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R and U density matrices

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This commit is contained in:
Pierre-Francois Loos 2020-03-15 14:33:53 +01:00
parent e14e8ac278
commit f8bdfb1ceb
16 changed files with 200 additions and 69 deletions
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2
examples/molecule.F2
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@ -2,4 +2,4 @@
2 9 9 0 0
# Znuc x y z
F 0. 0. 0.
F 0. 0. 2.1
F 0. 0. 3.3

10
input/dft
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@ -1,14 +1,14 @@
# Restricted or unrestricted KS calculation
RKS
GOK-RKS
# exchange rung: Hartree = 0, LDA = 1 (S51), GGA = 2(G96,B88), hybrid = 4, Hartree-Fock = 666
1 S51
1 RS51
# correlation rung: Hartree = 0, LDA = 1 (W38,VWN5,C16,LF19), GGA = 2(LYP), hybrid = 4(B3LYP), Hartree-Fock = 666
0 LF19
0 HF
# quadrature grid SG-n
1
# Number of states in ensemble (nEns)
3
2
# Ensemble weights: wEns(1),...,wEns(nEns-1)
0.00000 0.50000
0.50000 0.00000
# eKS: maxSCF thresh DIIS n_diis guess_type ortho_type
64 0.0000001 T 15 1 1

4
input/options
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@ -9,8 +9,8 @@
# GF: maxSCF thresh DIIS n_diis renormalization
256 0.00001 T 5 3
# GW: maxSCF thresh DIIS n_diis COHSEX SOSEX BSE TDA G0W GW0 lin eta
1 0.00001 T 5 F F T F F F T 0.000
256 0.00001 T 5 F F T F F F F 0.000
# ACFDT: AC Kx XBS
T F T
T F F
# MCMP2: nMC nEq nWalk dt nPrint iSeed doDrift
1000000 100000 10 0.3 10000 1234 T

4
scan_LiH.sh
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@ -2,8 +2,8 @@
MOL="LiH"
BASIS="cc-pvqz"
R_START=3.5
R_END=3.5
R_START=2.5
R_END=3.6
DR=0.1
for R in $(seq $R_START $DR $R_END)

2
src/eDFT/GOK_RKS.f90
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@ -182,7 +182,7 @@ subroutine GOK_RKS(x_rung,x_DFA,c_rung,c_DFA,nEns,wEns,nGrid,weight,maxSCF,thres
! Compute density matrix
!------------------------------------------------------------------------
call density_matrix(nBas,nEns,nO,c(:,:),P(:,:,:))
call restricted_density_matrix(nBas,nEns,nO,c(:,:),P(:,:,:))
! Weight-dependent density matrix

4
src/eDFT/GOK_UKS.f90
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@ -192,7 +192,7 @@ subroutine GOK_UKS(x_rung,x_DFA,c_rung,c_DFA,nEns,wEns,nGrid,weight,maxSCF,thres
! Compute density matrix
!------------------------------------------------------------------------
call density_matrix(nBas,nEns,nO(:),c(:,:,:),P(:,:,:,:))
call unrestricted_density_matrix(nBas,nEns,nO(:),c(:,:,:),P(:,:,:,:))
! Weight-dependent density matrix
@ -224,7 +224,7 @@ subroutine GOK_UKS(x_rung,x_DFA,c_rung,c_DFA,nEns,wEns,nGrid,weight,maxSCF,thres
do ispin=1,nspin
do iEns=1,nEns
! call gradient_density(nGrid,nBas,P(:,:,ispin,iEns),AO(:,:),dAO(:,:,:),drho(:,:,ispin,iEns))
call gradient_density(nGrid,nBas,P(:,:,ispin,iEns),AO(:,:),dAO(:,:,:),drho(:,:,ispin,iEns))
end do
end do

10
src/eDFT/RMFL20_lda_exchange_energy.f90
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@ -16,8 +16,9 @@ subroutine RMFL20_lda_exchange_energy(nEns,wEns,nGrid,weight,rho,Ex)
! Local variables
integer :: iG
double precision :: Cx0
double precision :: Cx1
double precision :: CxLDA
double precision :: Cx2
double precision :: Cxw
double precision :: r
@ -27,10 +28,11 @@ subroutine RMFL20_lda_exchange_energy(nEns,wEns,nGrid,weight,rho,Ex)
! Cx coefficient for Slater LDA exchange
CxLDA = -(4d0/3d0)*(1d0/pi)**(1d0/3d0)
Cx2 = -(176d0/105d0)*(1d0/pi)**(1d0/3d0)
Cx0 = -(4d0/3d0)*(1d0/pi)**(1d0/3d0)
Cx1 = -(176d0/105d0)*(1d0/pi)**(1d0/3d0)
CxLDA = -(3d0/4d0)*(3d0/pi)**(1d0/3d0)
Cxw = (1d0 - wEns(2))*CxLDA + wEns(2)*(Cx2 - CxLDA)
Cxw = CxLDA + wEns(1)*(Cx1 - Cx0)
! Compute LDA exchange energy

