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graph sol for UGW

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This commit is contained in:
Pierre-Francois Loos 2020-09-23 14:23:40 +02:00
parent ce10bbaf56
commit 2b1b2096c4
12 changed files with 218 additions and 48 deletions
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4
input/methods
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@ -9,11 +9,11 @@
# CIS CID CISD
F F F
# RPA RPAx ppRPA
T F F
F F F
# G0F2 evGF2 G0F3 evGF3
F F F F
# G0W0 evGW qsGW
F F F
T F F
# G0T0 evGT qsGT
F F F
# MCMP2

4
input/options
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@ -5,11 +5,11 @@
# CC: maxSCF thresh DIIS n_diis
64 0.0000001 T 5
# spin: singlet triplet spin_conserved spin_flip TDA
T T T T F
T T T F F
# GF: maxSCF thresh DIIS n_diis lin eta renorm
256 0.00001 T 5 T 0.0 3
# GW/GT: maxSCF thresh DIIS n_diis lin eta COHSEX SOSEX TDA_W G0W GW0
256 0.00001 T 5 T 0.001 F F F F F
256 0.00001 T 5 F 0.0 F F F F F
# ACFDT: AC Kx XBS
F F T
# BSE: BSE dBSE dTDA evDyn

22
src/QuAcK/SigmaC.f90
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@ -1,4 +1,4 @@
double precision function SigmaC(x,w,eta,nBas,nC,nO,nV,nR,nS,e,Omega,rho)
double precision function SigmaC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Omega,rho)
! Compute diagonal of the correlation part of the self-energy
@ -7,7 +7,7 @@ double precision function SigmaC(x,w,eta,nBas,nC,nO,nV,nR,nS,e,Omega,rho)
! Input variables
integer,intent(in) :: x
integer,intent(in) :: p
double precision,intent(in) :: w
double precision,intent(in) :: eta
integer,intent(in) :: nBas
@ -22,7 +22,7 @@ double precision function SigmaC(x,w,eta,nBas,nC,nO,nV,nR,nS,e,Omega,rho)
! Local variables
integer :: i,j,a,b,p,jb
integer :: i,a,jb
double precision :: eps
! Initialize
@ -32,26 +32,18 @@ double precision function SigmaC(x,w,eta,nBas,nC,nO,nV,nR,nS,e,Omega,rho)
! Occupied part of the correlation self-energy
do i=nC+1,nO
jb = 0
do j=nC+1,nO
do b=nO+1,nBas-nR
jb = jb + 1
do jb=1,nS
eps = w - e(i) + Omega(jb)
SigmaC = SigmaC + 2d0*rho(x,i,jb)**2*eps/(eps**2 + eta**2)
enddo
SigmaC = SigmaC + 2d0*rho(p,i,jb)**2*eps/(eps**2 + eta**2)
enddo
enddo
! Virtual part of the correlation self-energy
do a=nO+1,nBas-nR
jb = 0
do j=nC+1,nO
do b=nO+1,nBas-nR
jb = jb + 1
do jb=1,nS
eps = w - e(a) - Omega(jb)
SigmaC = SigmaC + 2d0*rho(x,a,jb)**2*eps/(eps**2 + eta**2)
enddo
SigmaC = SigmaC + 2d0*rho(p,a,jb)**2*eps/(eps**2 + eta**2)
enddo
enddo

13
src/QuAcK/UG0W0.f90
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@ -45,6 +45,7 @@ subroutine UG0W0(doACFDT,exchange_kernel,doXBS,COHSEX,BSE,TDA_W,TDA,dBSE,dTDA,ev
! Local variables
logical :: print_W = .true.
integer :: is
integer :: ispin
double precision :: EcRPA(nspin)
double precision :: EcBSE(nspin)
@ -126,13 +127,13 @@ subroutine UG0W0(doACFDT,exchange_kernel,doXBS,COHSEX,BSE,TDA_W,TDA,dBSE,dTDA,ev
! Compute self-energy !
!---------------------!
call unrestricted_self_energy_correlation_diag(eta,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sc,eHF,Omega_sc,rho_sc,SigC)
call unrestricted_self_energy_correlation_diag(eta,nBas,nC,nO,nV,nR,nS_sc,eHF,Omega_sc,rho_sc,SigC)
!--------------------------------!
! Compute renormalization factor !
!--------------------------------!
call unrestricted_renormalization_factor(eta,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sc,eHF,Omega_sc,rho_sc,Z)
call unrestricted_renormalization_factor(eta,nBas,nC,nO,nV,nR,nS_sc,eHF,Omega_sc,rho_sc,Z)
!-----------------------------------!
! Solve the quasi-particle equation !
@ -151,10 +152,10 @@ subroutine UG0W0(doACFDT,exchange_kernel,doXBS,COHSEX,BSE,TDA_W,TDA,dBSE,dTDA,ev
! Find graphical solution of the QP equation
! do is=1,nspin
! call QP_graph(nBas,nC(:,is),nO(:,is),nV(:,is),nR(:,is),nS(:,is),eta,eHF(:,is),Omega(:,is), &
! rho(:,:,:,ispin),eGWlin(:,is),eGW(:,is))
! end do
do is=1,nspin
call unrestricted_QP_graph(nBas,nC(is),nO(is),nV(is),nR(is),nS_sc,eta,eHF(:,is),Omega_sc, &
rho_sc,eGWlin(:,is),eGW(:,is))
end do
end if

