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Multi-state corrections

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This commit is contained in:
Anthony Scemama 2023-11-02 12:29:53 +01:00
parent c4794b62ba
commit adec973978
4 changed files with 136 additions and 96 deletions
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79
devel/sr_correction/alpha.irp.f
View File

@ -16,70 +16,79 @@ BEGIN_PROVIDER [ double precision, alpha_coef, (0:1) ]
END_PROVIDER END_PROVIDER
BEGIN_PROVIDER [ double precision, alpha_coef_r, (0:1) ] BEGIN_PROVIDER [ double precision, alpha_coef_r, (0:1,N_states) ]
implicit none implicit none
BEGIN_DOC BEGIN_DOC
! SavCar-JCP-23, corrected for small mu ! SavCar-JCP-23, corrected for small mu
END_DOC END_DOC
integer :: istate
double precision :: num, den double precision :: num, den
double precision :: a0, b0, delta_E, E double precision :: a0, b0, delta_E, E
E = energy_mu + correction_alpha_1 do istate = 1,N_states
delta_E = (energy_mu(istate) + correction_alpha_1(istate)) - energy_mu0(istate)
a0 = delta_E * correction_mu0(istate) + 2.d0/dsqrt(dacos(-1.d0))*(delta_E - correction_mu0(istate)) * mu_erf
b0 = correction_mu0(istate)*correction_mu0(istate)
delta_E = E - energy_mu0 num = 0.319820d0 + mu_erf * (1.063846d0 + mu_erf)
den = 0.487806d0 + mu_erf * (1.375439d0 + mu_erf)
alpha_coef_r(0,istate) = (a0 + mu_erf*num)/(b0 + mu_erf*den)
a0 = delta_E * correction_mu0 + 2.d0/dsqrt(dacos(-1.d0))*(delta_E - correction_mu0) * mu_erf
b0 = correction_mu0*correction_mu0
num = 0.319820d0 + mu_erf * (1.063846d0 + mu_erf) ! delta_E = (energy_mu + correction_alpha_1) - energy_mu0
den = 0.487806d0 + mu_erf * (1.375439d0 + mu_erf) ! a0 = delta_E * correction_mu0 + 2.d0/dsqrt(dacos(-1.d0))*(delta_E - correction_mu0) * mu_erf
alpha_coef_r(0) = (a0 + mu_erf*num)/(b0 + mu_erf*den) ! b0 = correction_mu0*correction_mu0
num = 0.113074d0 + mu_erf * (0.638308d0 + mu_erf)
den = 0.122652d0 + mu_erf * (0.674813d0 + mu_erf)
alpha_coef_r(1) = (a0 + mu_erf*num)/(b0 + mu_erf*den)
num = 0.113074d0 + mu_erf * (0.638308d0 + mu_erf)
den = 0.122652d0 + mu_erf * (0.674813d0 + mu_erf)
alpha_coef_r(1,istate) = (a0 + mu_erf*num)/(b0 + mu_erf*den)
enddo
END_PROVIDER END_PROVIDER
BEGIN_PROVIDER [ double precision, energy_mu0 ] BEGIN_PROVIDER [ double precision, energy_mu0, (N_states) ]
implicit none implicit none
BEGIN_DOC BEGIN_DOC
! E(mu=0) ! E(mu=0)
END_DOC END_DOC
integer :: l integer :: l, istate
double precision, external :: ddot double precision, external :: ddot
energy_mu0 = 0.d0 do istate = 1,N_states
do l=1,mo_num energy_mu0(istate) = 0.d0
energy_mu0 += ddot(mo_num, one_e_dm_mo(1,l), 1, mo_one_e_integrals(1,l), 1) do l=1,mo_num
energy_mu0(istate) += ddot(mo_num, one_e_dm_mo_alpha(1,l,istate), 1, mo_one_e_integrals(1,l), 1)
energy_mu0(istate) += ddot(mo_num, one_e_dm_mo_beta(1,l,istate), 1, mo_one_e_integrals(1,l), 1)
enddo
energy_mu0(istate) = energy_mu0(istate) + nuclear_repulsion
enddo enddo
energy_mu0 = energy_mu0 + nuclear_repulsion
