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updated DOC for correct normalization of two-rdms

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eginer 2023-02-27 17:48:42 +01:00
parent c95f1ee0ac
commit 8515fcf93f
4 changed files with 27 additions and 42 deletions
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19
src/two_body_rdm/act_2_rdm.irp.f
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@ -4,21 +4,18 @@
BEGIN_DOC BEGIN_DOC
! 12 12 ! 12 12
! 1 2 1 2 == <ij|kl> ! 1 2 1 2 == <ij|kl>
! act_2_rdm_ab_mo(i,j,k,l,istate) = STATE SPECIFIC physicist notation for 2RDM of alpha/beta electrons ! act_2_rdm_ab_mo(i,j,k,l,istate) = STATE SPECIFIC physicist notation for 2RDM of alpha/beta+beta/alpha electrons
! !
! <Psi_{istate}| a^{\dagger}_{i \alpha} a^{\dagger}_{j \beta} a_{l \beta} a_{k \alpha} |Psi_{istate}> ! <Psi_{istate}| a^{\dagger}_{i \alpha} a^{\dagger}_{j \beta} a_{l \beta} a_{k \alpha} |Psi_{istate}>
!
! + <Psi_{istate}| a^{\dagger}_{i \beta} a^{\dagger}_{j \alpha} a_{l \alpha} a_{k \beta} |Psi_{istate}>
! !
! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO AN ACTIVE SPACE DEFINED BY "list_act" ! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO AN ACTIVE SPACE DEFINED BY "list_act"
! !
! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\alpha}^{act} * N_{\beta}^{act} ! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\alpha}^{act} * N_{\beta}^{act} * 2
! !
! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act" ! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act"
! !
! !!!!! WARNING !!!!! For efficiency reasons, electron 1 is alpha, electron 2 is beta
!
! act_2_rdm_ab_mo(i,j,k,l,istate) = i:alpha, j:beta, j:alpha, l:beta
!
! Therefore you don't necessary have symmetry between electron 1 and 2
END_DOC END_DOC
integer :: ispin integer :: ispin
double precision :: wall_1, wall_2 double precision :: wall_1, wall_2
@ -57,7 +54,7 @@
! !
! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO AN ACTIVE SPACE DEFINED BY "list_act" ! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO AN ACTIVE SPACE DEFINED BY "list_act"
! !
! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\alpha}^{act} * (N_{\alpha}^{act} - 1)/2 ! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\alpha}^{act} * (N_{\alpha}^{act} - 1)
! !
! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act" ! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act"
END_DOC END_DOC
@ -98,7 +95,7 @@
! !
! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO AN ACTIVE SPACE DEFINED BY "list_act" ! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO AN ACTIVE SPACE DEFINED BY "list_act"
! !
! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\beta}^{act} * (N_{\beta}^{act} - 1)/2 ! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\beta}^{act} * (N_{\beta}^{act} - 1)
! !
! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act" ! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act"
END_DOC END_DOC
@ -138,7 +135,7 @@
! !
! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO AN ACTIVE SPACE DEFINED BY "list_act" ! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO AN ACTIVE SPACE DEFINED BY "list_act"
! !
! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{elec}^{act} * (N_{elec}^{act} - 1)/2 ! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{elec}^{act} * (N_{elec}^{act} - 1)
! !
! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act" ! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act"
END_DOC END_DOC

22
src/two_body_rdm/full_orb_2_rdm.irp.f
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@ -4,22 +4,18 @@
full_occ_2_rdm_ab_mo = 0.d0 full_occ_2_rdm_ab_mo = 0.d0
integer :: i,j,k,l,iorb,jorb,korb,lorb,istate integer :: i,j,k,l,iorb,jorb,korb,lorb,istate
BEGIN_DOC BEGIN_DOC
! full_occ_2_rdm_ab_mo(i,j,k,l,istate) = STATE SPECIFIC physicist notation for 2RDM of alpha/beta electrons ! full_occ_2_rdm_ab_mo(i,j,k,l,istate) = STATE SPECIFIC physicist notation for 2RDM of alpha/beta + beta/alpha electrons
! !
