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T-matrix in spinorbitals

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This commit is contained in:
Pierre-Francois Loos 2019-10-22 23:03:01 +02:00
parent c22278f497
commit 877f78f1a5
13 changed files with 357 additions and 147 deletions
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75
input/basis
View File

@ -1,52 +1,39 @@
1 9
1 10
S 9 1.00
1.469000D+03 7.660000D-04
2.205000D+02 5.892000D-03
5.026000D+01 2.967100D-02
1.424000D+01 1.091800D-01
4.581000D+00 2.827890D-01
1.580000D+00 4.531230D-01
5.640000D-01 2.747740D-01
7.345000D-02 9.751000D-03
2.805000D-02 -3.180000D-03
6863.0000000 0.0002360
1030.0000000 0.0018260
234.7000000 0.0094520
66.5600000 0.0379570
21.6900000 0.1199650
7.7340000 0.2821620
2.9160000 0.4274040
1.1300000 0.2662780
0.1101000 -0.0072750
S 9 1.00
1.469000D+03 -1.200000D-04
2.205000D+02 -9.230000D-04
5.026000D+01 -4.689000D-03
1.424000D+01 -1.768200D-02
4.581000D+00 -4.890200D-02
1.580000D+00 -9.600900D-02
5.640000D-01 -1.363800D-01
7.345000D-02 5.751020D-01
2.805000D-02 5.176610D-01
6863.0000000 -0.0000430
1030.0000000 -0.0003330
234.7000000 -0.0017360
66.5600000 -0.0070120
21.6900000 -0.0231260
7.7340000 -0.0581380
2.9160000 -0.1145560
1.1300000 -0.1359080
0.1101000 0.5774410
S 1 1.00
2.805000D-02 1.000000D+00
0.2577000 1.0000000
S 1 1.00
8.600000D-03 1.000000D+00
P 4 1.00
1.534000D+00 2.278400D-02
2.749000D-01 1.391070D-01
7.362000D-02 5.003750D-01
2.403000D-02 5.084740D-01
0.0440900 1.0000000
P 3 1.00
7.4360000 0.0107360
1.5770000 0.0628540
0.4352000 0.2481800
P 1 1.00
2.403000D-02 1.000000D+00
0.1438000 1.0000000
P 1 1.00
5.800000D-03 1.000000D+00
0.0499400 1.0000000
D 1 1.00
1.144000D-01 1.0000000
0.3480000 1.0000000
D 1 1.00
7.330000D-02 1.000000D+00
2 5
S 4 1.00
1.301000D+01 1.968500D-02
1.962000D+00 1.379770D-01
4.446000D-01 4.781480D-01
1.220000D-01 5.012400D-01
S 1 1.00
1.220000D-01 1.000000D+00
S 1 1.00
0.0297400 1.0000000
P 1 1.00
7.270000D-01 1.0000000
P 1 1.00
0.1410000 1.0000000
0.1803000 1.0000000
F 1 1.00
0.3250000 1.0000000

2
input/methods
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@ -7,7 +7,7 @@
# CIS TDHF ppRPA ADC
F F F F
# GF2 GF3
T F
F F
# G0W0 evGW qsGW
F F F
# G0T0 evGT qsGT

5
input/molecule
View File

@ -1,5 +1,4 @@
# nAt nEla nElb nCore nRyd
2 2 2 0 0
1 2 2 0 0
# Znuc x y z
Li 0. 0. 0.
H 0. 0. 3.09839495
Be 0.0 0.0 0.0