END_PROVIDER END_PROVIDER
BEGIN_PROVIDER [ double precision, correction_alpha_0_r ] BEGIN_PROVIDER [ double precision, correction_alpha_0_r, (N_states) ]
implicit none implicit none
BEGIN_DOC BEGIN_DOC
! alpha_0r(mu) * <Psi(mu)|W_bar_mu|Psi(mu)> ! alpha_0r(mu) * <Psi(mu)|W_bar_mu|Psi(mu)>
END_DOC END_DOC
integer :: k,l integer :: k,l, istate
double precision :: c0 double precision :: c0
double precision, external :: ddot double precision, external :: ddot
c0 = 0.5d0 * alpha_coef_r(0) do istate = 1,N_states
correction_alpha_0_r = 0.d0 c0 = 0.5d0 * alpha_coef_r(0,istate)
do l=1,mo_num correction_alpha_0_r(istate) = 0.d0
do k=1,mo_num do l=1,mo_num
correction_alpha_0_r += c0 * ddot (mo_num*mo_num, two_e_dm_mo(1,1,k,l), 1, W_bar_mu(1,1,k,l), 1) do k=1,mo_num
correction_alpha_0_r += c0 * ddot (mo_num*mo_num, full_occ_2_rdm_ab_mo(1,1,k,l,istate), 1, W_bar_mu(1,1,k,l), 1)
enddo
enddo enddo
enddo enddo
END_PROVIDER END_PROVIDER
BEGIN_PROVIDER [ double precision, correction_alpha_1_r ] BEGIN_PROVIDER [ double precision, correction_alpha_1_r, (N_states) ]
implicit none implicit none
BEGIN_DOC BEGIN_DOC
! alpha_0(mu) * <Psi(mu)|W_bar_mu|Psi(mu)>_s + alpha_1(mu) * <Psi(mu)|W_bar_mu|Psi(mu)>_t ! alpha_0(mu) * <Psi(mu)|W_bar_mu|Psi(mu)>_s + alpha_1(mu) * <Psi(mu)|W_bar_mu|Psi(mu)>_t
@ -87,17 +96,19 @@ BEGIN_PROVIDER [ double precision, correction_alpha_1_r ]
double precision :: c1, c0 double precision :: c1, c0
integer :: k,l integer :: k,l, istate
double precision, external :: ddot double precision, external :: ddot
c0 = 0.5d0 * alpha_coef_r(0) do istate = 1,N_states
c1 = 0.5d0 * alpha_coef_r(1) c0 = 0.5d0 * alpha_coef_r(0,istate)
c1 = 0.5d0 * alpha_coef_r(1,istate)
correction_alpha_1_r = 0.d0 correction_alpha_1_r(istate) = 0.d0
do l=1,mo_num do l=1,mo_num
do k=1,mo_num do k=1,mo_num
correction_alpha_1_r += c0 * ddot (mo_num*mo_num, two_e_dm_mo_singlet(1,1,k,l), 1, W_bar_mu(1,1,k,l), 1) correction_alpha_1_r(istate) += c0 * ddot (mo_num*mo_num, two_e_dm_mo_singlet(1,1,k,l,istate), 1, W_bar_mu(1,1,k,l), 1)
correction_alpha_1_r += c1 * ddot (mo_num*mo_num, two_e_dm_mo_triplet(1,1,k,l), 1, W_bar_mu(1,1,k,l), 1) correction_alpha_1_r(istate) += c1 * ddot (mo_num*mo_num, two_e_dm_mo_triplet(1,1,k,l,istate), 1, W_bar_mu(1,1,k,l), 1)
enddo
enddo enddo
enddo enddo
END_PROVIDER END_PROVIDER

32
devel/sr_correction/density_matrices.irp.f
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@ -1,33 +1,37 @@
BEGIN_PROVIDER [ double precision, two_e_dm_mo_singlet, (mo_num, mo_num, mo_num, mo_num) ] BEGIN_PROVIDER [ double precision, two_e_dm_mo_singlet, (mo_num, mo_num, mo_num, mo_num, N_states) ]
implicit none implicit none
BEGIN_DOC BEGIN_DOC
! Ps(r1,r2,r1',r2') = 1/2 (P(r1,r2,r1',r2') + P(r1,r2,r2',r1')) ! Ps(r1,r2,r1',r2') = 1/2 (P(r1,r2,r1',r2') + P(r1,r2,r2',r1'))
END_DOC END_DOC
integer :: i,j,k,l integer :: i,j,k,l,istate
do l=1,mo_num do istate = 1,N_states
do k=1,mo_num do l=1,mo_num
do j=1,mo_num do k=1,mo_num
do i=1,mo_num do j=1,mo_num