48
src/QuAcK/USigmaC.f90 Normal file
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@ -0,0 +1,48 @@
double precision function USigmaC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Omega,rho)
! Compute diagonal of the correlation part of the self-energy
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: p
double precision,intent(in) :: w
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) :: nS
double precision,intent(in) :: e(nBas)
double precision,intent(in) :: Omega(nS)
double precision,intent(in) :: rho(nBas,nBas,nS,nspin)
! Local variables
integer :: i,a,jb
double precision :: eps
! Initialize
USigmaC = 0d0
! Occupied part of the correlation self-energy
do i=nC+1,nO
do jb=1,nS
eps = w - e(i) + Omega(jb)
USigmaC = uSigmaC + rho(p,i,jb,1)**2*eps/(eps**2 + eta**2)
end do
end do
do a=nO+1,nBas-nR
do jb=1,nS
eps = w - e(a) - Omega(jb)
USigmaC = USigmaC + rho(p,a,jb,1)**2*eps/(eps**2 + eta**2)
end do
end do
end function USigmaC

50
src/QuAcK/dUSigmaC.f90 Normal file
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@ -0,0 +1,50 @@
double precision function dUSigmaC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Omega,rho)
! Compute the derivative of the correlation part of the self-energy
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: p
double precision,intent(in) :: w
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) :: nS
double precision,intent(in) :: e(nBas)
double precision,intent(in) :: Omega(nS)
double precision,intent(in) :: rho(nBas,nBas,nS,nspin)
! Local variables
integer :: i,a,jb
double precision :: eps
! Initialize
dUSigmaC = 0d0
! Occupied part of the correlation self-energy
do i=nC+1,nO
do jb=1,nS
eps = w - e(i) + Omega(jb)
dUSigmaC = dUSigmaC + rho(p,i,jb,1)**2*(eps/(eps**2 + eta**2))**2
end do
end do
! Virtual part of the correlation self-energy
do a=nO+1,nBas-nR
do jb=1,nS
eps = w - e(a) - Omega(jb)
dUSigmaC = dUSigmaC + rho(p,a,jb,1)**2*(eps/(eps**2 + eta**2))**2
end do
end do
end function dUSigmaC

2
src/QuAcK/unrestricted_Bethe_Salpeter.f90
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@ -76,6 +76,8 @@ subroutine unrestricted_Bethe_Salpeter(TDA_W,TDA,dBSE,dTDA,evDyn,spin_conserved,
eW,ERI_aaaa,ERI_aabb,ERI_bbbb,ERI_abab,rho_RPA_sc,EcRPA(ispin), &
OmRPA_sc,XpY_RPA_sc,XmY_RPA_sc)
! call print_excitation('RPA@UG0W0',5,nS_sc,OmRPA_sc)
call unrestricted_excitation_density(nBas,nC,nO,nR,nS_aa,nS_bb,nS_sc,ERI_aaaa,ERI_aabb,ERI_bbbb, &
XpY_RPA_sc,rho_RPA_sc)