75
input/weight
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@ -1,52 +1,39 @@
1 9
1 10
S 9 1.00
1.469000D+03 7.660000D-04
2.205000D+02 5.892000D-03
5.026000D+01 2.967100D-02
1.424000D+01 1.091800D-01
4.581000D+00 2.827890D-01
1.580000D+00 4.531230D-01
5.640000D-01 2.747740D-01
7.345000D-02 9.751000D-03
2.805000D-02 -3.180000D-03
6863.0000000 0.0002360
1030.0000000 0.0018260
234.7000000 0.0094520
66.5600000 0.0379570
21.6900000 0.1199650
7.7340000 0.2821620
2.9160000 0.4274040
1.1300000 0.2662780
0.1101000 -0.0072750
S 9 1.00
1.469000D+03 -1.200000D-04
2.205000D+02 -9.230000D-04
5.026000D+01 -4.689000D-03
1.424000D+01 -1.768200D-02
4.581000D+00 -4.890200D-02
1.580000D+00 -9.600900D-02
5.640000D-01 -1.363800D-01
7.345000D-02 5.751020D-01
2.805000D-02 5.176610D-01
6863.0000000 -0.0000430
1030.0000000 -0.0003330
234.7000000 -0.0017360
66.5600000 -0.0070120
21.6900000 -0.0231260
7.7340000 -0.0581380
2.9160000 -0.1145560
1.1300000 -0.1359080
0.1101000 0.5774410
S 1 1.00
2.805000D-02 1.000000D+00
0.2577000 1.0000000
S 1 1.00
8.600000D-03 1.000000D+00
P 4 1.00
1.534000D+00 2.278400D-02
2.749000D-01 1.391070D-01
7.362000D-02 5.003750D-01
2.403000D-02 5.084740D-01
0.0440900 1.0000000
P 3 1.00
7.4360000 0.0107360
1.5770000 0.0628540
0.4352000 0.2481800
P 1 1.00
2.403000D-02 1.000000D+00
0.1438000 1.0000000
P 1 1.00
5.800000D-03 1.000000D+00
0.0499400 1.0000000
D 1 1.00
1.144000D-01 1.0000000
0.3480000 1.0000000
D 1 1.00
7.330000D-02 1.000000D+00
2 5
S 4 1.00
1.301000D+01 1.968500D-02
1.962000D+00 1.379770D-01
4.446000D-01 4.781480D-01
1.220000D-01 5.012400D-01
S 1 1.00
1.220000D-01 1.000000D+00
S 1 1.00
0.0297400 1.0000000
P 1 1.00
7.270000D-01 1.0000000
P 1 1.00
0.1410000 1.0000000
0.1803000 1.0000000
F 1 1.00
0.3250000 1.0000000

1
src/QuAcK/QuAcK.f90
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@ -536,6 +536,7 @@ program QuAcK
call cpu_time(start_G0T0)
call G0T0(BSE,singlet_manifold,triplet_manifold,eta, &
nBas,nC(1),nO(1),nV(1),nR(1),ENuc,ERHF,ERI_MO_basis,eHF,eG0T0)
call soG0T0(eta,nBas,nC(1),nO(1),nV(1),nR(1),ENuc,ERHF,ERI_MO_basis,eHF)
call cpu_time(end_G0T0)
t_G0T0 = end_G0T0 - start_G0T0

