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QP solutions

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This commit is contained in:
Pierre-Francois Loos 2020-02-12 12:25:24 +01:00
parent af17fb153f
commit b09cff2ff7
31 changed files with 1103 additions and 212 deletions
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98
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examples/basis.LiF.cc-pvqz Normal file
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72
examples/basis.LiH.cc-pvqz Normal file
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2
examples/molecule.BF
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@ -2,4 +2,4 @@
2 7 7 0 0 2 7 7 0 0
# Znuc x y z # Znuc x y z
B 0. 0. 0. B 0. 0. 0.
F 0. 0. 2.41 F 0. 0. 2.39

2
examples/molecule.CO
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@ -2,4 +2,4 @@
2 7 7 0 0 2 7 7 0 0
# Znuc x y z # Znuc x y z
C 0. 0. 0. C 0. 0. 0.
O 0. 0. 2.154 O 0. 0. 2.106

2
examples/molecule.F2
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@ -2,4 +2,4 @@
2 9 9 0 0 2 9 9 0 0
# Znuc x y z # Znuc x y z
F 0. 0. 0. F 0. 0. 0.
F 0. 0. 2.67 F 0. 0. 2.64

2
examples/molecule.HCl
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@ -2,4 +2,4 @@
2 9 9 0 0 2 9 9 0 0
# Znuc x y z # Znuc x y z
H 0. 0. 0. H 0. 0. 0.
Cl 0. 0. 2.41 Cl 0. 0. 2.37

2
examples/molecule.LiF
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@ -2,4 +2,4 @@
2 6 6 0 0 2 6 6 0 0
# Znuc x y z # Znuc x y z
Li 0. 0. 0. Li 0. 0. 0.
F 0. 0. 3.003 F 0. 0. 2.965

2
examples/molecule.LiH
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@ -2,4 +2,4 @@
2 2 2 0 0 2 2 2 0 0
# Znuc x y z # Znuc x y z
Li 0. 0. 0. Li 0. 0. 0.
H 0. 0. 3 H 0. 0. 2.994

2
examples/molecule.N2
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@ -2,4 +2,4 @@
2 7 7 0 0 2 7 7 0 0
# Znuc x y z # Znuc x y z
N 0. 0. 0. N 0. 0. 0.
N 0. 0. 2.07 N 0. 0. 2.072

98
input/basis
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S 3 S 3
1 33.8700000 0.0060680 1 13.0100000 0.0196850
2 5.0950000 0.0453080 2 1.9620000 0.1379770
3 1.1590000 0.2028220 3 0.4446000 0.4781480
S 1 S 1
1 0.3258000 1.0000000 1 0.1220000 1.0000000
P 1
1 0.7270000 1.0000000
2 3
S 3
1 13.0100000 0.0196850
2 1.9620000 0.1379770
3 0.4446000 0.4781480
S 1 S 1
1 0.1027000 1.0000000 1 0.1220000 1.0000000
P 1 P 1
1 1.4070000 1.0000000 1 0.7270000 1.0000000
P 1
1 0.3880000 1.0000000
D 1
1 1.0570000 1.0000000
2 12
S 13
1 456100.0000000 0.492970E-04
2 68330.0000000 0.383029E-03
3 15550.0000000 0.200854E-02
4 4405.0000000 0.838558E-02
5 1439.0000000 0.294703E-01
6 520.4000000 0.878325E-01
7 203.1000000 0.211473E+00
8 83.9600000 0.365364E+00
9 36.2000000 0.340884E+00
10 15.8300000 0.102133E+00
11 6.3340000 0.311675E-02
12 2.6940000 0.105751E-02
13 0.4313000 0.156136E-03
S 13
1 456100.0000000 -0.138304E-04
2 68330.0000000 -0.107279E-03
3 15550.0000000 -0.565083E-03
4 4405.0000000 -0.236135E-02
5 1439.0000000 -0.845886E-02
6 520.4000000 -0.259638E-01
7 203.1000000 -0.686362E-01
8 83.9600000 -0.141874E+00
9 36.2000000 -0.199319E+00
10 15.8300000 -0.195662E-01
11 6.3340000 0.499741E+00
12 2.6940000 0.563736E+00
13 0.4313000 -0.835091E-02
S 13
1 456100.0000000 0.418546E-05
2 68330.0000000 0.324395E-04
3 15550.0000000 0.171105E-03
4 4405.0000000 0.714176E-03
5 1439.0000000 0.256705E-02
6 520.4000000 0.788552E-02
7 203.1000000 0.210867E-01
8 83.9600000 0.442264E-01
9 36.2000000 0.651670E-01
10 15.8300000 0.603012E-02
11 6.3340000 -0.206495E+00
12 2.6940000 -0.405871E+00
13 0.4313000 0.725661E+00
S 1
1 0.9768000 1.0000000
S 1
1 0.1625000 1.0000000
P 7
1 663.3000000 0.240448E-02
2 156.8000000 0.192148E-01
3 49.9800000 0.885097E-01
4 18.4200000 0.256020E+00
5 7.2400000 0.436927E+00
6 2.9220000 0.350334E+00
7 0.3818000 -0.458423E-02
P 7
1 663.3000000 -0.652145E-03
2 156.8000000 -0.519445E-02
3 49.9800000 -0.246938E-01
4 18.4200000 -0.728167E-01
5 7.2400000 -0.134030E+00
6 2.9220000 -0.947742E-01
7 0.3818000 0.564667E+00
P 1
1 1.0220000 1.0000000
P 1
1 0.1301000 1.0000000
D 1
1 1.0460000 1.0000000
D 1
1 0.3440000 1.0000000
F 1
1 0.7060000 1.0000000

