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OK with GGA exchange functionals

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This commit is contained in:
Pierre-Francois Loos 2021-02-12 16:47:40 +01:00
parent a97b1881b7
commit 44dfbef766
9 changed files with 193 additions and 30 deletions
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8
input/dft
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@ -4,13 +4,13 @@
# Hartree = 0
# LDA = 1: S51,CC-S51
# GGA = 2: B88,G96,PBE
# Hybrid = 4
# Hybrid = 4: B3LYP,PBE0
# Hartree-Fock = 666
2 PBE
2 B88
# correlation rung:
# Hartree = 0
# Hartree = 0: H
# LDA = 1: VWN5,eVWN5
# GGA = 2:
# GGA = 2: LYP,PBE
# Hybrid = 4:
# Hartree-Fock = 666
0 H

2
input/methods
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@ -1,5 +1,5 @@
# RHF UHF KS MOM
F F T F
T F T F
# MP2* MP3 MP2-F12
F F F
# CCD DCD CCSD CCSD(T)

2
input/options
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@ -5,7 +5,7 @@
# CC: maxSCF thresh DIIS n_diis
64 0.00001 T 5
# spin: TDA singlet triplet spin_conserved spin_flip
T T T T T
F T T T T
# 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

7
src/eDFT/UB88_gga_exchange_energy.f90
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@ -16,7 +16,7 @@ subroutine UB88_gga_exchange_energy(nGrid,weight,rho,drho,Ex)
! Local variables
integer :: iG
double precision :: alpha,beta
double precision :: alpha,b
double precision :: r,g,x
! Output variables
@ -26,7 +26,7 @@ subroutine UB88_gga_exchange_energy(nGrid,weight,rho,drho,Ex)
! Coefficients for B88 GGA exchange functional
alpha = -(3d0/2d0)*(3d0/(4d0*pi))**(1d0/3d0)
beta = 0.0042d0
b = 0.0042d0
! Compute GGA exchange energy
@ -40,8 +40,7 @@ subroutine UB88_gga_exchange_energy(nGrid,weight,rho,drho,Ex)
g = drho(1,iG)**2 + drho(2,iG)**2 + drho(3,iG)**2
x = sqrt(g)/r**(4d0/3d0)
Ex = Ex + weight(iG)*alpha*r**(4d0/3d0) &
- weight(iG)*beta*x**2*r**(4d0/3d0)/(1d0 + 6d0*beta*x*asinh(x))
Ex = Ex + weight(iG)*r**(4d0/3d0)*(alpha - b*x**2/(1d0 + 6d0*b*x*asinh(x)))
end if

27
src/eDFT/UB88_gga_exchange_potential.f90
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@ -18,8 +18,9 @@ subroutine UB88_gga_exchange_potential(nGrid,weight,nBas,AO,dAO,rho,drho,Fx)
! Local variables
integer :: mu,nu,iG
double precision :: alpha,beta
double precision :: r,g,vAO,gAO
double precision :: alpha,b
double precision :: vAO,gAO
double precision :: r,g,x,dxdr,dxdg,f
! Output variables
@ -28,7 +29,7 @@ subroutine UB88_gga_exchange_potential(nGrid,weight,nBas,AO,dAO,rho,drho,Fx)
! Coefficients for B88 GGA exchange functional
alpha = -(3d0/2d0)*(3d0/(4d0*pi))**(1d0/3d0)
beta = 0.0042d0
b = 0.0042d0
! Compute GGA exchange matrix in the AO basis
@ -42,19 +43,27 @@ subroutine UB88_gga_exchange_potential(nGrid,weight,nBas,AO,dAO,rho,drho,Fx)
if(r > threshold) then
g = drho(1,iG)**2 + drho(2,iG)**2 + drho(3,iG)**2
vAO = weight(iG)*AO(mu,iG)*AO(nu,iG)
Fx(mu,nu) = Fx(mu,nu) &
+ vAO*(4d0/3d0*r**(1d0/3d0)*(alpha - beta*g**(3d0/4d0)/r**2) &
+ 2d0*beta*g**(3d0/4d0)/r**(5d0/3d0))
g = drho(1,iG)**2 + drho(2,iG)**2 + drho(3,iG)**2
x = sqrt(g)/r**(4d0/3d0)
dxdr = - 4d0*sqrt(g)/(3d0*r**(7d0/3d0))/x
dxdg = + 1d0/(2d0*sqrt(g)*r**(4d0/3d0))/x
f = b*x**2/(1d0 + 6d0*b*x*asinh(x))
Fx(mu,nu) = Fx(mu,nu) + vAO*( &
4d0/3d0*r**(1d0/3d0)*(alpha - f) &
- 2d0*r**(4d0/3d0)*dxdr*f &
+ r**(4d0/3d0)*dxdr*(6d0*b*x*asinh(x) + 6d0*b*x**2/sqrt(1d0+x**2))*f/(1d0 + 6d0*b*x*asinh(x)) )
gAO = drho(1,iG)*(dAO(1,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(1,nu,iG)) &
+ drho(2,iG)*(dAO(2,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(2,nu,iG)) &
+ drho(3,iG)*(dAO(3,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(3,nu,iG))
gAO = weight(iG)*gAO
Fx(mu,nu) = Fx(mu,nu) - 2d0*gAO*3d0/4d0*beta*g**(-1d0/4d0)/r**(2d0/3d0)
Fx(mu,nu) = Fx(mu,nu) + 2d0*gAO*r**(4d0/3d0)*dxdg*( &
- 2d0*f + (6d0*b*x*asinh(x) + 6d0*b*x**2/sqrt(1d0+x**2))*f/(1d0 + 6d0*b*x*asinh(x)) )
end if

