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beyond TDA for dynamic BSE

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This commit is contained in:
Pierre-Francois Loos 2020-05-20 16:46:07 +02:00
parent 61832f1259
commit 0c6153de3f
9 changed files with 244 additions and 120 deletions
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2
GoQCaml
View File

@ -1,5 +1,5 @@
#! /bin/bash
cd int
../utils/QCaml/run_integrals -b ../input/basis.qcaml -x ../input/molecule.xyz
../utils/QCaml/run_integrals -b ../input/basis.qcaml -x ../input/molecule.xyz || ../utils/QCaml/run_integrals -b ../input/basis.qcaml -x ../input/molecule.xyz -c 1
###../utils/QCaml/run_integrals -b ../input/basis.qcaml -x ../input/molecule.xyz -m 0.5

2
examples/molecule.H2
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@ -2,4 +2,4 @@
2 1 1 0 0
# Znuc x y z
H 0. 0. 0.
H 0. 0. 1.4
H 0. 0. 3.7

125
input/basis
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@ -1,71 +1,92 @@
1 9
1 14
S 8
1 9046.0000000 0.0007000
2 1357.0000000 0.0053890
3 309.3000000 0.0274060
4 87.7300000 0.1032070
5 28.5600000 0.2787230
6 10.2100000 0.4485400
7 3.8380000 0.2782380
8 0.7466000 0.0154400
1 11420.0000000 0.0005230
2 1712.0000000 0.0040450
3 389.3000000 0.0207750
4 110.0000000 0.0807270
5 35.5700000 0.2330740
6 12.5400000 0.4335010
7 4.6440000 0.3474720
8 0.5118000 -0.0085080
S 8
1 9046.0000000 -0.0001530
2 1357.0000000 -0.0012080
3 309.3000000 -0.0059920
4 87.7300000 -0.0245440
5 28.5600000 -0.0674590
6 10.2100000 -0.1580780
7 3.8380000 -0.1218310
8 0.7466000 0.5490030
1 11420.0000000 -0.0001150
2 1712.0000000 -0.0008950
3 389.3000000 -0.0046240
4 110.0000000 -0.0185280
5 35.5700000 -0.0573390
6 12.5400000 -0.1320760
7 4.6440000 -0.1725100
8 0.5118000 0.5999440
S 1
1 0.2248000 1.0000000
1 1.2930000 1.0000000
S 1
1 0.0612400 1.0000000
1 0.1787000 1.0000000
S 1
1 0.0576000 1.0000000
P 3
1 13.5500000 0.0399190
2 2.9170000 0.2171690
3 0.7973000 0.5103190
1 26.6300000 0.0146700
2 5.9480000 0.0917640
3 1.7420000 0.2986830
P 1
1 0.2185000 1.0000000
1 0.5550000 1.0000000
P 1
1 0.0561100 1.0000000
1 0.1725000 1.0000000
P 1
1 0.0491000 1.0000000
D 1
1 0.8170000 1.0000000
1 1.6540000 1.0000000
D 1
1 0.2300000 1.0000000
2 9
1 0.4690000 1.0000000
D 1
1 0.1510000 1.0000000
F 1
1 1.0930000 1.0000000
F 1
1 0.3640000 1.0000000
2 14
S 8
1 9046.0000000 0.0007000
2 1357.0000000 0.0053890
3 309.3000000 0.0274060
4 87.7300000 0.1032070
5 28.5600000 0.2787230
6 10.2100000 0.4485400
7 3.8380000 0.2782380
8 0.7466000 0.0154400
1 11420.0000000 0.0005230
2 1712.0000000 0.0040450
3 389.3000000 0.0207750
4 110.0000000 0.0807270
5 35.5700000 0.2330740
6 12.5400000 0.4335010
7 4.6440000 0.3474720
8 0.5118000 -0.0085080
S 8
1 9046.0000000 -0.0001530
2 1357.0000000 -0.0012080
3 309.3000000 -0.0059920
4 87.7300000 -0.0245440
5 28.5600000 -0.0674590
6 10.2100000 -0.1580780
7 3.8380000 -0.1218310
8 0.7466000 0.5490030
1 11420.0000000 -0.0001150
2 1712.0000000 -0.0008950
3 389.3000000 -0.0046240
4 110.0000000 -0.0185280
5 35.5700000 -0.0573390
6 12.5400000 -0.1320760
7 4.6440000 -0.1725100
8 0.5118000 0.5999440
S 1
1 0.2248000 1.0000000
1 1.2930000 1.0000000
S 1
1 0.0612400 1.0000000
1 0.1787000 1.0000000
S 1
1 0.0576000 1.0000000
P 3
1 13.5500000 0.0399190
2 2.9170000 0.2171690
3 0.7973000 0.5103190
1 26.6300000 0.0146700
2 5.9480000 0.0917640
3 1.7420000 0.2986830
P 1
1 0.2185000 1.0000000
1 0.5550000 1.0000000
P 1
1 0.0561100 1.0000000
1 0.1725000 1.0000000
P 1
1 0.0491000 1.0000000
D 1
1 0.8170000 1.0000000
1 1.6540000 1.0000000
D 1
1 0.2300000 1.0000000
1 0.4690000 1.0000000
D 1
1 0.1510000 1.0000000
F 1
1 1.0930000 1.0000000
F 1
1 0.3640000 1.0000000