4
input/methods
View File

@ -1,11 +1,11 @@
# RHF UHF MOM # RHF UHF MOM
T F F T F F
# MP2 MP3 MP2-F12 # MP2 MP3 MP2-F12
T F F F F F
# CCD CCSD CCSD(T) ringCCD ladderCCD # CCD CCSD CCSD(T) ringCCD ladderCCD
F F F F F F F F F F
# CIS RPA RPAx ppRPA ADC # CIS RPA RPAx ppRPA ADC
T T T F F F F F F F
# GF2 GF3 # GF2 GF3
F F F F
# G0W0 evGW qsGW # G0W0 evGW qsGW

4
input/molecule
View File

@ -1,5 +1,5 @@
# nAt nEla nElb nCore nRyd # nAt nEla nElb nCore nRyd
2 9 9 0 0 2 1 1 0 0
# Znuc x y z # Znuc x y z
H 0. 0. 0. H 0. 0. 0.
Cl 0. 0. 2.41 H 0. 0. 1.4

2
input/molecule.xyz
View File

@ -1,4 +1,4 @@
2 2
H 0.0000000000 0.0000000000 0.0000000000 H 0.0000000000 0.0000000000 0.0000000000
Cl 0.0000000000 0.0000000000 1.2753171701 H 0.0000000000 0.0000000000 0.7408481486

4
input/options
View File

@ -5,11 +5,11 @@
# CC: maxSCF thresh DIIS n_diis # CC: maxSCF thresh DIIS n_diis
64 0.0000001 F 1 64 0.0000001 F 1
# CIS/TDHF/BSE: singlet triplet # CIS/TDHF/BSE: singlet triplet
T T T F
# GF: maxSCF thresh DIIS n_diis renormalization # GF: maxSCF thresh DIIS n_diis renormalization
64 0.00001 T 5 3 64 0.00001 T 5 3
# GW: maxSCF thresh DIIS n_diis COHSEX SOSEX BSE TDA G0W GW0 lin eta # GW: maxSCF thresh DIIS n_diis COHSEX SOSEX BSE TDA G0W GW0 lin eta
256 0.00001 T 5 F F T F F F F 0.000 256 0.00001 T 5 F F F F F F F 0.000
# ACFDT: AC Kx XBS # ACFDT: AC Kx XBS
T F T T F T
# MCMP2: nMC nEq nWalk dt nPrint iSeed doDrift # MCMP2: nMC nEq nWalk dt nPrint iSeed doDrift