24
src/QuAcK/excitation_density_Tmatrix.f90
View File

@ -46,9 +46,9 @@ subroutine excitation_density_Tmatrix(ispin,nBas,nC,nO,nR,nOO,nVV,ERI,X1,Y1,rho1
do d=nO+1,c
cd = cd + 1
rho1(p,i,ab) = rho1(p,i,ab) &
+ (ERI(p,i,c,d) - ERI(p,i,d,c))*X1(cd,ab)
! + (ERI(p,i,c,d) + ERI(p,i,d,c))*X1(cd,ab) &
! /sqrt((1d0 + Kronecker_delta(p,i))*(1d0 + Kronecker_delta(c,d)))
! + ERI(p,i,c,d)*X1(cd,ab)
+ (ERI(p,i,c,d) + ERI(p,i,d,c))*X1(cd,ab) &
/sqrt((1d0 + Kronecker_delta(p,i))*(1d0 + Kronecker_delta(c,d)))
end do
end do
@ -57,9 +57,9 @@ subroutine excitation_density_Tmatrix(ispin,nBas,nC,nO,nR,nOO,nVV,ERI,X1,Y1,rho1
do l=nC+1,k
kl = kl + 1
rho1(p,i,ab) = rho1(p,i,ab) &
+ (ERI(p,i,k,l) - ERI(p,i,l,k))*Y1(kl,ab)
! + (ERI(p,i,k,l) + ERI(p,i,l,k))*Y1(kl,ab) &
! /sqrt((1d0 + Kronecker_delta(p,i))*(1d0 + Kronecker_delta(k,l)))
! + ERI(p,i,k,l)*Y1(kl,ab)
+ (ERI(p,i,k,l) + ERI(p,i,l,k))*Y1(kl,ab) &
/sqrt((1d0 + Kronecker_delta(p,i))*(1d0 + Kronecker_delta(k,l)))
end do
end do
@ -74,9 +74,9 @@ subroutine excitation_density_Tmatrix(ispin,nBas,nC,nO,nR,nOO,nVV,ERI,X1,Y1,rho1
do d=nO+1,c
cd = cd + 1
rho2(p,a,ij) = rho2(p,a,ij) &
+ (ERI(p,a,c,d) - ERI(p,a,d,c))*X2(cd,ij)
! + (ERI(p,a,c,d) + ERI(p,a,d,c))*X2(cd,ij) &
! /sqrt((1d0 + Kronecker_delta(p,a))*(1d0 + Kronecker_delta(c,d)))
! + ERI(p,a,c,d)*X2(cd,ij)
+ (ERI(p,a,c,d) + ERI(p,a,d,c))*X2(cd,ij) &
/sqrt((1d0 + Kronecker_delta(p,a))*(1d0 + Kronecker_delta(c,d)))
end do
end do
@ -86,9 +86,9 @@ subroutine excitation_density_Tmatrix(ispin,nBas,nC,nO,nR,nOO,nVV,ERI,X1,Y1,rho1
do l=nC+1,k
kl = kl + 1
rho2(p,a,ij) = rho2(p,a,ij) &
+ (ERI(p,a,k,l) - ERI(p,a,l,k))*Y2(kl,ij)
! + (ERI(p,a,k,l) + ERI(p,a,l,k))*Y2(kl,ij) &
! /sqrt((1d0 + Kronecker_delta(p,a))*(1d0 + Kronecker_delta(k,l)))
! + ERI(p,a,k,l)*Y2(kl,ij)
+ (ERI(p,a,k,l) + ERI(p,a,l,k))*Y2(kl,ij) &
/sqrt((1d0 + Kronecker_delta(p,a))*(1d0 + Kronecker_delta(k,l)))
end do
end do

12
src/QuAcK/linear_response_pp.f90
View File

@ -1,4 +1,4 @@
subroutine linear_response_pp(ispin,BSE,nBas,nC,nO,nV,nR,nOO,nVV,e,ERI,Omega1,X1,Y1,Omega2,X2,Y2,Ec_ppRPA)
subroutine linear_response_pp(ispin,BSE,nBas,nC,nO,nV,nR,nOO,nVV,e,ERI,Omega1,X1,Y1,Omega2,X2,Y2,EcppRPA)
! Compute the p-p channel of the linear response: see Scueria et al. JCP 139, 104113 (2013)
@ -32,7 +32,7 @@ subroutine linear_response_pp(ispin,BSE,nBas,nC,nO,nV,nR,nOO,nVV,e,ERI,Omega1,X1
double precision,intent(out) :: Omega2(nOO)
double precision,intent(out) :: X2(nVV,nOO)
double precision,intent(out) :: Y2(nOO,nOO)
double precision,intent(out) :: Ec_ppRPA
double precision,intent(out) :: EcppRPA
! Memory allocation
@ -81,9 +81,9 @@ subroutine linear_response_pp(ispin,BSE,nBas,nC,nO,nV,nR,nOO,nVV,e,ERI,Omega1,X1
! Compute the RPA correlation energy
! Ec_ppRPA = 0.5d0*( sum(Omega1(:)) - sum(Omega2(:)) - trace_matrix(nVV,C(:,:)) - trace_matrix(nOO,D(:,:)) )
Ec_ppRPA = +sum(Omega1(:)) - trace_matrix(nVV,C(:,:))
! Ec_ppRPA = -sum(Omega2(:)) - trace_matrix(nOO,D(:,:))
! EcppRPA = 0.5d0*( sum(Omega1(:)) - sum(Omega2(:)) - trace_matrix(nVV,C(:,:)) - trace_matrix(nOO,D(:,:)) )
EcppRPA = +sum(Omega1(:)) - trace_matrix(nVV,C(:,:))
! EcppRPA = -sum(Omega2(:)) - trace_matrix(nOO,D(:,:))
! write(*,*)'X1'
! call matout(nVV,nVV,X1)
@ -94,6 +94,6 @@ subroutine linear_response_pp(ispin,BSE,nBas,nC,nO,nV,nR,nOO,nVV,e,ERI,Omega1,X1
! write(*,*)'Y2'
! call matout(nOO,nOO,Y2)
! print*,'Ec(pp-RPA) = ',Ec_ppRPA
! print*,'Ec(pp-RPA) = ',EcppRPA
end subroutine linear_response_pp