! <Psi| a^{\dagger}_{i \alpha} a^{\dagger}_{j \beta} a_{l \beta} a_{k \alpha} |Psi> ! <Psi| a^{\dagger}_{i \alpha} a^{\dagger}_{j \beta} a_{l \beta} a_{k \alpha} |Psi>
!
! + <Psi| a^{\dagger}_{i \beta} a^{\dagger}_{j \alpha} a_{l \alpha} a_{k \beta} |Psi>
! !
! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO ALL OCCUPIED ORBITALS : core, inactive and active ! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO ALL OCCUPIED ORBITALS : core, inactive and active
! !
! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\alpha} * N_{\beta} ! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\alpha} * N_{\beta} * 2
! !
! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act" ! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act"
! !
! !!!!! WARNING !!!!! For efficiency reasons, electron 1 is ALPHA, electron 2 is BETA
!
! full_occ_2_rdm_ab_mo(i,j,k,l,istate) = i:alpha, j:beta, j:alpha, l:beta
!
! Therefore you don't necessary have symmetry between electron 1 and 2
!
! !!!!! WARNING !!!!! IF "no_core_density" then all elements involving at least one CORE MO ARE SET TO ZERO ! !!!!! WARNING !!!!! IF "no_core_density" then all elements involving at least one CORE MO ARE SET TO ZERO
END_DOC END_DOC
full_occ_2_rdm_ab_mo = 0.d0 full_occ_2_rdm_ab_mo = 0.d0
@ -139,7 +135,7 @@
! !
! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO ALL OCCUPIED ORBITALS : core, inactive and active ! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO ALL OCCUPIED ORBITALS : core, inactive and active
! !
! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\alpha} * (N_{\alpha} - 1)/2 ! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\alpha} * (N_{\alpha} - 1)
! !
! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act" ! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act"
! !
@ -237,7 +233,7 @@
! !
! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO ALL OCCUPIED ORBITALS : core, inactive and active ! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO ALL OCCUPIED ORBITALS : core, inactive and active
! !
! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\beta} * (N_{\beta} - 1)/2 ! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\beta} * (N_{\beta} - 1)
! !
! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act" ! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act"
! !
@ -335,14 +331,14 @@
! !
! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO ALL OCCUPIED ORBITALS : core, inactive and active ! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO ALL OCCUPIED ORBITALS : core, inactive and active
! !
! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{elec} * (N_{elec} - 1)/2 ! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{elec} * (N_{elec} - 1)
! !
! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act" ! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act"
! !
! !!!!! WARNING !!!!! IF "no_core_density" then all elements involving at least one CORE MO is set to zero ! !!!!! WARNING !!!!! IF "no_core_density" then all elements involving at least one CORE MO is set to zero
! The two-electron energy of each state can be computed as: ! The two-electron energy of each state can be computed as:
! !
! \sum_{i,j,k,l = 1, n_core_inact_act_orb} full_occ_2_rdm_spin_trace_mo(i,j,k,l,istate) * < ii jj | kk ll > ! \sum_{i,j,k,l = 1, n_core_inact_act_orb} full_occ_2_rdm_spin_trace_mo(i,j,k,l,istate) * 1/2 * < ii jj | kk ll >
! !
! with ii = list_core_inact_act(i), jj = list_core_inact_act(j), kk = list_core_inact_act(k), ll = list_core_inact_act(l) ! with ii = list_core_inact_act(i), jj = list_core_inact_act(j), kk = list_core_inact_act(k), ll = list_core_inact_act(l)
END_DOC END_DOC

12
src/two_body_rdm/state_av_act_2rdm.irp.f
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@ -2,21 +2,16 @@
implicit none implicit none
double precision, allocatable :: state_weights(:) double precision, allocatable :: state_weights(:)
BEGIN_DOC BEGIN_DOC
! state_av_act_2_rdm_ab_mo(i,j,k,l) = state average physicist two-body rdm restricted to the ACTIVE indices for alpha-beta electron pairs ! state_av_act_2_rdm_ab_mo(i,j,k,l) = state average physicist two-body rdm restricted to the ACTIVE indices for alpha/beta+beta/alpha electron pairs
! !