19
src/QuAcK/unrestricted_Bethe_Salpeter_A_matrix.f90
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@ -1,6 +1,5 @@
subroutine unrestricted_Bethe_Salpeter_A_matrix(eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt,lambda, &
ERI_aaaa,ERI_aabb,ERI_bbbb,ERI_abab, &
Omega,rho,A_lr)
ERI_aaaa,ERI_aabb,ERI_bbbb,ERI_abab,Omega,rho,A_lr)
! Compute the extra term for Bethe-Salpeter equation for linear response in the unrestricted formalism
@ -40,7 +39,7 @@ subroutine unrestricted_Bethe_Salpeter_A_matrix(eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt
! Build part A of the BSE matrix !
!--------------------------------!
! alpha-alpha block
! aaaa block
ia = 0
do i=nC(1)+1,nO(1)
@ -55,7 +54,7 @@ subroutine unrestricted_Bethe_Salpeter_A_matrix(eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt
do kc=1,nSt
eps = Omega(kc)**2 + eta**2
chi = chi + rho(i,j,kc,1)*rho(a,b,kc,1)*Omega(kc)/eps &
+ rho(i,j,kc,2)*rho(a,b,kc,2)*Omega(kc)/eps
+ rho(i,j,kc,1)*rho(a,b,kc,1)*Omega(kc)/eps
enddo
A_lr(ia,jb) = A_lr(ia,jb) - lambda*ERI_aaaa(i,b,j,a) + 2d0*lambda*chi
@ -65,7 +64,7 @@ subroutine unrestricted_Bethe_Salpeter_A_matrix(eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt
enddo
enddo
! alpha-beta block
! aabb block
ia = 0
do i=nC(1)+1,nO(1)
@ -90,7 +89,7 @@ subroutine unrestricted_Bethe_Salpeter_A_matrix(eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt
enddo
enddo
! beta-alpha block
! bbaa block
ia = 0
do i=nC(2)+1,nO(2)
@ -104,8 +103,8 @@ subroutine unrestricted_Bethe_Salpeter_A_matrix(eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt
chi = 0d0
do kc=1,nSt
eps = Omega(kc)**2 + eta**2
chi = chi + rho(i,j,kc,1)*rho(a,b,kc,1)*Omega(kc)/eps &
+ rho(i,j,kc,2)*rho(a,b,kc,2)*Omega(kc)/eps
chi = chi + rho(i,j,kc,2)*rho(a,b,kc,2)*Omega(kc)/eps &
+ rho(i,j,kc,1)*rho(a,b,kc,1)*Omega(kc)/eps
enddo
A_lr(nSa+ia,jb) = A_lr(nSa+ia,jb) - lambda*ERI_aabb(b,i,a,j) + 2d0*lambda*chi
@ -115,7 +114,7 @@ subroutine unrestricted_Bethe_Salpeter_A_matrix(eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt
enddo
enddo
! beta-beta block
! bbbb block
ia = 0
do i=nC(2)+1,nO(2)
@ -129,7 +128,7 @@ subroutine unrestricted_Bethe_Salpeter_A_matrix(eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt
chi = 0d0
do kc=1,nSt
eps = Omega(kc)**2 + eta**2
chi = chi + rho(i,j,kc,1)*rho(a,b,kc,1)*Omega(kc)/eps &
chi = chi + rho(i,j,kc,2)*rho(a,b,kc,2)*Omega(kc)/eps &
+ rho(i,j,kc,2)*rho(a,b,kc,2)*Omega(kc)/eps
enddo

8
src/QuAcK/unrestricted_Bethe_Salpeter_B_matrix.f90
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@ -51,7 +51,7 @@ subroutine unrestricted_Bethe_Salpeter_B_matrix(eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt
do kc=1,nSt
eps = Omega(kc)**2 + eta**2
chi = chi + rho(i,b,kc,1)*rho(a,j,kc,1)*Omega(kc)/eps &
+ rho(i,b,kc,2)*rho(a,j,kc,2)*Omega(kc)/eps
+ rho(i,b,kc,1)*rho(a,j,kc,1)*Omega(kc)/eps
enddo
B_lr(ia,jb) = B_lr(ia,jb) - lambda*ERI_aaaa(i,j,b,a) + 2d0*lambda*chi
@ -100,8 +100,8 @@ subroutine unrestricted_Bethe_Salpeter_B_matrix(eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt
chi = 0d0
do kc=1,nSt
eps = Omega(kc)**2 + eta**2
chi = chi + rho(i,b,kc,1)*rho(a,j,kc,1)*Omega(kc)/eps &
+ rho(i,b,kc,2)*rho(a,j,kc,2)*Omega(kc)/eps
chi = chi + rho(i,b,kc,2)*rho(a,j,kc,2)*Omega(kc)/eps &
+ rho(i,b,kc,1)*rho(a,j,kc,1)*Omega(kc)/eps
enddo
B_lr(nSa+ia,jb) = B_lr(nSa+ia,jb) - lambda*ERI_aabb(j,i,a,b) + 2d0*lambda*chi
@ -125,7 +125,7 @@ subroutine unrestricted_Bethe_Salpeter_B_matrix(eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt
chi = 0d0
do kc=1,nSt
eps = Omega(kc)**2 + eta**2
chi = chi + rho(i,b,kc,1)*rho(a,j,kc,1)*Omega(kc)/eps &
chi = chi + rho(i,b,kc,2)*rho(a,j,kc,2)*Omega(kc)/eps &
+ rho(i,b,kc,2)*rho(a,j,kc,2)*Omega(kc)/eps
enddo