two_e_dm_mo_singlet(i,j,k,l) = 0.5d0 * (two_e_dm_mo(i,j,k,l) + two_e_dm_mo(i,j,l,k)) do i=1,mo_num
two_e_dm_mo_singlet(i,j,k,l,istate) = 0.5d0 * (full_occ_2_rdm_ab_mo(i,j,k,l,istate) + full_occ_2_rdm_ab_mo(i,j,l,k,istate))
enddo
enddo enddo
enddo enddo
enddo enddo
enddo enddo
END_PROVIDER END_PROVIDER
BEGIN_PROVIDER [ double precision, two_e_dm_mo_triplet, (mo_num, mo_num, mo_num, mo_num) ] BEGIN_PROVIDER [ double precision, two_e_dm_mo_triplet, (mo_num, mo_num, mo_num, mo_num, N_states) ]
implicit none implicit none
BEGIN_DOC BEGIN_DOC
! Ps(r1,r2,r1',r2') = 1/2 (P(r1,r2,r1',r2') - P(r1,r2,r2',r1')) ! Ps(r1,r2,r1',r2') = 1/2 (P(r1,r2,r1',r2') - P(r1,r2,r2',r1'))
END_DOC END_DOC
integer :: i,j,k,l integer :: i,j,k,l, istate
do l=1,mo_num do istate = 1,N_states
do k=1,mo_num do l=1,mo_num
do j=1,mo_num do k=1,mo_num
do i=1,mo_num do j=1,mo_num
two_e_dm_mo_triplet(i,j,k,l) = 0.5d0 * (two_e_dm_mo(i,j,k,l) - two_e_dm_mo(i,j,l,k)) do i=1,mo_num
two_e_dm_mo_triplet(i,j,k,l,istate) = 0.5d0 * (full_occ_2_rdm_ab_mo(i,j,k,l,istate) - full_occ_2_rdm_ab_mo(i,j,l,k,istate))
enddo
enddo enddo
enddo enddo
enddo enddo

82
devel/sr_correction/energy_mu.irp.f
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@ -55,7 +55,7 @@ BEGIN_PROVIDER [ double precision, W_bar_mu, (mo_num, mo_num, mo_num, mo_num) ]
enddo enddo
END_PROVIDER END_PROVIDER
BEGIN_PROVIDER [ double precision, energy_mu ] BEGIN_PROVIDER [ double precision, energy_mu, (N_states) ]
implicit none implicit none
BEGIN_DOC BEGIN_DOC
! E(mu) ! E(mu)
@ -63,40 +63,45 @@ BEGIN_PROVIDER [ double precision, energy_mu ]
double precision :: one_e, two_e double precision :: one_e, two_e
integer :: k,l integer :: k,l, istate
double precision, external :: ddot double precision, external :: ddot
one_e = 0.d0 do istate = 1,N_states
two_e = 0.d0 one_e = 0.d0
do l=1,mo_num two_e = 0.d0
one_e += ddot(mo_num, one_e_dm_mo(1,l), 1, mo_one_e_integrals(1,l), 1) do l=1,mo_num
do k=1,mo_num one_e += ddot(mo_num, one_e_dm_mo_alpha(1,l,istate), 1, mo_one_e_integrals(1,l), 1)
two_e += 0.5d0 * ddot (mo_num*mo_num, two_e_dm_mo(1,1,k,l), 1, W_mu(1,1,k,l), 1) one_e += ddot(mo_num, one_e_dm_mo_beta (1,l,istate), 1, mo_one_e_integrals(1,l), 1)
do k=1,mo_num
two_e += 0.5d0 * ddot (mo_num*mo_num, full_occ_2_rdm_ab_mo(1,1,k,l,istate), 1, W_mu(1,1,k,l), 1)
enddo
enddo
energy_mu(istate) = one_e + two_e + nuclear_repulsion
enddo enddo
enddo
energy_mu = one_e + two_e + nuclear_repulsion
END_PROVIDER END_PROVIDER
BEGIN_PROVIDER [ double precision, correction_alpha_0 ] BEGIN_PROVIDER [ double precision, correction_alpha_0, (N_states) ]
implicit none implicit none
BEGIN_DOC BEGIN_DOC
! alpha_0(mu) * <Psi(mu)|W_bar_mu|Psi(mu)> ! alpha_0(mu) * <Psi(mu)|W_bar_mu|Psi(mu)>
END_DOC END_DOC
integer :: k,l integer :: k,l, istate
double precision :: c0 double precision :: c0
double precision, external :: ddot double precision, external :: ddot
c0 = 0.5d0 * alpha_coef(0) c0 = 0.5d0 * alpha_coef(0)
correction_alpha_0 = 0.d0 do istate=1,N_states
do l=1,mo_num correction_alpha_0(istate) = 0.d0
