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208 lines
7.0 KiB
Fortran
208 lines
7.0 KiB
Fortran
BEGIN_PROVIDER [double precision, super_ci_dm, (mo_num,mo_num)]
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implicit none
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BEGIN_DOC
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! density matrix of the super CI matrix, in the basis of NATURAL ORBITALS OF THE CASCI WF
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!
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! This is obtained from annex B of Roos et. al. Chemical Physics 48 (1980) 157-173
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!
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! WARNING ::: in the equation B3.d there is a TYPO with a forgotten MINUS SIGN (see variable mat_tmp_dm_super_ci )
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END_DOC
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super_ci_dm = 0.d0
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integer :: i,j,iorb,jorb
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integer :: a,aorb,b,borb
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integer :: t,torb,v,vorb,u,uorb,x,xorb
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double precision :: c0,ci
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c0 = SXeigenvec(1,1)
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! equation B3.a of the annex B of Roos et. al. Chemical Physics 48 (1980) 157-173
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! loop over the core/inact
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do i = 1, n_core_inact_orb
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iorb = list_core_inact(i)
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super_ci_dm(iorb,iorb) = 2.d0 ! first term of B3.a
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! loop over the core/inact
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do j = 1, n_core_inact_orb
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jorb = list_core_inact(j)
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! loop over the virtual
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do a = 1, n_virt_orb
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aorb = list_virt(a)
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super_ci_dm(jorb,iorb) += -2.d0 * lowest_super_ci_coef_mo(aorb,iorb) * lowest_super_ci_coef_mo(aorb,jorb) ! second term in B3.a
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enddo
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do t = 1, n_act_orb
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torb = list_act(t)
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! thrid term of the B3.a
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super_ci_dm(jorb,iorb) += - lowest_super_ci_coef_mo(iorb,torb) * lowest_super_ci_coef_mo(jorb,torb) * (2.d0 - occ_act(t))
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enddo
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enddo
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enddo
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! equation B3.b of the annex B of Roos et. al. Chemical Physics 48 (1980) 157-173
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do i = 1, n_core_inact_orb
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iorb = list_core_inact(i)
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do t = 1, n_act_orb
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torb = list_act(t)
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super_ci_dm(iorb,torb) = c0 * lowest_super_ci_coef_mo(torb,iorb) * (2.d0 - occ_act(t))
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super_ci_dm(torb,iorb) = c0 * lowest_super_ci_coef_mo(torb,iorb) * (2.d0 - occ_act(t))
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do a = 1, n_virt_orb
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aorb = list_virt(a)
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super_ci_dm(iorb,torb) += - lowest_super_ci_coef_mo(aorb,iorb) * lowest_super_ci_coef_mo(aorb,torb) * occ_act(t)
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super_ci_dm(torb,iorb) += - lowest_super_ci_coef_mo(aorb,iorb) * lowest_super_ci_coef_mo(aorb,torb) * occ_act(t)
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enddo
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enddo
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enddo
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! equation B3.c of the annex B of Roos et. al. Chemical Physics 48 (1980) 157-173
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do i = 1, n_core_inact_orb
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iorb = list_core_inact(i)
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do a = 1, n_virt_orb
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aorb = list_virt(a)
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super_ci_dm(aorb,iorb) = 2.d0 * c0 * lowest_super_ci_coef_mo(aorb,iorb)
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super_ci_dm(iorb,aorb) = 2.d0 * c0 * lowest_super_ci_coef_mo(aorb,iorb)
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enddo
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enddo
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! equation B3.d of the annex B of Roos et. al. Chemical Physics 48 (1980) 157-173
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do t = 1, n_act_orb
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torb = list_act(t)
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super_ci_dm(torb,torb) = occ_act(t) ! first term of equation B3.d
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do x = 1, n_act_orb
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xorb = list_act(x)
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super_ci_dm(torb,torb) += - occ_act(x) * occ_act(t)* mat_tmp_dm_super_ci(x,x) ! second term involving the ONE-rdm
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enddo
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do u = 1, n_act_orb
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uorb = list_act(u)
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! second term of equation B3.d
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do x = 1, n_act_orb
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xorb = list_act(x)
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do v = 1, n_act_orb
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vorb = list_act(v)
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super_ci_dm(torb,uorb) += 2.d0 * P0tuvx_no(v,x,t,u) * mat_tmp_dm_super_ci(v,x) ! second term involving the TWO-rdm
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enddo
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enddo
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! third term of equation B3.d
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do i = 1, n_core_inact_orb
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iorb = list_core_inact(i)
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super_ci_dm(torb,uorb) += lowest_super_ci_coef_mo(iorb,torb) * lowest_super_ci_coef_mo(iorb,uorb) * (2.d0 - occ_act(t) - occ_act(u))
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enddo
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enddo
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enddo
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! equation B3.e of the annex B of Roos et. al. Chemical Physics 48 (1980) 157-173
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do t = 1, n_act_orb
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torb = list_act(t)
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do a = 1, n_virt_orb
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aorb = list_virt(a)
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super_ci_dm(aorb,torb) += c0 * lowest_super_ci_coef_mo(aorb,torb) * occ_act(t)
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super_ci_dm(torb,aorb) += c0 * lowest_super_ci_coef_mo(aorb,torb) * occ_act(t)
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do i = 1, n_core_inact_orb