38
src/QuAcK/renormalization_factor_Tmatrix.f90
View File

@ -11,8 +11,8 @@ subroutine renormalization_factor_Tmatrix(eta,nBas,nC,nO,nV,nR,nOOs,nVVs,nOOt,nV
double precision,intent(in) :: eta
integer,intent(in) :: nBas,nC,nO,nV,nR
integer,intent(in) :: nOOs,nVVs
integer,intent(in) :: nOOt,nVVt
integer,intent(in) :: nOOs,nOOt
integer,intent(in) :: nVVs,nVVt
double precision,intent(in) :: e(nBas)
double precision,intent(in) :: Omega1s(nVVs),Omega1t(nVVt)
double precision,intent(in) :: rho1s(nBas,nBas,nVVs),rho1t(nBas,nBas,nVVt)
@ -100,40 +100,6 @@ subroutine renormalization_factor_Tmatrix(eta,nBas,nC,nO,nV,nR,nOOs,nVVs,nOOt,nV
enddo
enddo
!----------------------------------------------
! Singlet part of the T-matrix self-energy
!----------------------------------------------
! Occupied part of the T-matrix self-energy
do p=nC+1,nBas-nR
do i=nC+1,nO
cd = 0
do c=nO+1,nBas-nR
do d=nO+1,c
cd = cd + 1
eps = e(p) + e(i) - Omega1s(cd)
Z(p) = Z(p) - 2d0*rho1s(p,i,cd)**2/eps**2
enddo
enddo
enddo
enddo
! Virtual part of the T-matrix self-energy
do p=nC+1,nBas-nR
do a=nO+1,nBas-nR
kl = 0
do k=nC+1,nO
do l=nC+1,k
kl = kl + 1
eps = e(p) + e(a) - Omega2s(kl)
Z(p) = Z(p) - 2d0*rho2s(p,a,kl)**2/eps**2
enddo
enddo
enddo
enddo
! Compute renormalization factor from derivative of SigT
Z(:) = 1d0/(1d0 - Z(:))

71
src/QuAcK/renormalization_factor_Tmatrix_so.f90 Normal file
View File

@ -0,0 +1,71 @@
subroutine renormalization_factor_Tmatrix_so(eta,nBas,nC,nO,nV,nR,nOO,nVV,e,Omega1,rho1,Omega2,rho2,Z)
! Compute renormalization factor of the T-matrix self-energy
implicit none
include 'parameters.h'
! Input variables
double precision,intent(in) :: eta
integer,intent(in) :: nBas,nC,nO,nV,nR
integer,intent(in) :: nOO
integer,intent(in) :: nVV
double precision,intent(in) :: e(nBas)
double precision,intent(in) :: Omega1(nVV)
double precision,intent(in) :: rho1(nBas,nBas,nVV)
double precision,intent(in) :: Omega2(nOO)
double precision,intent(in) :: rho2(nBas,nBas,nOO)
! Local variables
integer :: i,j,k,l,a,b,c,d,p,cd,kl
double precision :: eps
! Output variables
double precision,intent(out) :: Z(nBas)
! Initialize
Z(:) = 0d0
!----------------------------------------------
! T-matrix renormalization factor in the spinorbital basis
!----------------------------------------------
! Occupied part of the T-matrix self-energy
do p=nC+1,nBas-nR
do i=nC+1,nO
cd = 0
do c=nO+1,nBas-nR
do d=nO+1,c-1
cd = cd + 1
eps = e(p) + e(i) - Omega1(cd)
Z(p) = Z(p) - rho1(p,i,cd)**2/eps**2
enddo
enddo
enddo
enddo
! Virtual part of the T-matrix self-energy
do p=nC+1,nBas-nR
do a=nO+1,nBas-nR
kl = 0
do k=nC+1,nO
do l=nC+1,k-1
kl = kl + 1
eps = e(p) + e(a) - Omega2(kl)
Z(p) = Z(p) - rho2(p,a,kl)**2/eps**2
enddo
enddo
enddo
enddo
! Compute renormalization factor from derivative of SigT
Z(:) = 1d0/(1d0 - Z(:))
end subroutine renormalization_factor_Tmatrix_so