98
input/weight
View File

@ -1,88 +1,18 @@
1 6 1 3
S 3 S 3
1 33.8700000 0.0060680 1 13.0100000 0.0196850
2 5.0950000 0.0453080 2 1.9620000 0.1379770
3 1.1590000 0.2028220 3 0.4446000 0.4781480
S 1 S 1
1 0.3258000 1.0000000 1 0.1220000 1.0000000
P 1
1 0.7270000 1.0000000
2 3
S 3
1 13.0100000 0.0196850
2 1.9620000 0.1379770
3 0.4446000 0.4781480
S 1 S 1
1 0.1027000 1.0000000 1 0.1220000 1.0000000
P 1 P 1
1 1.4070000 1.0000000 1 0.7270000 1.0000000
P 1
1 0.3880000 1.0000000
D 1
1 1.0570000 1.0000000
2 12
S 13
1 456100.0000000 0.492970E-04
2 68330.0000000 0.383029E-03
3 15550.0000000 0.200854E-02
4 4405.0000000 0.838558E-02
5 1439.0000000 0.294703E-01
6 520.4000000 0.878325E-01
7 203.1000000 0.211473E+00
8 83.9600000 0.365364E+00
9 36.2000000 0.340884E+00
10 15.8300000 0.102133E+00
11 6.3340000 0.311675E-02
12 2.6940000 0.105751E-02
13 0.4313000 0.156136E-03
S 13
1 456100.0000000 -0.138304E-04
2 68330.0000000 -0.107279E-03
3 15550.0000000 -0.565083E-03
4 4405.0000000 -0.236135E-02
5 1439.0000000 -0.845886E-02
6 520.4000000 -0.259638E-01
7 203.1000000 -0.686362E-01
8 83.9600000 -0.141874E+00
9 36.2000000 -0.199319E+00
10 15.8300000 -0.195662E-01
11 6.3340000 0.499741E+00
12 2.6940000 0.563736E+00
13 0.4313000 -0.835091E-02
S 13
1 456100.0000000 0.418546E-05
2 68330.0000000 0.324395E-04
3 15550.0000000 0.171105E-03
4 4405.0000000 0.714176E-03
5 1439.0000000 0.256705E-02
6 520.4000000 0.788552E-02
7 203.1000000 0.210867E-01
8 83.9600000 0.442264E-01
9 36.2000000 0.651670E-01
10 15.8300000 0.603012E-02
11 6.3340000 -0.206495E+00
12 2.6940000 -0.405871E+00
13 0.4313000 0.725661E+00
S 1
1 0.9768000 1.0000000
S 1
1 0.1625000 1.0000000
P 7
1 663.3000000 0.240448E-02
2 156.8000000 0.192148E-01
3 49.9800000 0.885097E-01
4 18.4200000 0.256020E+00
5 7.2400000 0.436927E+00
6 2.9220000 0.350334E+00
7 0.3818000 -0.458423E-02
P 7
1 663.3000000 -0.652145E-03
2 156.8000000 -0.519445E-02
3 49.9800000 -0.246938E-01
4 18.4200000 -0.728167E-01
5 7.2400000 -0.134030E+00
6 2.9220000 -0.947742E-01
7 0.3818000 0.564667E+00
P 1
1 1.0220000 1.0000000
P 1
1 0.1301000 1.0000000
D 1
1 1.0460000 1.0000000
D 1
1 0.3440000 1.0000000
F 1
1 0.7060000 1.0000000

6
scan_LiF.sh
View File

@ -1,9 +1,9 @@
#! /bin/bash #! /bin/bash
MOL="LiF" MOL="LiF"
BASIS="cc-pvtz" BASIS="cc-pvqz"
R_START=3.980 R_START=2.965
R_END=2.990 R_END=2.965
DR=0.001 DR=0.001
for R in $(seq $R_START $DR $R_END) for R in $(seq $R_START $DR $R_END)

4
scan_LiH.sh
View File

@ -2,8 +2,8 @@
MOL="LiH" MOL="LiH"
BASIS="cc-pvqz" BASIS="cc-pvqz"
R_START=2.990 R_START=3.013
R_END=3.000 R_END=3.013
DR=0.001 DR=0.001
for R in $(seq $R_START $DR $R_END) for R in $(seq $R_START $DR $R_END)

4
scan_N2.sh
View File

@ -1,8 +1,8 @@
#! /bin/bash #! /bin/bash
MOL="N2" MOL="N2"
BASIS="cc-pvtz" BASIS="cc-pvqz"
R_START=2.066 R_START=2.071
R_END=2.080 R_END=2.080
DR=0.001 DR=0.001

6
src/QuAcK/G0W0.f90
View File

@ -95,10 +95,14 @@ subroutine G0W0(doACFDT,exchange_kernel,doXBS,COHSEX,SOSEX,BSE,TDA,singlet_manif
call renormalization_factor(COHSEX,SOSEX,eta,nBas,nC,nO,nV,nR,nS,eHF, & call renormalization_factor(COHSEX,SOSEX,eta,nBas,nC,nO,nV,nR,nS,eHF, &
Omega(:,ispin),rho(:,:,:,ispin),rhox(:,:,:,ispin),Z(:)) Omega(:,ispin),rho(:,:,:,ispin),rhox(:,:,:,ispin),Z(:))
! Find all the roots of the QP equation if necessary
call QP_roots(nBas,nC,nO,nV,nR,nS,eta,eHF,Omega,rho)
! Solve the quasi-particle equation ! Solve the quasi-particle equation
eGW(:) = eHF(:) + Z(:)*SigC(:) eGW(:) = eHF(:) + Z(:)*SigC(:)
! Dump results ! Dump results
! call print_excitation('RPA ',ispin,nS,Omega(:,ispin)) ! call print_excitation('RPA ',ispin,nS,Omega(:,ispin))