59
src/eDFT/RMFL20_lda_exchange_potential.f90 Normal file
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@ -0,0 +1,59 @@
subroutine RMFL20_lda_exchange_potential(nEns,wEns,nGrid,weight,nBas,AO,rho,Fx)
! Compute the restricted version of the weight-dependent MFL20 exchange potential
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: nEns
double precision,intent(in) :: wEns(nEns)
integer,intent(in) :: nGrid
double precision,intent(in) :: weight(nGrid)
integer,intent(in) :: nBas
double precision,intent(in) :: AO(nBas,nGrid)
double precision,intent(in) :: rho(nGrid)
! Local variables
integer :: mu,nu,iG
double precision :: Cx0
double precision :: Cx1
double precision :: CxLDA
double precision :: Cxw
double precision :: r,vAO
! Output variables
double precision,intent(out) :: Fx(nBas,nBas)
! Cx coefficient for Slater LDA exchange
Cx0 = -(4d0/3d0)*(1d0/pi)**(1d0/3d0)
Cx1 = -(176d0/105d0)*(1d0/pi)**(1d0/3d0)
CxLDA = -(3d0/4d0)*(3d0/pi)**(1d0/3d0)
Cxw = CxLDA + wEns(1)*(Cx1 - Cx0)
! Compute LDA exchange matrix in the AO basis
Fx(:,:) = 0d0
do mu=1,nBas
do nu=1,nBas
do iG=1,nGrid
r = max(0d0,rho(iG))
if(r > threshold) then
vAO = weight(iG)*AO(mu,iG)*AO(nu,iG)
Fx(mu,nu) = Fx(mu,nu) + vAO*4d0/3d0*Cxw*r**(1d0/3d0)
endif
enddo
enddo
enddo
end subroutine RMFL20_lda_exchange_potential

42
src/eDFT/RS51_lda_exchange_energy.f90 Normal file
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@ -0,0 +1,42 @@
subroutine RS51_lda_exchange_energy(nGrid,weight,rho,Ex)
! Compute restriced version of Slater's LDA exchange energy
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: nGrid
double precision,intent(in) :: weight(nGrid)
double precision,intent(in) :: rho(nGrid)
! Local variables
integer :: iG
double precision :: alpha,r
! Output variables
double precision :: Ex
! Cx coefficient for Slater LDA exchange
alpha = -(3d0/4d0)*(3d0/pi)**(1d0/3d0)
! Compute LDA exchange energy
Ex = 0d0
do iG=1,nGrid
r = max(0d0,rho(iG))
if(r > threshold) then
Ex = Ex + weight(iG)*alpha*r**(4d0/3d0)
endif
enddo
end subroutine RS51_lda_exchange_energy

50
src/eDFT/RS51_lda_exchange_potential.f90 Normal file
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@ -0,0 +1,50 @@
subroutine RS51_lda_exchange_potential(nGrid,weight,nBas,AO,rho,Fx)
! Compute the restricted version of Slater's LDA exchange potential
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: nGrid
double precision,intent(in) :: weight(nGrid)
integer,intent(in) :: nBas
double precision,intent(in) :: AO(nBas,nGrid)
double precision,intent(in) :: rho(nGrid)
! Local variables
integer :: mu,nu,iG
double precision :: Cx
double precision :: r,vAO
! Output variables
double precision,intent(out) :: Fx(nBas,nBas)
! Cx coefficient for Slater LDA exchange
Cx = -(3d0/4d0)*(3d0/pi)**(1d0/3d0)
! Compute LDA exchange matrix in the AO basis
Fx(:,:) = 0d0
do mu=1,nBas
do nu=1,nBas
do iG=1,nGrid
r = max(0d0,rho(iG))
if(r > threshold) then
vAO = weight(iG)*AO(mu,iG)*AO(nu,iG)
Fx(mu,nu) = Fx(mu,nu) + vAO*4d0/3d0*Cx*r**(1d0/3d0)
endif
enddo
enddo
enddo
end subroutine RS51_lda_exchange_potential