do k=1,mo_num do l=1,mo_num
correction_alpha_0 += c0 * ddot (mo_num*mo_num, two_e_dm_mo(1,1,k,l), 1, W_bar_mu(1,1,k,l), 1) do k=1,mo_num
correction_alpha_0(istate) += c0 * ddot (mo_num*mo_num, full_occ_2_rdm_ab_mo(1,1,k,l,istate), 1, W_bar_mu(1,1,k,l), 1)
enddo
enddo enddo
enddo enddo
END_PROVIDER END_PROVIDER
BEGIN_PROVIDER [ double precision, correction_alpha_1 ] BEGIN_PROVIDER [ double precision, correction_alpha_1, (N_states) ]
implicit none implicit none
BEGIN_DOC BEGIN_DOC
! alpha_0(mu) * <Psi(mu)|W_bar_mu|Psi(mu)>_s + alpha_1(mu) * <Psi(mu)|W_bar_mu|Psi(mu)>_t ! alpha_0(mu) * <Psi(mu)|W_bar_mu|Psi(mu)>_s + alpha_1(mu) * <Psi(mu)|W_bar_mu|Psi(mu)>_t
@ -104,55 +109,62 @@ BEGIN_PROVIDER [ double precision, correction_alpha_1 ]
double precision :: c1, c0 double precision :: c1, c0
integer :: k,l integer :: k,l, istate
double precision, external :: ddot double precision, external :: ddot
c0 = 0.5d0 * alpha_coef(0) c0 = 0.5d0 * alpha_coef(0)
c1 = 0.5d0 * alpha_coef(1) c1 = 0.5d0 * alpha_coef(1)
correction_alpha_1 = 0.d0 do istate=1,N_states
do l=1,mo_num correction_alpha_1(istate) = 0.d0
do k=1,mo_num do l=1,mo_num
correction_alpha_1 += c0 * ddot (mo_num*mo_num, two_e_dm_mo_singlet(1,1,k,l), 1, W_bar_mu(1,1,k,l), 1) do k=1,mo_num
correction_alpha_1 += c1 * ddot (mo_num*mo_num, two_e_dm_mo_triplet(1,1,k,l), 1, W_bar_mu(1,1,k,l), 1) correction_alpha_1(istate) += c0 * ddot (mo_num*mo_num, two_e_dm_mo_singlet(1,1,k,l,istate), 1, W_bar_mu(1,1,k,l), 1)
correction_alpha_1(istate) += c1 * ddot (mo_num*mo_num, two_e_dm_mo_triplet(1,1,k,l,istate), 1, W_bar_mu(1,1,k,l), 1)
enddo
enddo enddo
enddo enddo
END_PROVIDER END_PROVIDER
BEGIN_PROVIDER [ double precision, correction_mu ] BEGIN_PROVIDER [ double precision, correction_mu, (N_states) ]
implicit none implicit none
BEGIN_DOC BEGIN_DOC
! <Psi(mu)|W_bar_mu|Psi(mu)> ! <Psi(mu)|W_bar_mu|Psi(mu)>
END_DOC END_DOC
integer :: k,l integer :: k,l, istate
double precision :: c0 double precision :: c0
double precision, external :: ddot double precision, external :: ddot
c0 = 0.5d0 c0 = 0.5d0
correction_mu = 0.d0
do l=1,mo_num do istate=1,N_states
do k=1,mo_num correction_mu(istate) = 0.d0
correction_mu += c0 * ddot (mo_num*mo_num, two_e_dm_mo(1,1,k,l), 1, W_bar_mu(1,1,k,l), 1) do l=1,mo_num
do k=1,mo_num
correction_mu(istate) += c0 * ddot (mo_num*mo_num, full_occ_2_rdm_ab_mo(1,1,k,l,istate), 1, W_bar_mu(1,1,k,l), 1)
enddo
enddo enddo
enddo enddo
END_PROVIDER END_PROVIDER
BEGIN_PROVIDER [ double precision, correction_mu0 ] BEGIN_PROVIDER [ double precision, correction_mu0, (N_states) ]
implicit none implicit none
BEGIN_DOC BEGIN_DOC
! <Psi(mu)|W|Psi(mu)> : Should be <Psi(0)|W|Psi(0)> ! <Psi(mu)|W|Psi(mu)> : Should be <Psi(0)|W|Psi(0)>
END_DOC END_DOC
integer :: k,l integer :: k,l,istate
double precision :: c0 double precision :: c0
double precision, external :: ddot double precision, external :: ddot
c0 = 0.5d0 c0 = 0.5d0
correction_mu0 = 0.d0 do istate=1,N_states
do l=1,mo_num correction_mu0(istate) = 0.d0
do k=1,mo_num do l=1,mo_num
