(p,i,a,b)/eps
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enddo
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enddo
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enddo
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enddo
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! Total second-order Green function
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Sig2(:) = Bpp(:,1) + Bpp(:,2)
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! Frequency-dependent third-order contribution: "C" terms
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Cpp(:,:) = 0d0
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do p=nC+1,nBas-nR
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do i=nC+1,nO
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do a=nO+1,nBas-nR
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do b=nO+1,nBas-nR
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do c=nO+1,nBas-nR
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do d=nO+1,nBas-nR
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eps1 = eGF3(p) + e0(i) - e0(a) - e0(b)
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eps2 = eGF3(p) + e0(i) - e0(c) - e0(d)
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Cpp(p,1) = Cpp(p,1) &
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+ (2d0*V(p,i,a,b) - V(p,i,b,a))*V(a,b,c,d)*V(p,i,c,d)/(eps1*eps2)
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enddo
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enddo
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enddo
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enddo
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enddo
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enddo
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do p=nC+1,nBas-nR
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do i=nC+1,nO
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do j=nC+1,nO
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do k=nC+1,nO
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do a=nO+1,nBas-nR
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do b=nO+1,nBas-nR
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eps1 = eGF3(p) + e0(i) - e0(a) - e0(b)
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eps2 = e0(j) + e0(k) - e0(a) - e0(b)
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Cpp(p,2) = Cpp(p,2) &
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+ (2d0*V(p,i,a,b) - V(p,i,b,a))*V(a,b,j,k)*V(p,i,j,k)/(eps1*eps2)
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enddo
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enddo
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enddo
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enddo
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enddo
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enddo
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Cpp(:,3) = Cpp(:,2)
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do p=nC+1,nBas-nR
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do i=nC+1,nO
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do j=nC+1,nO
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do a=nO+1,nBas-nR
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do b=nO+1,nBas-nR
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do c=nO+1,nBas-nR
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eps1 = eGF3(p) + e0(a) - e0(i) - e0(j)
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eps2 = e0(i) + e0(j) - e0(b) - e0(c)
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Cpp(p,4) = Cpp(p,4) &
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+ (2d0*V(p,a,i,j) - V(p,a,j,i))*V(i,j,b,c)*V(p,a,b,c)/(eps1*eps2)
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enddo
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enddo
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enddo
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enddo
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enddo