71
src/QuAcK/self_energy_Tmatrix_diag_so.f90 Normal file
View File

@ -0,0 +1,71 @@
subroutine self_energy_Tmatrix_diag_so(eta,nBas,nC,nO,nV,nR,nOO,nVV,e,Omega1,rho1,Omega2,rho2,SigT)
! Compute diagonal of the correlation part of the T-matrix self-energy
implicit none
include 'parameters.h'
! Input variables
double precision,intent(in) :: eta
integer,intent(in) :: nBas
integer,intent(in) :: nC
integer,intent(in) :: nO
integer,intent(in) :: nV
integer,intent(in) :: nR
integer,intent(in) :: nOO
integer,intent(in) :: nVV
double precision,intent(in) :: e(nBas)
double precision,intent(in) :: Omega1(nVV)
double precision,intent(in) :: rho1(nBas,nBas,nVV)
double precision,intent(in) :: Omega2(nOO)
double precision,intent(in) :: rho2(nBas,nBas,nOO)
! Local variables
integer :: i,j,k,l,a,b,c,d,p,cd,kl
double precision :: eps
! Output variables
double precision,intent(out) :: SigT(nBas)
! Initialize
SigT(:) = 0d0
!----------------------------------------------
! T-matrix self-energy in the spinorbital basis
!----------------------------------------------
! Occupied part of the T-matrix self-energy
do p=nC+1,nBas-nR
do i=nC+1,nO
cd = 0
do c=nO+1,nBas-nR
do d=nO+1,c-1
cd = cd + 1
eps = e(p) + e(i) - Omega1(cd)
SigT(p) = SigT(p) + rho1(p,i,cd)**2/eps
enddo
enddo
enddo
enddo
! Virtual part of the T-matrix self-energy
do p=nC+1,nBas-nR
do a=nO+1,nBas-nR
kl = 0
do k=nC+1,nO
do l=nC+1,k-1
kl = kl + 1
eps = e(p) + e(a) - Omega2(kl)
SigT(p) = SigT(p) + rho2(p,a,kl)**2/eps
enddo
enddo
enddo
enddo
end subroutine self_energy_Tmatrix_diag_so