! = \sum_{istate} w(istate) * <Psi_{istate}| a^{\dagger}_{i,alpha} a^{\dagger}_{j,beta} a_{l,beta} a_{k,alpha} |Psi_{istate}> ! = \sum_{istate} w(istate) * <Psi_{istate}| a^{\dagger}_{i,alpha} a^{\dagger}_{j,beta} a_{l,beta} a_{k,alpha} |Psi_{istate}>
! !
! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO AN ACTIVE SPACE DEFINED BY "list_act" ! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO AN ACTIVE SPACE DEFINED BY "list_act"
! !
! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\alpha}^{act} * N_{\beta}^{act} ! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\alpha}^{act} * N_{\beta}^{act} * 2
! !
! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act" ! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act"
! !
! !!!!! WARNING !!!!! For efficiency reasons, electron 1 is alpha, electron 2 is beta
!
! state_av_act_2_rdm_ab_mo(i,j,k,l) = i:alpha, j:beta, j:alpha, l:beta
!
! Therefore you don't necessary have symmetry between electron 1 and 2
END_DOC END_DOC
allocate(state_weights(N_states)) allocate(state_weights(N_states))
state_weights = state_average_weight state_weights = state_average_weight
@ -34,6 +29,7 @@
call orb_range_2_rdm_state_av_openmp(state_av_act_2_rdm_ab_mo,n_act_orb,n_act_orb,list_act,state_weights,ispin,psi_coef,size(psi_coef,2),size(psi_coef,1)) call orb_range_2_rdm_state_av_openmp(state_av_act_2_rdm_ab_mo,n_act_orb,n_act_orb,list_act,state_weights,ispin,psi_coef,size(psi_coef,2),size(psi_coef,1))
call wall_time(wall_2) call wall_time(wall_2)
print*,'Wall time to provide state_av_act_2_rdm_ab_mo',wall_2 - wall_1 print*,'Wall time to provide state_av_act_2_rdm_ab_mo',wall_2 - wall_1
! factor 2 to have the correct normalization factor
state_av_act_2_rdm_ab_mo *= 2.d0 state_av_act_2_rdm_ab_mo *= 2.d0
END_PROVIDER END_PROVIDER
@ -64,6 +60,7 @@
call orb_range_2_rdm_state_av_openmp(state_av_act_2_rdm_aa_mo,n_act_orb,n_act_orb,list_act,state_weights,ispin,psi_coef,size(psi_coef,2),size(psi_coef,1)) call orb_range_2_rdm_state_av_openmp(state_av_act_2_rdm_aa_mo,n_act_orb,n_act_orb,list_act,state_weights,ispin,psi_coef,size(psi_coef,2),size(psi_coef,1))
call wall_time(wall_2) call wall_time(wall_2)
print*,'Wall time to provide state_av_act_2_rdm_aa_mo',wall_2 - wall_1 print*,'Wall time to provide state_av_act_2_rdm_aa_mo',wall_2 - wall_1
! factor 2 to have the correct normalization factor
state_av_act_2_rdm_aa_mo *= 2.d0 state_av_act_2_rdm_aa_mo *= 2.d0
END_PROVIDER END_PROVIDER
@ -93,6 +90,7 @@
call orb_range_2_rdm_state_av_openmp(state_av_act_2_rdm_bb_mo,n_act_orb,n_act_orb,list_act,state_weights,ispin,psi_coef,size(psi_coef,2),size(psi_coef,1)) call orb_range_2_rdm_state_av_openmp(state_av_act_2_rdm_bb_mo,n_act_orb,n_act_orb,list_act,state_weights,ispin,psi_coef,size(psi_coef,2),size(psi_coef,1))
call wall_time(wall_2) call wall_time(wall_2)
print*,'Wall time to provide state_av_act_2_rdm_bb_mo',wall_2 - wall_1 print*,'Wall time to provide state_av_act_2_rdm_bb_mo',wall_2 - wall_1
! factor 2 to have the correct normalization factor
state_av_act_2_rdm_bb_mo *= 2.d0 state_av_act_2_rdm_bb_mo *= 2.d0
END_PROVIDER END_PROVIDER

16
src/two_body_rdm/state_av_full_orb_2_rdm.irp.f
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@ -4,22 +4,16 @@
state_av_full_occ_2_rdm_ab_mo = 0.d0 state_av_full_occ_2_rdm_ab_mo = 0.d0