156
src/QuAcK/QP_roots.f90 Normal file
View File

@ -0,0 +1,156 @@
subroutine QP_roots(nBas,nC,nO,nV,nR,nS,eta,eHF,Omega,rho)
! Compute all the roots of the QP equation for each orbital
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)
! Local variables
integer :: i,j,a,b,x,jb,g
integer :: nRoot
integer,parameter :: nGrid = 10000
double precision,parameter :: wmin = -10d0
double precision,parameter :: wmax = +10d0
double precision :: dw
double precision :: eps
double precision :: left_sign,right_sign
double precision :: left_QP,right_QP
double precision,allocatable :: w(:)
double precision,allocatable :: SigC(:)
double precision,allocatable :: dSigC(:)
integer :: nIt
integer,parameter :: maxIt = 64
double precision,parameter :: thresh = 1d-6
double precision,external :: SigmaC,dSigmaC
double precision :: f,df
double precision :: s,ds
double precision :: om
! Construct grid
allocate(w(nGrid),SigC(nGrid),dSigC(nGrid))
! Minimum and maximum frequency values
dw = (wmax - wmin)/dble(nGrid)
do g=1,nGrid
w(g) = wmin + dble(g)*dw
enddo
! Main loop over the orbitals
do x=nC+1,nBas-nR
SigC(:) = 0d0
dSigC(:) = 0d0
! Loop over grid points
do g=1,nGrid
! Occupied part of the self-energy and spectral weight
do i=nC+1,nO
jb = 0
do j=nC+1,nO
do b=nO+1,nBas-nR
jb = jb + 1
eps = w(g) - eHF(i) + Omega(jb)
SigC(g) = SigC(g) + 2d0*rho(x,i,jb)**2*eps/(eps**2 + eta**2)
dSigC(g) = dSigC(g) - 2d0*rho(x,i,jb)**2*(eps**2 - eta**2)/(eps**2 + eta**2)**2
enddo
enddo
enddo
! Virtual part of the self-energy and spectral weight
do a=nO+1,nBas-nR
jb = 0
do j=nC+1,nO
do b=nO+1,nBas-nR
jb = jb + 1
eps = w(g) - eHF(a) - Omega(jb)
SigC(g) = SigC(g) + 2d0*rho(x,a,jb)**2*eps/(eps**2 + eta**2)
dSigC(g) = dSigC(g) - 2d0*rho(x,a,jb)**2*(eps**2 - eta**2)/(eps**2 + eta**2)**2
enddo
enddo
enddo
enddo
! Find the zeros of the QP equation
nRoot = 0
write(*,*) '-----------------'
write(*,'(A10,I3)') 'Orbital ',x
write(*,*) '-----------------'
write(*,*)
left_QP = w(1) - eHF(x) - SigC(1)
left_sign = sign(1d0,left_QP)
do g=2,nGrid
right_QP = w(g) - eHF(x) - SigC(g)
right_sign = sign(1d0,right_QP)
if(left_sign /= right_sign .and. left_sign == sign(1d0,-1d0)) then
nRoot = nRoot + 1
write(*,'(A20,I6,F10.6,F10.6,I6,F10.6,F10.6,F10.6)') &
'root right here!',g-1,w(g-1),left_QP,g,w(g),right_QP,1d0/(1d0-dSigC(g))
! Run Newton's algorithm to find the root
om = w(g-1)
nIt = 0
f = 1d0
do while (abs(f) > thresh .and. nIt < maxIt)
nIt = nIt + 1
s = SigmaC(x,om,eta,nBas,nC,nO,nV,nR,nS,eHF,Omega,rho)
ds = dSigmaC(x,om,eta,nBas,nC,nO,nV,nR,nS,eHF,Omega,rho)
f = om - eHF(x) - s
df = 1d0 - ds
write(*,'(A3,I3,A1,1X,4F15.9)') 'It.',nIt,':',om,f,s,1d0/(1d0-ds)
om = om - f/df
end do
end if
left_sign = right_sign
left_QP = right_QP
end do
write(*,*)
write(*,'(A32,I3,A1,I3)') 'Number of roots for orbital ',x,':',nRoot
write(*,*)
end do
end subroutine QP_roots