2
input/methods
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@ -13,7 +13,7 @@
# G0F2 evGF2 G0F3 evGF3
F F F F
# G0W0 evGW qsGW
T F F
T T F
# G0T0 evGT qsGT
F F F
# MCMP2

2
input/options
View File

@ -9,7 +9,7 @@
# GF: maxSCF thresh DIIS n_diis lin renorm
256 0.00001 T 5 T 3
# GW/GT: maxSCF thresh DIIS n_diis COHSEX SOSEX BSE TDA G0W GW0 lin eta
256 0.00001 T 5 F F T F F F T 0.0
256 0.00001 T 5 F F T F F F T 0.00367493
# ACFDT: AC Kx XBS
F F T
# MCMP2: nMC nEq nWalk dt nPrint iSeed doDrift

125
input/weight
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@ -1,71 +1,92 @@
1 9
1 14
S 8
1 9046.0000000 0.0007000
2 1357.0000000 0.0053890
3 309.3000000 0.0274060
4 87.7300000 0.1032070
5 28.5600000 0.2787230
6 10.2100000 0.4485400
7 3.8380000 0.2782380
8 0.7466000 0.0154400
1 11420.0000000 0.0005230
2 1712.0000000 0.0040450
3 389.3000000 0.0207750
4 110.0000000 0.0807270
5 35.5700000 0.2330740
6 12.5400000 0.4335010
7 4.6440000 0.3474720
8 0.5118000 -0.0085080
S 8
1 9046.0000000 -0.0001530
2 1357.0000000 -0.0012080
3 309.3000000 -0.0059920
4 87.7300000 -0.0245440
5 28.5600000 -0.0674590
6 10.2100000 -0.1580780
7 3.8380000 -0.1218310
8 0.7466000 0.5490030
1 11420.0000000 -0.0001150
2 1712.0000000 -0.0008950
3 389.3000000 -0.0046240
4 110.0000000 -0.0185280
5 35.5700000 -0.0573390
6 12.5400000 -0.1320760
7 4.6440000 -0.1725100
8 0.5118000 0.5999440
S 1
1 0.2248000 1.0000000
1 1.2930000 1.0000000
S 1
1 0.0612400 1.0000000
1 0.1787000 1.0000000
S 1
1 0.0576000 1.0000000
P 3
1 13.5500000 0.0399190
2 2.9170000 0.2171690
3 0.7973000 0.5103190
1 26.6300000 0.0146700
2 5.9480000 0.0917640
3 1.7420000 0.2986830
P 1
1 0.2185000 1.0000000
1 0.5550000 1.0000000
P 1
1 0.0561100 1.0000000
1 0.1725000 1.0000000
P 1
1 0.0491000 1.0000000
D 1
1 0.8170000 1.0000000
1 1.6540000 1.0000000
D 1
1 0.2300000 1.0000000
2 9
1 0.4690000 1.0000000
D 1
1 0.1510000 1.0000000
F 1
1 1.0930000 1.0000000
F 1
1 0.3640000 1.0000000
2 14
S 8
1 9046.0000000 0.0007000
2 1357.0000000 0.0053890
3 309.3000000 0.0274060
4 87.7300000 0.1032070
5 28.5600000 0.2787230
6 10.2100000 0.4485400
7 3.8380000 0.2782380
8 0.7466000 0.0154400
1 11420.0000000 0.0005230
2 1712.0000000 0.0040450
3 389.3000000 0.0207750
4 110.0000000 0.0807270
5 35.5700000 0.2330740
6 12.5400000 0.4335010
7 4.6440000 0.3474720
8 0.5118000 -0.0085080
S 8
1 9046.0000000 -0.0001530
2 1357.0000000 -0.0012080
3 309.3000000 -0.0059920
4 87.7300000 -0.0245440
5 28.5600000 -0.0674590
6 10.2100000 -0.1580780
7 3.8380000 -0.1218310
8 0.7466000 0.5490030
1 11420.0000000 -0.0001150
2 1712.0000000 -0.0008950
3 389.3000000 -0.0046240
4 110.0000000 -0.0185280
5 35.5700000 -0.0573390
6 12.5400000 -0.1320760
7 4.6440000 -0.1725100
8 0.5118000 0.5999440
S 1
1 0.2248000 1.0000000
1 1.2930000 1.0000000
S 1
1 0.0612400 1.0000000
1 0.1787000 1.0000000
S 1
1 0.0576000 1.0000000
P 3
1 13.5500000 0.0399190
2 2.9170000 0.2171690
3 0.7973000 0.5103190
1 26.6300000 0.0146700
2 5.9480000 0.0917640
3 1.7420000 0.2986830
P 1
1 0.2185000 1.0000000
1 0.5550000 1.0000000
P 1
1 0.0561100 1.0000000
1 0.1725000 1.0000000
P 1
1 0.0491000 1.0000000
D 1
1 0.8170000 1.0000000
1 1.6540000 1.0000000
D 1
1 0.2300000 1.0000000
1 0.4690000 1.0000000
D 1
1 0.1510000 1.0000000
F 1
1 1.0930000 1.0000000
F 1
1 0.3640000 1.0000000

