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https://github.com/pfloos/quack
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added <Si Sj>
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@ -225,6 +225,10 @@ subroutine print_GHFspin(nBas, nBas2, nO, C, S)
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double precision :: Na, Nb
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double precision :: nonco_z, contam_ghf
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double precision :: S2, Sz, Sz2
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complex*16 :: Sc_x, Sc_y, Sc_z
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complex*16 :: Sc_xx, Sc_xy, Sc_xz
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complex*16 :: Sc_yx, Sc_yy, Sc_yz
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complex*16 :: Sc_zx, Sc_zy, Sc_zz
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double precision, allocatable :: Ca(:,:), Cb(:,:)
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double precision, allocatable :: Paa(:,:), Pab(:,:), Pba(:,:), Pbb(:,:)
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double precision, allocatable :: Mc(:,:), Eigc(:)
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@ -276,6 +280,77 @@ subroutine print_GHFspin(nBas, nBas2, nO, C, S)
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print *, 'Sz, Sz^2 = ', Sz, Sz2
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print *, 'S^2 = ', S2
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! --- --- --- --- --- --- --- --- ---
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! Compute <Si> & <SiSj> for all i, j
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! --- --- --- --- --- --- --- --- ---
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Sc_x = (0.d0,0.d0)
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Sc_y = (0.d0,0.d0)
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Sc_z = (0.d0,0.d0)
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do i = 1, nO
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Sc_x = Sc_x + (+0.5d0,0.d0) * (Pab(i,i) + Pba(i,i))
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Sc_y = Sc_y + (0.d0,-0.5d0) * (Pab(i,i) - Pba(i,i))
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Sc_z = Sc_z + (+0.5d0,0.d0) * (Paa(i,i) - Pbb(i,i))
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enddo
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print *, " < Sx > = ", Sc_x
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print *, " < Sy > = ", Sc_y
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print *, " < Sz > = ", Sc_z
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Sc_xx = Sc_x * Sc_x + 0.25d0*dble(nO)*(1.d0,0.d0)
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Sc_yy = Sc_y * Sc_y + 0.25d0*dble(nO)*(1.d0,0.d0)
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Sc_zz = Sc_z * Sc_z + 0.25d0*dble(nO)*(1.d0,0.d0)
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do i = 1, nO
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do j = 1, nO
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Sc_xx = Sc_xx - zabs((+0.5d0,0.d0) * (Pab(i,j) + Pba(i,j)))**2
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Sc_yy = Sc_yy - zabs((0.d0,-0.5d0) * (Pab(i,j) - Pba(i,j)))**2
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Sc_zz = Sc_zz - zabs((+0.5d0,0.d0) * (Paa(i,j) - Pbb(i,j)))**2
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enddo
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enddo
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print *, " < Sx^2 > = ", Sc_xx
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print *, " < Sy^2 > = ", Sc_yy
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print *, " < Sz^2 > = ", Sc_zz
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Sc_xy = Sc_x * Sc_y
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Sc_yx = Sc_x * Sc_y
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do i = 1, nO
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Sc_xy = Sc_xy + (0.d0,0.5d0) * (+0.5d0,0.0d0) * (Paa(i,i) - Pbb(i,i))
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Sc_yx = Sc_yx - (0.d0,0.5d0) * (+0.5d0,0.0d0) * (Paa(i,i) - Pbb(i,i))
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do j = 1, nO
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Sc_xy = Sc_xy - (+0.5d0,0.d0) * (Pab(i,j) + Pba(i,j)) * (0.d0,-0.5d0) * (Pab(j,i) - Pba(j,i))
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Sc_yx = Sc_yx - (+0.5d0,0.d0) * (Pab(j,i) + Pba(j,i)) * (0.d0,-0.5d0) * (Pab(i,j) - Pba(i,j))
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enddo
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enddo
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print *, " < Sx Sy > = ", Sc_xy
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print *, " < Sy Sx > = ", Sc_yx
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Sc_xz = Sc_x * Sc_z
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Sc_zx = Sc_x * Sc_z
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do i = 1, nO
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Sc_xz = Sc_xz - (0.d0,0.5d0) * (0.d0,-0.5d0) * (Pab(i,i) - Pba(i,i))
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Sc_zx = Sc_zx + (0.d0,0.5d0) * (0.d0,-0.5d0) * (Pab(i,i) - Pba(i,i))
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do j = 1, nO
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Sc_xz = Sc_xz - (+0.5d0,0.d0) * (Pab(i,j) + Pba(i,j)) * (+0.5d0,0.d0) * (Paa(j,i) - Pbb(j,i))
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Sc_zx = Sc_zx - (+0.5d0,0.d0) * (Pab(j,i) + Pba(j,i)) * (+0.5d0,0.d0) * (Paa(i,j) - Pbb(i,j))
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enddo
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enddo
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print *, " < Sx Sz > = ", Sc_xz
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print *, " < Sz Sx > = ", Sc_zx
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Sc_yz = Sc_y * Sc_z
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Sc_zy = Sc_y * Sc_z
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do i = 1, nO
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Sc_yz = Sc_yz + (0.d0,0.5d0) * (+0.5d0,0.d0) * (Pab(i,i) + Pba(i,i))
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Sc_zy = Sc_zy - (0.d0,0.5d0) * (+0.5d0,0.d0) * (Pab(i,i) + Pba(i,i))
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do j = 1, nO
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Sc_yz = Sc_yz - (0.d0,-0.5d0) * (Pab(i,j) - Pba(i,j)) * (+0.5d0,0.d0) * (Paa(j,i) - Pbb(j,i))
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Sc_zy = Sc_zy - (0.d0,-0.5d0) * (Pab(j,i) - Pba(j,i)) * (+0.5d0,0.d0) * (Paa(i,j) - Pbb(i,j))
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enddo
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enddo
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print *, " < Sy Sz > = ", Sc_yz
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print *, " < Sz Sy > = ", Sc_zy
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! --- --- --- --- --- --- --- --- ---
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! --- --- --- --- --- --- --- --- ---
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@ -298,6 +373,8 @@ subroutine print_GHFspin(nBas, nBas2, nO, C, S)
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enddo
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Mc(3,1) = Mc(1,3)
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print *, " The Spin matrix is:", Mc
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call diagonalize_matrix(3, Mc, Eigc)
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print *, ' eigenvalues of Collinearity matrix:', Eigc
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deallocate(Mc, Eigc)
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