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enddo
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Cpp(:,5) = Cpp(:,4)
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do p=nC+1,nBas-nR
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do i=nC+1,nO
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do j=nC+1,nO
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do k=nC+1,nO
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do l=nC+1,nO
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do a=nO+1,nBas-nR
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eps1 = eGF3(p) + e0(a) - e0(i) - e0(j)
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eps2 = eGF3(p) + e0(a) - e0(k) - e0(l)
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Cpp(p,6) = Cpp(p,6) &
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- (2d0*V(p,a,k,l) - V(p,a,l,k))*V(k,l,i,j)*V(p,a,i,j)/(eps1*eps2)
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enddo
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enddo
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enddo
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enddo
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enddo
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enddo
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! Frequency-dependent third-order contribution: "D" terms
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Dpp(:,:) = 0d0
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do p=nC+1,nBas-nR
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do i=nC+1,nO
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do j=nC+1,nO
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do a=nO+1,nBas-nR
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do b=nO+1,nBas-nR
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do c=nO+1,nBas-nR
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eps1 = eGF3(p) + e0(i) - e0(a) - e0(b)
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eps2 = eGF3(p) + e0(j) - e0(b) - e0(c)
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Dpp(p,1) = Dpp(p,1) &
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+ V(p,i,a,b)*(V(a,j,i,c)*( V(p,j,c,b) - 2d0*V(p,j,b,c)) &
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+ V(a,j,c,i)*( V(p,j,b,c) - 2d0*V(p,j,c,b)))/(eps1*eps2)
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Dpp(p,1) = Dpp(p,1) &
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+ V(p,i,b,a)*(V(a,j,i,c)*(4d0*V(p,j,b,c) - 2d0*V(p,j,c,b)) &
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+ V(a,j,c,i)*( V(p,j,c,b) - 2d0*V(p,j,b,c)))/(eps1*eps2)
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enddo
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enddo
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enddo
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enddo
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enddo
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enddo
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do p=nC+1,nBas-nR
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do i=nC+1,nO
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do j=nC+1,nO
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do a=nO+1,nBas-nR
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do b=nO+1,nBas-nR
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do c=nO+1,nBas-nR
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eps1 = eGF3(p) + e0(i) - e0(a) - e0(c)
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eps2 = e0(i) + e0(j) - e0(a) - e0(b)
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Dpp(p,2) = Dpp(p,2) &
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+ V(p,i,c,a)*(V(a,b,i,j)*(4d0*V(p,b,c,j) - 2d0*V(p,b,j,c)) &
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+ V(a,b,j,i)*( V(p,b,j,c) - 2d0*V(p,b,c,j)))/(eps1*eps2)
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Dpp(p,2) = Dpp(p,2) &
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+ V(p,i,a,c)*(V(a,b,i,j)*( V(p,b,j,c) - 2d0*V(p,b,c,j)) &