correction_mu0 += c0 * ddot (mo_num*mo_num, two_e_dm_mo(1,1,k,l), 1, W_bar_mu0(1,1,k,l), 1) do k=1,mo_num
correction_mu0(istate) += c0 * ddot (mo_num*mo_num, full_occ_2_rdm_ab_mo(1,1,k,l,istate), 1, W_bar_mu0(1,1,k,l), 1)
enddo
enddo enddo
enddo enddo
END_PROVIDER END_PROVIDER

39
devel/sr_correction/sr_correction.irp.f
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@ -8,27 +8,40 @@ end
subroutine run subroutine run
implicit none implicit none
integer :: istate
do istate=1,N_states
print *, '', istate
print *, 'State ', istate
print *, '---' print *, '---'
print *, 'mu', mu_erf print *, 'mu', mu_erf
print *, 'E(mu)', energy_mu print *, 'E(mu)', energy_mu(istate)
print *, '---' print *, '---'
print *, 'W_bar(mu)', correction_mu print *, 'W_bar(mu)', correction_mu(istate)
print *, 'E(mu) + <W_bar(mu)>', energy_mu + correction_mu print *, 'E(mu) + <W_bar(mu)>', energy_mu(istate) + correction_mu(istate)
print *, '---' print *, '---'
print *, 'alpha_0', alpha_coef(0) print *, 'alpha_0', alpha_coef(0)
print *, 'correction 0', correction_alpha_0 print *, 'correction 0', correction_alpha_0(istate)
print *, 'E(mu) + alpha_0 <W_bar(mu)> = ', energy_mu + correction_alpha_0 print *, 'E(mu) + alpha_0 <W_bar(mu)> = ', energy_mu(istate) + correction_alpha_0(istate)
print *, '---' print *, '---'
print *, 'alpha_1', alpha_coef(1) print *, 'alpha_1', alpha_coef(1)
print *, 'correction 1', correction_alpha_1 print *, 'correction 1', correction_alpha_1(istate)
print *, 'E(mu) + alpha_0 <W_bar(mu)>_s + alpha_1 <W_bar(mu)>_t = ', energy_mu + correction_alpha_1 print *, 'E(mu) + alpha_0 <W_bar(mu)>_s + alpha_1 <W_bar(mu)>_t = ', energy_mu(istate) + correction_alpha_1(istate)
print *, '---' print *, '---'
print *, 'alpha_0_r', alpha_coef_r(0) print *, 'alpha_0_r', alpha_coef_r(0,istate)
print *, 'correction 0', correction_alpha_0_r print *, 'correction 0', correction_alpha_0_r(istate)
print *, 'E(mu) + alpha_0_r <W_bar(mu)> = ', energy_mu + correction_alpha_0_r print *, 'E(mu) + alpha_0_r <W_bar(mu)> = ', energy_mu(istate) + correction_alpha_0_r(istate)
print *, '---' print *, '---'
print *, 'alpha_1_r', alpha_coef_r(1) print *, 'alpha_1_r', alpha_coef_r(1,istate)
print *, 'correction 1', correction_alpha_1_r print *, 'correction 1', correction_alpha_1_r(istate)
print *, 'E(mu) + alpha_0_r <W_bar(mu)>_s + alpha_1_r <W_bar(mu)>_t = ', energy_mu + correction_alpha_1_r print *, 'E(mu) + alpha_0_r <W_bar(mu)>_s + alpha_1_r <W_bar(mu)>_t = ', energy_mu(istate) + correction_alpha_1_r(istate)
print *, '---' print *, '---'
print *,''
print '(''|'',A6,''|'',5(A20,''|''))', 'E(mu)', '<W>', 'E(mu) + <W>', 'E(mu) + \alpha_0<W>', &
'E(mu) + \alpha_0<W>_s + \alpha_1<W>_t', 'E(mu) + \alpha_0_r<W>_s + \alpha_1_r<W>_t'
print '(''|'',F6.1,''|'',5(F20.15,''|''))', mu_erf, energy_mu(istate), energy_mu(istate) + correction_mu(istate), energy_mu(istate) + &
correction_alpha_0(istate), energy_mu(istate) + correction_alpha_1(istate), energy_mu(istate) + &
correction_alpha_1_r(istate)
enddo
end end