83
src/QuAcK/unrestricted_QP_graph.f90 Normal file
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@ -0,0 +1,83 @@
subroutine unrestricted_QP_graph(nBas,nC,nO,nV,nR,nS,eta,eHF,Omega,rho,eGWlin,eGW)
! Compute the graphical solution of the QP equation
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: nBas
integer,intent(in) :: nC
integer,intent(in) :: nO
integer,intent(in) :: nV
integer,intent(in) :: nR
integer,intent(in) :: nS
double precision,intent(in) :: eta
double precision,intent(in) :: eHF(nBas)
double precision,intent(in) :: Omega(nS)
double precision,intent(in) :: rho(nBas,nBas,nS,nspin)
double precision,intent(in) :: eGWlin(nBas)
! Local variables
integer :: p
integer :: nIt
integer,parameter :: maxIt = 10
double precision,parameter :: thresh = 1d-6
double precision,external :: USigmaC,dUSigmaC
double precision :: sig,dsig
double precision :: f,df
double precision :: w
! Output variables
double precision,intent(out) :: eGW(nBas)
! Run Newton's algorithm to find the root
do p=nC+1,nBas-nR
write(*,*) '-----------------'
write(*,'(A10,I3)') 'Orbital ',p
write(*,*) '-----------------'
w = eGWlin(p)
nIt = 0
f = 1d0
write(*,'(A3,I3,A1,1X,3F15.9)') 'It.',nIt,':',w*HaToeV,f
do while (abs(f) > thresh .and. nIt < maxIt)
nIt = nIt + 1
sig = USigmaC(p,w,eta,nBas,nC,nO,nV,nR,nS,eHF,Omega,rho)
dsig = dUSigmaC(p,w,eta,nBas,nC,nO,nV,nR,nS,eHF,Omega,rho)
f = w - eHF(p) - sig
df = 1d0 - dsig
w = w - f/df
write(*,'(A3,I3,A1,1X,3F15.9)') 'It.',nIt,':',w*HaToeV,f,sig
end do
if(nIt == maxIt) then
write(*,*) 'Newton root search has not converged!'
eGW(p) = eGWlin(p)
else
eGW(p) = w
write(*,'(A32,F16.10)') 'Quasiparticle energy (eV) ',eGW(p)*HaToeV
write(*,*)
end if
end do
end subroutine unrestricted_QP_graph

5
src/QuAcK/unrestricted_renormalization_factor.f90
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@ -1,4 +1,4 @@
subroutine unrestricted_renormalization_factor(eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt,e,Omega,rho,Z)
subroutine unrestricted_renormalization_factor(eta,nBas,nC,nO,nV,nR,nSt,e,Omega,rho,Z)
! Compute the renormalization factor in the unrestricted formalism
@ -13,8 +13,6 @@ subroutine unrestricted_renormalization_factor(eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt,
integer,intent(in) :: nO(nspin)
integer,intent(in) :: nV(nspin)
integer,intent(in) :: nR(nspin)
integer,intent(in) :: nSa
integer,intent(in) :: nSb
integer,intent(in) :: nSt
double precision,intent(in) :: e(nBas,nspin)
double precision,intent(in) :: Omega(nSt)
@ -89,5 +87,4 @@ subroutine unrestricted_renormalization_factor(eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt,
Z(:,:) = 1d0/(1d0 + Z(:,:))
end subroutine unrestricted_renormalization_factor

4
src/QuAcK/unrestricted_self_energy_correlation_diag.f90
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@ -1,4 +1,4 @@
subroutine unrestricted_self_energy_correlation_diag(eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt,e,Omega,rho,SigC)
subroutine unrestricted_self_energy_correlation_diag(eta,nBas,nC,nO,nV,nR,nSt,e,Omega,rho,SigC)
! Compute diagonal of the correlation part of the self-energy
@ -13,8 +13,6 @@ subroutine unrestricted_self_energy_correlation_diag(eta,nBas,nC,nO,nV,nR,nSa,nS
integer,intent(in) :: nO(nspin)
integer,intent(in) :: nV(nspin)
integer,intent(in) :: nR(nspin)
integer,intent(in) :: nSa
integer,intent(in) :: nSb
integer,intent(in) :: nSt
double precision,intent(in) :: e(nBas,nspin)
double precision,intent(in) :: Omega(nSt)