43
src/eDFT/density_matrix.f90
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@ -1,43 +0,0 @@
subroutine density_matrix(nBas,nEns,nO,c,P)
! Calculate density matrices
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: nBas
integer,intent(in) :: nEns
integer,intent(in) :: nO(nspin)
double precision,intent(in) :: c(nBas,nBas,nspin)
! Local variables
integer :: ispin
! Output variables
double precision,intent(out) :: P(nBas,nBas,nspin,nEns)
! Ground state density matrix
do ispin=1,nspin
P(:,:,ispin,1) = matmul(c(:,1:nO(ispin),ispin),transpose(c(:,1:nO(ispin),ispin)))
end do
! Singly-excited state density matrix
P(:,:,1,2) = matmul(c(:,1:nO(1)-1,1),transpose(c(:,1:nO(1)-1,1))) &
+ matmul(c(:,nO(1)+1:nO(1)+1,1),transpose(c(:,nO(1)+1:nO(1)+1,1)))
P(:,:,2,2) = matmul(c(:,1:nO(2),2),transpose(c(:,1:nO(2),2)))
! Doubly-excited state density matrix
do ispin=1,nspin
P(:,:,ispin,3) = matmul(c(:,1:nO(ispin)-1,ispin),transpose(c(:,1:nO(ispin)-1,ispin))) &
+ matmul(c(:,nO(ispin)+1:nO(ispin)+1,ispin),transpose(c(:,nO(ispin)+1:nO(ispin)+1,ispin)))
end do
end subroutine density_matrix

1
src/eDFT/exchange_energy.f90
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@ -69,6 +69,7 @@ subroutine exchange_energy(rung,DFA,nEns,wEns,nGrid,weight,nBas,P,FxHF,rho,drho,
+ aX*(ExGGA - ExLDA)
! Hartree-Fock calculation
case(666)
call fock_exchange_energy(nBas,P,FxHF,ExHF)

12
src/eDFT/lda_exchange_energy.f90
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@ -22,13 +22,21 @@ subroutine lda_exchange_energy(DFA,nEns,wEns,nGrid,weight,rho,Ex)
select case (DFA)
! Slater's LDA correlation functional: Slater, Phys. Rev. 81 (1951) 385
! Slater's LDA correlation functional
case ('RS51')
call RS51_lda_exchange_energy(nGrid,weight,rho,Ex)
! Restricted version of Slater's LDA correlation functional
case ('S51')
call S51_lda_exchange_energy(nGrid,weight,rho,Ex)
case ('MFL20')
! Restricted version of the weight-dependent Marut-Fromager-Loos 2020 exchange functional
case ('RMFL20')
call RMFL20_lda_exchange_energy(nEns,wEns,nGrid,weight,rho,Ex)

14
src/eDFT/lda_exchange_potential.f90
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@ -25,12 +25,24 @@ subroutine lda_exchange_potential(DFA,nEns,wEns,nGrid,weight,nBas,AO,rho,Fx)
select case (DFA)
! Slater's LDA correlation functional: Slater, Phys. Rev. 81 (1951) 385
! Restricted version of Slater's LDA correlation functional
case ('RS51')
call RS51_lda_exchange_potential(nGrid,weight,nBas,AO,rho,Fx)
! Slater's LDA correlation functional
case ('S51')
call S51_lda_exchange_potential(nGrid,weight,nBas,AO,rho,Fx)
! Restricted version of the weight-dependent Marut-Fromager-Loos 2020 functional
case ('RMFL20')
call RMFL20_lda_exchange_potential(nEns,wEns,nGrid,weight,nBas,AO,rho,Fx)
case default
call print_warning('!!! LDA exchange functional not available !!!')

6
src/eDFT/read_options.f90
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@ -14,7 +14,7 @@ subroutine read_options(method,x_rung,x_DFA,c_rung,c_DFA,SGn,nEns,wEns,maxSCF,th
character(len=7),intent(out) :: method
integer,intent(out) :: x_rung,c_rung
character(len=3),intent(out) :: x_DFA, c_DFA
character(len=12),intent(out) :: x_DFA, c_DFA
integer,intent(out) :: SGn
integer,intent(out) :: nEns
double precision,intent(out) :: wEns(maxEns)
@ -32,7 +32,7 @@ subroutine read_options(method,x_rung,x_DFA,c_rung,c_DFA,SGn,nEns,wEns,maxSCF,th
! Open file with method specification
open(unit=40,file='input/dft')
open(unit=1,file='input/dft')
! Default values
@ -108,6 +108,6 @@ subroutine read_options(method,x_rung,x_DFA,c_rung,c_DFA,SGn,nEns,wEns,maxSCF,th
! Close file with options
close(unit=40)
close(unit=1)
end subroutine read_options