73
src/eDFT/ULYP_gga_correlation_energy.f90 Normal file
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@ -0,0 +1,73 @@
subroutine ULYP_gga_correlation_energy(nGrid,weight,rho,drho,Ec)
! Compute unrestricted LYP GGA correlation energy
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: nGrid
double precision,intent(in) :: weight(nGrid)
double precision,intent(in) :: rho(nGrid,nspin)
double precision,intent(in) :: drho(ncart,nGrid,nspin)
! Local variables
integer :: iG
double precision :: ra,rb,r
double precision :: ga,gab,gb,g
double precision :: a,b,c,d
double precision :: Cf,omega,delta
! Output variables
double precision :: Ec(nsp)
! Parameters of the functional
a = 0.04918d0
b = 0.132d0
c = 0.2533d0
d = 0.349d0
Cf = 3d0/10d0*(3d0*pi**2)**(2d0/3d0)
! Initialization
Ec(:) = 0d0
do iG=1,nGrid
ra = max(0d0,rho(iG,1))
rb = max(0d0,rho(iG,2))
r = ra + rb
if(r > threshold) then
ga = drho(1,iG,1)**2 + drho(2,iG,1)**2 + drho(3,iG,1)**2
gb = drho(1,iG,2)**2 + drho(2,iG,2)**2 + drho(3,iG,2)**2
gab = drho(1,iG,1)*drho(1,iG,2) + drho(2,iG,1)*drho(2,iG,2) + drho(3,iG,1)*drho(3,iG,2)
g = ga + gab + gb
omega = exp(-c*r**(-1d0/3d0))/(1d0 + d*r**(-1d0/3d0))*r**(-11d0/3d0)
delta = c*r**(-1d0/3d0) + d*r**(-1d0/3d0)/(1d0 + d*r**(-1d0/3d0))
Ec(2) = Ec(2) - weight(iG)*4d0*a/(1d0 + d*r**(-1d0/3d0))*ra*rb/r &
- weight(iG)*a*b*omega*ra*rb*( &
2d0**(11d0/3d0)*Cf*(ra**(8d0/3d0) + rb**(8d0/3d0)) &
+ (47d0/18d0 - 7d0*delta/18d0)*g &
- (5d0/2d0 - delta/18d0)*(ga + gb) &
- (delta - 11d0)/9d0*(ra/r*ga + rb/r*gb) ) &
- weight(iG)*a*b*omega*( &
- 2d0*r**2/3d0*g &
+ (2d0*r**2/3d0 - ra**2)*gb &
+ (2d0*r**2/3d0 - rb**2)*ga )
end if
end do
end subroutine ULYP_gga_correlation_energy