integer :: i,j,k,l,iorb,jorb,korb,lorb integer :: i,j,k,l,iorb,jorb,korb,lorb
BEGIN_DOC BEGIN_DOC
! state_av_full_occ_2_rdm_ab_mo(i,j,k,l) = STATE AVERAGE physicist notation for 2RDM of alpha/beta electrons ! state_av_full_occ_2_rdm_ab_mo(i,j,k,l) = STATE AVERAGE physicist notation for 2RDM of alpha/beta + beta/alpha electrons
! !
! = \sum_{istate} w(istate) * <Psi_{istate}| a^{\dagger}_{i,alpha} a^{\dagger}_{j,beta} a_{l,beta} a_{k,alpha} |Psi_{istate}> ! = \sum_{istate} w(istate) * <Psi_{istate}| a^{\dagger}_{i,alpha} a^{\dagger}_{j,beta} a_{l,beta} a_{k,alpha} |Psi_{istate}>
! !
! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO ALL OCCUPIED ORBITALS : core, inactive and active ! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO ALL OCCUPIED ORBITALS : core, inactive and active
! !
! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\alpha} * N_{\beta} ! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\alpha} * N_{\beta} * 2
! !
! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act" ! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act"
! !
! !!!!! WARNING !!!!! For efficiency reasons, electron 1 is ALPHA, electron 2 is BETA
!
! state_av_full_occ_2_rdm_ab_mo(i,j,k,l) = i:alpha, j:beta, j:alpha, l:beta
!
! Therefore you don't necessary have symmetry between electron 1 and 2
!
! !!!!! WARNING !!!!! IF "no_core_density" then all elements involving at least one CORE MO is set to zero ! !!!!! WARNING !!!!! IF "no_core_density" then all elements involving at least one CORE MO is set to zero
END_DOC END_DOC
state_av_full_occ_2_rdm_ab_mo = 0.d0 state_av_full_occ_2_rdm_ab_mo = 0.d0
@ -135,7 +129,7 @@
! !
! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO ALL OCCUPIED ORBITALS : core, inactive and active ! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO ALL OCCUPIED ORBITALS : core, inactive and active
! !
! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\alpha} * (N_{\alpha} - 1)/2 ! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\alpha} * (N_{\alpha} - 1)
! !
! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act" ! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act"
! !
@ -231,7 +225,7 @@
! !
! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO ALL OCCUPIED ORBITALS : core, inactive and active ! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO ALL OCCUPIED ORBITALS : core, inactive and active
! !
! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\beta} * (N_{\beta} - 1)/2 ! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{\beta} * (N_{\beta} - 1)
! !
! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act" ! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act"
! !
@ -328,7 +322,7 @@
! !
! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO ALL OCCUPIED ORBITALS : core, inactive and active ! WHERE ALL ORBITALS (i,j,k,l) BELONGS TO ALL OCCUPIED ORBITALS : core, inactive and active
! !
! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{elec} * (N_{elec} - 1)/2 ! THE NORMALIZATION (i.e. sum of diagonal elements) IS SET TO N_{elec} * (N_{elec} - 1)
! !
! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act" ! !!!!! WARNING !!!!! ALL SLATER DETERMINANTS IN PSI_DET MUST BELONG TO AN ACTIVE SPACE DEFINED BY "list_act"
! !