127
src/QuAcK/soG0T0.f90 Normal file
View File

@ -0,0 +1,127 @@
subroutine soG0T0(eta,nBas,nC,nO,nV,nR,ENuc,ERHF,ERI,eHF)
! Perform G0W0 calculation with a T-matrix self-energy (G0T0) in the spinorbital basis
implicit none
include 'parameters.h'
! Input variables
double precision,intent(in) :: eta
integer,intent(in) :: nBas,nC,nO,nV,nR
double precision,intent(in) :: ENuc
double precision,intent(in) :: ERHF
double precision,intent(in) :: eHF(nBas)
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
! Local variables
integer :: ispin
integer :: nOO
integer :: nVV
double precision :: EcRPA
integer :: nBas2,nC2,nO2,nV2,nR2
double precision,allocatable :: Omega1(:)
double precision,allocatable :: X1(:,:)
double precision,allocatable :: Y1(:,:)
double precision,allocatable :: rho1(:,:,:)
double precision,allocatable :: Omega2(:)
double precision,allocatable :: X2(:,:)
double precision,allocatable :: Y2(:,:)
double precision,allocatable :: rho2(:,:,:)
double precision,allocatable :: SigT(:)
double precision,allocatable :: Z(:)
double precision,allocatable :: eG0T0(:)
double precision,allocatable :: seHF(:)
double precision,allocatable :: sERI(:,:,:,:)
! Output variables
! Hello world
write(*,*)
write(*,*)'************************************************'
write(*,*)'| One-shot soG0T0 calculation |'
write(*,*)'************************************************'
write(*,*)
! Spatial to spin orbitals
nBas2 = 2*nBas
allocate(seHF(nBas2),sERI(nBas2,nBas2,nBas2,nBas2))
call spatial_to_spin_MO_energy(nBas,eHF,nBas2,seHF)
call spatial_to_spin_ERI(nBas,ERI,nBas2,sERI)
! Define occupied and virtual spaces
nO2 = 2*nO
nV2 = 2*nV
nC2 = 2*nC
nR2 = 2*nR
! Dimensions of the rr-RPA linear reponse matrices
nOO = nO2*(nO2-1)/2
nVV = nV2*(nV2-1)/2
! Memory allocation
allocate(Omega1(nVV),X1(nVV,nVV),Y1(nOO,nVV), &
Omega2(nOO),X2(nVV,nOO),Y2(nOO,nOO), &
rho1(nBas2,nBas2,nVV),rho2(nBas2,nBas2,nOO), &
eG0T0(nBas2),SigT(nBas2),Z(nBas2))
!----------------------------------------------
! Spinorbital basis
!----------------------------------------------
ispin = 2
! Compute linear response
call linear_response_pp(ispin,.false.,nBas2,nC2,nO2,nV2,nR2, &
nOO,nVV,seHF(:),sERI(:,:,:,:), &
Omega1(:),X1(:,:),Y1(:,:), &
Omega2(:),X2(:,:),Y2(:,:), &
EcRPA)
call print_excitation('pp-RPA (N+2)',ispin,nVV,Omega1(:))
call print_excitation('pp-RPA (N-2)',ispin,nOO,Omega2(:))
! Compute excitation densities for the T-matrix
call excitation_density_Tmatrix(ispin,nBas2,nC2,nO2,nR2,nOO,nVV,sERI(:,:,:,:), &
X1(:,:),Y1(:,:),rho1(:,:,:), &
X2(:,:),Y2(:,:),rho2(:,:,:))
!----------------------------------------------
! Compute T-matrix version of the self-energy
!----------------------------------------------
call self_energy_Tmatrix_diag_so(eta,nBas2,nC2,nO2,nV2,nR2,nOO,nVV,seHF(:), &
Omega1(:),rho1(:,:,:),Omega2(:),rho2(:,:,:), &
SigT(:))
! Compute renormalization factor for T-matrix self-energy
call renormalization_factor_Tmatrix_so(eta,nBas2,nC2,nO2,nV2,nR2,nOO,nVV,seHF(:), &
Omega1(:),rho1(:,:,:),Omega2(:),rho2(:,:,:), &
Z(:))
!----------------------------------------------
! Solve the quasi-particle equation
!----------------------------------------------
eG0T0(:) = seHF(:) + Z(:)*SigT(:)
!----------------------------------------------
! Dump results
!----------------------------------------------
call print_G0T0(nBas2,nO2,seHF(:),ENuc,ERHF,SigT(:),Z(:),eG0T0(:),EcRPA)
end subroutine soG0T0

1
src/QuAcK/sort_ppRPA.f90
View File

@ -32,6 +32,7 @@ subroutine sort_ppRPA(nOO,nVV,Omega,Z,Omega1,X1,Y1,Omega2,X2,Y2)
ab = 0
ij = 0
do pq=1,nOO+nVV
if(Omega(pq) > 0d0) then

2
src/utils/wrap_lapack.f90
View File

@ -53,7 +53,7 @@ subroutine diagonalize_general_matrix(N,A,e,X)
lwork = 4*N
allocate(WI(N),VL(N,N),work(lwork))
call dgeev('V','V',N,A,N,e,WI,VL,N,X,N,work,lwork,info)
call dgeev('N','V',N,A,N,e,WI,VL,N,X,N,work,lwork,info)
if(info /= 0) then
print*,'Problem in diagonalize_matrix (dgeev)!!'