10
src/QuAcK/Bethe_Salpeter_Z_matrix_dynamic.f90 → src/QuAcK/Bethe_Salpeter_ZA_matrix_dynamic.f90
View File

@ -1,4 +1,4 @@
subroutine Bethe_Salpeter_Z_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,lambda,eGW,OmRPA,OmBSE,rho,Z_dyn)
subroutine Bethe_Salpeter_ZA_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,lambda,eGW,OmRPA,OmBSE,rho,ZA_dyn)
! Compute the dynamic part of the Bethe-Salpeter equation matrices
@ -24,11 +24,11 @@ subroutine Bethe_Salpeter_Z_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,lambda,eGW,Om
! Output variables
double precision,intent(out) :: Z_dyn(nS,nS)
double precision,intent(out) :: ZA_dyn(nS,nS)
! Initialization
Z_dyn(:,:) = 0d0
ZA_dyn(:,:) = 0d0
! Number of poles taken into account
@ -56,11 +56,11 @@ subroutine Bethe_Salpeter_Z_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,lambda,eGW,Om
enddo
Z_dyn(ia,jb) = Z_dyn(ia,jb) + 2d0*lambda*chi
ZA_dyn(ia,jb) = ZA_dyn(ia,jb) + 2d0*lambda*chi
enddo
enddo
enddo
enddo
end subroutine Bethe_Salpeter_Z_matrix_dynamic
end subroutine Bethe_Salpeter_ZA_matrix_dynamic

66
src/QuAcK/Bethe_Salpeter_ZB_matrix_dynamic.f90 Normal file
View File

@ -0,0 +1,66 @@
subroutine Bethe_Salpeter_ZB_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,lambda,eGW,OmRPA,OmBSE,rho,ZB_dyn)
! Compute the dynamic part of the Bethe-Salpeter equation matrices
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: nBas,nC,nO,nV,nR,nS
double precision,intent(in) :: eta
double precision,intent(in) :: lambda
double precision,intent(in) :: eGW(nBas)
double precision,intent(in) :: OmRPA(nS)
double precision,intent(in) :: OmBSE
double precision,intent(in) :: rho(nBas,nBas,nS)
! Local variables
integer :: maxS
double precision :: chi
double precision :: eps
integer :: i,j,a,b,ia,jb,kc
! Output variables
double precision,intent(out) :: ZB_dyn(nS,nS)
! Initialization
ZB_dyn(:,:) = 0d0
! Number of poles taken into account
maxS = nS
! Build dynamic A matrix
ia = 0
do i=nC+1,nO
do a=nO+1,nBas-nR
ia = ia + 1
jb = 0
do j=nC+1,nO
do b=nO+1,nBas-nR
jb = jb + 1
chi = 0d0
do kc=1,maxS
eps = (OmBSE - OmRPA(kc) - (eGW(a) - eGW(b)))**2 + eta**2
chi = chi + rho(i,b,kc)*rho(a,j,kc)*((OmBSE - OmRPA(kc) - (eGW(a) - eGW(b)))/eps)**2
eps = (OmBSE - OmRPA(kc) - (eGW(j) - eGW(i)))**2 + eta**2
chi = chi + rho(i,b,kc)*rho(a,j,kc)*((OmBSE - OmRPA(kc) - (eGW(j) - eGW(i)))/eps)**2
enddo
ZB_dyn(ia,jb) = ZB_dyn(ia,jb) + 2d0*lambda*chi
enddo
enddo
enddo
enddo
end subroutine Bethe_Salpeter_ZB_matrix_dynamic