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iorb = list_core_inact(i)
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super_ci_dm(aorb,torb) += lowest_super_ci_coef_mo(iorb,aorb) * lowest_super_ci_coef_mo(iorb,torb) * (2.d0 - occ_act(t))
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super_ci_dm(torb,aorb) += lowest_super_ci_coef_mo(iorb,aorb) * lowest_super_ci_coef_mo(iorb,torb) * (2.d0 - occ_act(t))
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enddo
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enddo
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enddo
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! equation B3.f of the annex B of Roos et. al. Chemical Physics 48 (1980) 157-173
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do a = 1, n_virt_orb
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aorb = list_virt(a)
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do b = 1, n_virt_orb
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borb= list_virt(b)
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! First term of equation B3.f
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do i = 1, n_core_inact_orb
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iorb = list_core_inact(i)
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super_ci_dm(borb,aorb) += 2.d0 * lowest_super_ci_coef_mo(iorb,aorb) * lowest_super_ci_coef_mo(iorb,borb)
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enddo
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! Second term of equation B3.f
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do t = 1, n_act_orb
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torb = list_act(t)
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super_ci_dm(borb,aorb) += lowest_super_ci_coef_mo(torb,aorb) * lowest_super_ci_coef_mo(torb,borb) * occ_act(t)
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enddo
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enddo
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enddo
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END_PROVIDER
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BEGIN_PROVIDER [double precision, superci_natorb, (ao_num,mo_num)
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&BEGIN_PROVIDER [double precision, superci_nat_occ, (mo_num)
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implicit none
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call general_mo_coef_new_as_svd_vectors_of_mo_matrix_eig(super_ci_dm,mo_num,mo_num,mo_num,NatOrbsFCI,superci_nat_occ,superci_natorb)
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END_PROVIDER
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BEGIN_PROVIDER [double precision, mat_tmp_dm_super_ci, (n_act_orb,n_act_orb)]
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implicit none
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BEGIN_DOC
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! computation of the term in [ ] in the equation B3.d of Roos et. al. Chemical Physics 48 (1980) 157-173
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!
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! !!!!! WARNING !!!!!! there is a TYPO: a MINUS SIGN SHOULD APPEAR in that term
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END_DOC
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integer :: a,aorb,i,iorb
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integer :: x,xorb,v,vorb
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mat_tmp_dm_super_ci = 0.d0
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do v = 1, n_act_orb
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vorb = list_act(v)
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do x = 1, n_act_orb
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xorb = list_act(x)
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do a = 1, n_virt_orb
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aorb = list_virt(a)
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mat_tmp_dm_super_ci(x,v) += lowest_super_ci_coef_mo(aorb,vorb) * lowest_super_ci_coef_mo(aorb,xorb)
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enddo
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do i = 1, n_core_inact_orb
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iorb = list_core_inact(i)
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! MARK THE MINUS SIGN HERE !!!!!!!!!!! BECAUSE OF TYPO IN THE ORIGINAL PAPER
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mat_tmp_dm_super_ci(x,v) -= lowest_super_ci_coef_mo(iorb,vorb) * lowest_super_ci_coef_mo(iorb,xorb)
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enddo
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enddo
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enddo
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END_PROVIDER
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BEGIN_PROVIDER [double precision, lowest_super_ci_coef_mo, (mo_num,mo_num)]
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implicit none
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integer :: i,j,iorb,jorb
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integer :: a, aorb,t, torb
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double precision :: sqrt2
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sqrt2 = 1.d0/dsqrt(2.d0)
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do i = 1, nMonoEx
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iorb = excit(1,i)
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jorb = excit(2,i)
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lowest_super_ci_coef_mo(iorb,jorb) = SXeigenvec(i+1,1)
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lowest_super_ci_coef_mo(jorb,iorb) = SXeigenvec(i+1,1)
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enddo
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! a_{it} of the equation B.2 of Roos et. al. Chemical Physics 48 (1980) 157-173
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do i = 1, n_core_inact_orb
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iorb = list_core_inact(i)
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do t = 1, n_act_orb
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torb = list_act(t)
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lowest_super_ci_coef_mo(torb,iorb) *= (2.d0 - occ_act(t))**(-0.5d0)
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lowest_super_ci_coef_mo(iorb,torb) *= (2.d0 - occ_act(t))**(-0.5d0)
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enddo
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enddo
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! a_{ia} of the equation B.2 of Roos et. al. Chemical Physics 48 (1980) 157-173
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do i = 1, n_core_inact_orb
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iorb = list_core_inact(i)
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do a = 1, n_virt_orb
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aorb = list_virt(a)
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lowest_super_ci_coef_mo(aorb,iorb) *= sqrt2
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lowest_super_ci_coef_mo(iorb,aorb) *= sqrt2
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enddo
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enddo
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! a_{ta} of the equation B.2 of Roos et. al. Chemical Physics 48 (1980) 157-173
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do a = 1, n_virt_orb
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aorb = list_virt(a)
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do t = 1, n_act_orb
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torb = list_act(t)
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lowest_super_ci_coef_mo(torb,aorb) *= occ_act(t)**(-0.5d0)
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lowest_super_ci_coef_mo(aorb,torb) *= occ_act(t)**(-0.5d0)
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enddo
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enddo
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END_PROVIDER
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