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+ V(a,b,j,i)*( V(p,b,c,j) - 2d0*V(p,b,j,c)))/(eps1*eps2)
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enddo
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enddo
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enddo
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enddo
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enddo
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enddo
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Dpp(:,3) = Dpp(:,2)
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do p=nC+1,nBas-nR
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do i=nC+1,nO
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do j=nC+1,nO
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do k=nC+1,nO
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do a=nO+1,nBas-nR
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do b=nO+1,nBas-nR
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eps1 = eGF3(p) + e0(a) - e0(j) - e0(k)
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eps2 = e0(i) + e0(j) - e0(a) - e0(b)
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Dpp(p,4) = Dpp(p,4) &
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+ V(p,a,k,j)*(V(j,i,a,b)*(4d0*V(p,i,k,b) - 2d0*V(p,i,b,k)) &
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+ V(j,i,b,a)*( V(p,i,b,k) - 2d0*V(p,i,k,b)))/(eps1*eps2)
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Dpp(p,4) = Dpp(p,4) &
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+ V(p,a,j,k)*(V(j,i,a,b)*( V(p,i,b,k) - 2d0*V(p,i,k,b)) &
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+ V(j,i,b,a)*( V(p,i,k,b) - 2d0*V(p,i,b,k)))/(eps1*eps2)
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enddo
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enddo
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enddo
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enddo
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enddo
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enddo
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Dpp(:,5) = Dpp(:,4)
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|
do p=nC+1,nBas-nR
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|
do i=nC+1,nO
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do j=nC+1,nO
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|
do k=nC+1,nO
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|
do a=nO+1,nBas-nR
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|
do b=nO+1,nBas-nR
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|
|
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|
eps1 = eGF3(p) + e0(a) - e0(i) - e0(k)
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|
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|
eps2 = eGF3(p) + e0(b) - e0(j) - e0(k)
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|
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Dpp(p,6) = Dpp(p,6) &
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|
- V(p,a,k,i)*(V(i,b,a,j)*(4d0*V(p,b,k,j) - 2d0*V(p,b,j,k)) &
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|
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|
+ V(i,b,j,a)*( V(p,b,j,k) - 2d0*V(p,b,k,j)))/(eps1*eps2)
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|
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Dpp(p,6) = Dpp(p,6) &
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|
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|
- V(p,a,i,k)*(V(i,b,a,j)*( V(p,b,j,k) - 2d0*V(p,b,k,j)) &
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|
+ V(i,b,j,a)*( V(p,b,k,j) - 2d0*V(p,b,j,k)))/(eps1*eps2)
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|
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|
enddo
|
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|
enddo
|
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|
enddo
|
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|
enddo
|
|
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|
enddo