85
src/eDFT/ULYP_gga_correlation_potential.f90 Normal file
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@ -0,0 +1,85 @@
subroutine ULYP_gga_correlation_potential(nGrid,weight,nBas,AO,dAO,rho,drho,Fc)
! Compute LYP correlation 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) :: dAO(ncart,nBas,nGrid)
double precision,intent(in) :: rho(nGrid,nspin)
double precision,intent(in) :: drho(ncart,nGrid,nspin)
! Local variables
integer :: mu,nu,iG
double precision :: vAO,gaAO,gbAO
double precision :: ra,rb,r
double precision :: ga,gab,gb,g
double precision :: a,b,c,d
double precision :: Cf,omega,delta
! Output variables
double precision,intent(out) :: Fc(nBas,nBas)
! Prameter of the functional
a = 0.04918d0
b = 0.132d0
c = 0.2533d0
d = 0.349d0
Cf = 3d0/10d0*(3d0*pi**2)**(2d0/3d0)
! Compute matrix elements in the AO basis
Fc(:,:) = 0d0
do mu=1,nBas
do nu=1,nBas
do iG=1,nGrid
ra = max(0d0,rho(iG,1))
rb = max(0d0,rho(iG,2))
r = ra + rb
if(r > threshold) then
ga = drho(1,iG,1)**2 + drho(2,iG,1)**2 + drho(3,iG,1)**2
gb = drho(1,iG,2)**2 + drho(2,iG,2)**2 + drho(3,iG,2)**2
gab = drho(1,iG,1)*drho(1,iG,2) + drho(2,iG,1)*drho(2,iG,2) + drho(3,iG,1)*drho(3,iG,2)
g = ga + gab + gb
omega = exp(-c*r**(-1d0/3d0))/(1d0 + d*r**(-1d0/3d0))*r**(-11d0/3d0)
delta = c*r**(-1d0/3d0) + d*r**(-1d0/3d0)/(1d0 + d*r**(-1d0/3d0))
vAO = weight(iG)*AO(mu,iG)*AO(nu,iG)
Fc(mu,nu) = Fc(mu,nu) + vAO
gaAO = drho(1,iG,1)*(dAO(1,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(1,nu,iG)) &
+ drho(2,iG,1)*(dAO(2,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(2,nu,iG)) &
+ drho(3,iG,1)*(dAO(3,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(3,nu,iG))
gaAO = weight(iG)*gaAO
gbAO = drho(1,iG,2)*(dAO(1,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(1,nu,iG)) &
+ drho(2,iG,2)*(dAO(2,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(2,nu,iG)) &
+ drho(3,iG,2)*(dAO(3,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(3,nu,iG))
gbAO = weight(iG)*gbAO
Fc(mu,nu) = Fc(mu,nu) + 2d0*gaAO + gbAO
end if
end do
end do
end do
end subroutine ULYP_gga_correlation_potential

1
src/eDFT/UPBE_gga_exchange_potential.f90
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@ -55,7 +55,6 @@ subroutine UPBE_gga_exchange_potential(nGrid,weight,nBas,AO,dAO,rho,drho,Fx)
gAO = drho(1,iG)*(dAO(1,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(1,nu,iG)) &
+ drho(2,iG)*(dAO(2,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(2,nu,iG)) &
+ drho(3,iG)*(dAO(3,mu,iG)*AO(nu,iG) + AO(mu,iG)*dAO(3,nu,iG))
gAO = weight(iG)*gAO
Fx(mu,nu) = Fx(mu,nu) + 2d0*gAO*alpha*r**(-4d0/3d0)*mupbe/(1d0 + mupbe*s2/kappa)**2

18
src/eDFT/unrestricted_gga_correlation_energy.f90
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@ -1,6 +1,6 @@
subroutine unrestricted_gga_correlation_energy(DFA,nEns,wEns,nGrid,weight,rho,drho,Ec)
! Compute unrstricted GGA correlation energy
! Compute unrestricted GGA correlation energy
implicit none
include 'parameters.h'
@ -24,19 +24,17 @@ subroutine unrestricted_gga_correlation_energy(DFA,nEns,wEns,nGrid,weight,rho,dr
double precision :: Ec(nsp)
! Coefficients for ??? GGA exchange functional
select case (DFA)
! Compute GGA exchange energy
case ('LYP')
Ec(:) = 0d0
call ULYP_gga_correlation_energy(nGrid,weight,rho,drho,Ec)
do iG=1,nGrid
case default
ra = rho(iG,1)
rb = rho(iG,2)
ga = drho(1,iG,1)**2 + drho(2,iG,1)**2 + drho(3,iG,1)**2
gb = drho(1,iG,2)**2 + drho(2,iG,2)**2 + drho(3,iG,2)**2
call print_warning('!!! GGA correlation energy not available !!!')
stop
enddo
end select
end subroutine unrestricted_gga_correlation_energy