30
src/QuAcK/Bethe_Salpeter_dynamic_perturbation.f90
View File

@ -25,6 +25,7 @@ subroutine Bethe_Salpeter_dynamic_perturbation(TDA,eta,nBas,nC,nO,nV,nR,nS,eGW,O
! Local variables
logical :: TDA_dyn = .false.
integer :: ia
integer,parameter :: maxS = 10
double precision :: gapGW
@ -35,11 +36,13 @@ subroutine Bethe_Salpeter_dynamic_perturbation(TDA,eta,nBas,nC,nO,nV,nR,nS,eGW,O
double precision,allocatable :: Y(:)
double precision,allocatable :: A_dyn(:,:)
double precision,allocatable :: B_dyn(:,:)
double precision,allocatable :: Z_dyn(:,:)
double precision,allocatable :: ZA_dyn(:,:)
double precision,allocatable :: ZB_dyn(:,:)
! Memory allocation
allocate(OmDyn(nS),ZDyn(nS),X(nS),Y(nS),A_dyn(nS,nS),B_dyn(nS,nS),Z_dyn(nS,nS))
allocate(OmDyn(nS),ZDyn(nS),X(nS),Y(nS),A_dyn(nS,nS),ZA_dyn(nS,nS))
if(TDA_dyn) allocate(B_dyn(nS,nS),ZB_dyn(nS,nS))
gapGW = eGW(nO+1) - eGW(nO)
@ -54,24 +57,36 @@ subroutine Bethe_Salpeter_dynamic_perturbation(TDA,eta,nBas,nC,nO,nV,nR,nS,eGW,O
X(:) = 0.5d0*(XpY(ia,:) + XmY(ia,:))
Y(:) = 0.5d0*(XpY(ia,:) - XmY(ia,:))
! Resonant part of the BSE correction
call Bethe_Salpeter_A_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,1d0,eGW(:),OmRPA(:),OmBSE(ia),rho(:,:,:),A_dyn(:,:))
! Renormalization factor
! Renormalization factor of the resonant part
call Bethe_Salpeter_Z_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,1d0,eGW(:),OmRPA(:),OmBSE(ia),rho(:,:,:),Z_dyn(:,:))
ZDyn(ia) = dot_product(X(:),matmul(Z_dyn(:,:),X(:)))
ZDyn(ia) = 1d0/(1d0 - ZDyn(ia))
call Bethe_Salpeter_ZA_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,1d0,eGW(:),OmRPA(:),OmBSE(ia),rho(:,:,:),ZA_dyn(:,:))
! First-order correction
if(.true.) then
if(TDA_dyn) then
ZDyn(ia) = dot_product(X(:),matmul(ZA_dyn(:,:),X(:)))
OmDyn(ia) = dot_product(X(:),matmul(A_dyn(:,:),X(:)))
else
! Anti-resonant part of the BSE correction
call Bethe_Salpeter_B_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,1d0,eGW(:),OmRPA(:),OmBSE(ia),rho(:,:,:),B_dyn(:,:))
! Renormalization factor of the anti-resonant part
call Bethe_Salpeter_ZB_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,1d0,eGW(:),OmRPA(:),OmBSE(ia),rho(:,:,:),ZB_dyn(:,:))
ZDyn(ia) = dot_product(X(:),matmul(ZA_dyn(:,:),X(:))) &
- dot_product(Y(:),matmul(ZA_dyn(:,:),Y(:))) &
+ dot_product(X(:),matmul(ZB_dyn(:,:),Y(:))) &
- dot_product(Y(:),matmul(ZB_dyn(:,:),X(:)))
OmDyn(ia) = dot_product(X(:),matmul(A_dyn(:,:),X(:))) &
- dot_product(Y(:),matmul(A_dyn(:,:),Y(:))) &
+ dot_product(X(:),matmul(B_dyn(:,:),Y(:))) &
@ -79,6 +94,7 @@ subroutine Bethe_Salpeter_dynamic_perturbation(TDA,eta,nBas,nC,nO,nV,nR,nS,eGW,O
end if
ZDyn(ia) = 1d0/(1d0 - ZDyn(ia))
OmDyn(ia) = ZDyn(ia)*OmDyn(ia)
write(*,'(2X,I5,5X,F15.6,5X,F15.6,5X,F15.6,5X,F15.6)') &