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
! Compute renormalization factor (if required)
|
|
|
|
|
|
|
|
|
|
Z(:) = 1d0
|
|
|
|
|
|
|
|
|
|
if(renormalization == 0) then
|
|
|
|
|
|
|
|
|
|
Sig3(:) = SigInf(:) &
|
|
|
|
|
+ Cpp(:,1) + Cpp(:,2) + Cpp(:,3) + Cpp(:,4) + Cpp(:,5) + Cpp(:,6) &
|
|
|
|
|
+ Dpp(:,1) + Dpp(:,2) + Dpp(:,3) + Dpp(:,4) + Dpp(:,5) + Dpp(:,6)
|
|
|
|
|
|
|
|
|
|
elseif(renormalization == 1) then
|
|
|
|
|
|
|
|
|
|
Sig3(:) = SigInf(:) &
|
|
|
|
|
+ Cpp(:,1) + Cpp(:,2) + Cpp(:,3) + Cpp(:,4) + Cpp(:,5) + Cpp(:,6) &
|
|
|
|
|
+ Dpp(:,1) + Dpp(:,2) + Dpp(:,3) + Dpp(:,4) + Dpp(:,5) + Dpp(:,6)
|
|
|
|
|
|
|
|
|
|
Z(:) = Cpp(:,2) + Cpp(:,3) + Cpp(:,4) + Cpp(:,5) &
|
|
|
|
|
+ Dpp(:,2) + Dpp(:,3) + Dpp(:,4) + Dpp(:,5)
|
|
|
|
|
|
|
|
|
|
Z(nC+1:nBas-nR) = Z(nC+1:nBas-nR)/Sig2(nC+1:nBas-nR)
|
|
|
|
|
Z(:) = 1d0/(1d0 - Z(:))
|
|
|
|
|
|
|
|
|
|
Sig3(:) = Z(:)*Sig3(:)
|
|
|
|
|
|
|
|
|
|
elseif(renormalization == 2) then
|
|
|
|
|
|
|
|
|
|
Sig2h1p(:) = Cpp(:,4) + Cpp(:,5) + Cpp(:,6) + Dpp(:,4) + Dpp(:,5) + Dpp(:,6)
|
|
|
|
|
Sig1h2p(:) = Cpp(:,1) + Cpp(:,2) + Cpp(:,3) + Dpp(:,1) + Dpp(:,2) + Dpp(:,3)
|
|
|
|
|
|
|
|
|
|
X2h1p(:) = Cpp(:,4) + Cpp(:,5) + Dpp(:,4) + Dpp(:,5)
|
|
|
|
|
X1h2p(:) = Cpp(:,2) + Cpp(:,3) + Dpp(:,2) + Dpp(:,3)
|
|
|
|
|
|
|
|
|
|
X2h1p(nC+1:nBas-nR) = X2h1p(nC+1:nBas-nR)/Bpp(nC+1:nBas-nR,1)
|
|
|
|
|
X1h2p(nC+1:nBas-nR) = X1h2p(nC+1:nBas-nR)/Bpp(nC+1:nBas-nR,2)
|
|
|
|
|
|
|
|
|
|
Sig3(:) = SigInf(:) + &
|
|
|
|
|
+ 1d0/(1d0 - X2h1p(:))*Sig2h1p(:) &
|
|
|
|
|
+ 1d0/(1d0 - X1h2p(:))*Sig1h2p(:)
|
|
|
|
|
|
|
|
|
|
elseif(renormalization == 3) then
|
|
|
|
|
|
|
|
|
|
Sig3(:) = SigInf(:) &
|
|
|
|
|
+ Cpp(:,1) + Cpp(:,2) + Cpp(:,3) + Cpp(:,4) + Cpp(:,5) + Cpp(:,6) &
|
|
|
|
|
+ Dpp(:,1) + Dpp(:,2) + Dpp(:,3) + Dpp(:,4) + Dpp(:,5) + Dpp(:,6)
|
|
|
|
|
|
|
|
|
|
Sig2h1p(:) = Cpp(:,4) + Cpp(:,5) + Cpp(:,6) + Dpp(:,4) + Dpp(:,5) + Dpp(:,6)
|
|
|
|
|
Sig1h2p(:) = Cpp(:,1) + Cpp(:,2) + Cpp(:,3) + Dpp(:,1) + Dpp(:,2) + Dpp(:,3)
|
|
|
|
|
|
|
|
|
|
X2h1p(:) = Cpp(:,4) + Cpp(:,5) + Dpp(:,4) + Dpp(:,5)
|
|
|
|
|
X1h2p(:) = Cpp(:,2) + Cpp(:,3) + Dpp(:,2) + Dpp(:,3)
|
|
|
|
|
|
|
|
|
|
X2h1p(nC+1:nBas-nR) = X2h1p(nC+1:nBas-nR)/Bpp(nC+1:nBas-nR,1)
|
|
|
|
|
X1h2p(nC+1:nBas-nR) = X1h2p(nC+1:nBas-nR)/Bpp(nC+1:nBas-nR,2)
|
|
|
|
|
|
|
|
|
|
Z(:) = X2h1p(:)*Sig2h1p(:) + X1h2p(:)*Sig1h2p(:)
|
|
|
|
|
Z(nC+1:nBas-nR) = Z(nC+1:nBas-nR)/(Sig3(nC+1:nBas-nR) - SigInf(nC+1:nBas-nR))
|
|
|
|
|
Z(:) = 1d0/(1d0 - Z(:))
|
|
|
|
|
|
|
|
|
|
Sig3(:) = Z(:)*Sig3(:)
|
|
|
|
|
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
! Total third-order Green function
|
|
|
|
|
|
|
|
|
|
eGF3(:) = e0(:) + Sig2(:) + Sig3(:)
|
|
|
|
|
|
|
|
|
|
! Convergence criteria
|
|
|
|
|
|
|
|
|
|
Conv = maxval(abs(eGF3 - eOld))
|
|
|
|
|
|
2019-04-29 09:54:36 +02:00
|
|
|
! Print results
|
|
|
|
|
|
2020-03-19 10:21:18 +01:00
|
|
|
call print_evGF3(nBas,nO,nSCF,Conv,e0,Z,eGF3)
|
2019-04-29 09:54:36 +02:00
|
|
|
|
2019-03-19 10:13:33 +01:00
|
|
|
! DIIS extrapolation
|
|
|
|
|
|
|
|
|
|
n_diis = min(n_diis+1,max_diis)
|
2019-04-24 15:33:04 +02:00
|
|
|
call DIIS_extrapolation(rcond,nBas,nBas,n_diis,error_diis,e_diis,eGF3-eOld,eGF3)
|
|
|
|
|
|
|
|
|
|
if(abs(rcond) < 1d-15) n_diis = 0
|
2019-03-19 10:13:33 +01:00
|
|
|
|
|
|
|
|
! Store result for next iteration
|
|
|
|
|
|
|
|
|
|
eOld(:) = eGF3(:)
|
|
|
|
|
|
|
|
|
|
! Increment
|
|
|
|
|
|
|
|
|
|
nSCF = nSCF + 1
|
|
|
|
|
|
|
|
|
|
enddo
|
|
|
|
|
!------------------------------------------------------------------------
|
|
|
|
|
! End main SCF loop
|
|
|
|
|
!------------------------------------------------------------------------
|
|
|
|
|
|
|
|
|
|
! Did it actually converge?
|
|
|
|
|
|
|
|
|
|
if(nSCF == maxSCF+1) then
|
|
|
|
|
|
|
|
|
|
write(*,*)
|
|
|
|
|
write(*,*)'!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'
|
|
|
|
|
write(*,*)' Convergence failed '
|
|
|
|
|
write(*,*)'!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'
|
|
|
|
|
write(*,*)
|
|
|
|
|
|
|
|
|
|
endif
|
|
|
|
|
|
2020-03-19 10:21:18 +01:00
|
|
|
end subroutine evGF3
|