44
src/QuAcK/RPA.f90
View File

@ -96,33 +96,33 @@ subroutine RPA(doACFDT,exchange_kernel,singlet_manifold,triplet_manifold,eta, &
! Compute the correlation energy via the adiabatic connection ! Compute the correlation energy via the adiabatic connection
! Switch off ACFDT for RPA as the trace formula is equivalent ! Switch off ACFDT for RPA as the trace formula is equivalent
if(doACFDT) then ! if(doACFDT) then
write(*,*) '------------------------------------------------------' ! write(*,*) '------------------------------------------------------'
write(*,*) 'Adiabatic connection version of RPA correlation energy' ! write(*,*) 'Adiabatic connection version of RPA correlation energy'
write(*,*) '------------------------------------------------------' ! write(*,*) '------------------------------------------------------'
write(*,*) ! write(*,*)
call ACFDT(exchange_kernel,.false.,.true.,.false.,.false.,singlet_manifold,triplet_manifold,eta, & ! call ACFDT(exchange_kernel,.false.,.true.,.false.,.false.,singlet_manifold,triplet_manifold,eta, &
nBas,nC,nO,nV,nR,nS,ERI,e,Omega,XpY,XmY,rho,EcAC) ! nBas,nC,nO,nV,nR,nS,ERI,e,Omega,XpY,XmY,rho,EcAC)
if(exchange_kernel) then ! if(exchange_kernel) then
!
EcAC(1) = 0.5d0*EcAC(1) ! EcAC(1) = 0.5d0*EcAC(1)
EcAC(2) = 1.5d0*EcAC(1) ! EcAC(2) = 1.5d0*EcAC(1)
!
end if ! end if
write(*,*) ! write(*,*)
write(*,*)'-------------------------------------------------------------------------------' ! write(*,*)'-------------------------------------------------------------------------------'
write(*,'(2X,A50,F20.10)') 'AC@RPA correlation energy (singlet) =',EcAC(1) ! write(*,'(2X,A50,F20.10)') 'AC@RPA correlation energy (singlet) =',EcAC(1)
write(*,'(2X,A50,F20.10)') 'AC@RPA correlation energy (triplet) =',EcAC(2) ! write(*,'(2X,A50,F20.10)') 'AC@RPA correlation energy (triplet) =',EcAC(2)
write(*,'(2X,A50,F20.10)') 'AC@RPA correlation energy =',EcAC(1) + EcAC(2) ! write(*,'(2X,A50,F20.10)') 'AC@RPA correlation energy =',EcAC(1) + EcAC(2)
write(*,'(2X,A50,F20.10)') 'AC@RPA total energy =',ENuc + ERHF + EcAC(1) + EcAC(2) ! write(*,'(2X,A50,F20.10)') 'AC@RPA total energy =',ENuc + ERHF + EcAC(1) + EcAC(2)
write(*,*)'-------------------------------------------------------------------------------' ! write(*,*)'-------------------------------------------------------------------------------'
write(*,*) ! write(*,*)
end if ! end if
end subroutine RPA end subroutine RPA

58
src/QuAcK/SigmaC.f90 Normal file
View File

@ -0,0 +1,58 @@
double precision function SigmaC(x,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) :: x
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)
! Local variables
integer :: i,j,a,b,p,jb
double precision :: eps
! Initialize
SigmaC = 0d0
! 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
eps = w - e(i) + Omega(jb)
SigmaC = SigmaC + 2d0*rho(x,i,jb)**2*eps/(eps**2 + eta**2)
enddo
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
eps = w - e(a) - Omega(jb)
SigmaC = SigmaC + 2d0*rho(x,a,jb)**2*eps/(eps**2 + eta**2)
enddo
enddo
enddo
end function SigmaC

58
src/QuAcK/dSigmaC.f90 Normal file
View File

@ -0,0 +1,58 @@
double precision function dSigmaC(x,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) :: x
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)
! Local variables
integer :: i,j,a,b,p,jb
double precision :: eps
! Initialize
dSigmaC = 0d0
! 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
eps = w - e(i) + Omega(jb)
dSigmaC = dSigmaC - 2d0*rho(x,i,jb)**2*(eps**2 - eta**2)/(eps**2 + eta**2)**2
enddo
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
eps = w - e(a) - Omega(jb)
dSigmaC = dSigmaC - 2d0*rho(x,a,jb)**2*(eps**2 - eta**2)/(eps**2 + eta**2)**2
enddo
enddo
enddo
end function dSigmaC