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UVWN3 for Gaussian B3LYP

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This commit is contained in:
Pierre-Francois Loos 2021-02-25 10:55:08 +01:00
parent ede8862d67
commit 272e47ed27
16 changed files with 570 additions and 15 deletions
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2
input/dft
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@ -9,7 +9,7 @@
4 BHHLYP
# correlation rung:
# Hartree = 0: H
# LDA = 1: VWN5,eVWN5
# LDA = 1: VWN3,VWN5,eVWN5
# GGA = 2: LYP,PBE
# MGGA = 3:
# Hybrid = 4: HF,LYP,PBE

4
input/methods
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@ -1,5 +1,5 @@
# RHF UHF KS MOM
T F F F
F F T F
# MP2* MP3 MP2-F12
F F F
# CCD DCD CCSD CCSD(T)
@ -15,7 +15,7 @@
# G0W0* evGW* qsGW*
F F F
# G0T0 evGT qsGT
T F F
F F F
# MCMP2
F
# * unrestricted version available

2
input/options
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@ -9,7 +9,7 @@
# 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 0.0000001 T 5 T 0.000 F F F F F
256 0.0000001 T 5 T 0.00367493 F F F F F
# ACFDT: AC Kx XBS
F F T
# BSE: BSE dBSE dTDA evDyn

4
src/MBPT/Bethe_Salpeter.f90
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@ -88,7 +88,7 @@ subroutine Bethe_Salpeter(TDA_W,TDA,dBSE,dTDA,evDyn,singlet,triplet,eta,nBas,nC,
OmBSE(:,ispin),XpY_BSE(:,:,ispin),XmY_BSE(:,:,ispin))
else
call Bethe_Salpeter_dynamic_perturbation(dTDA,eta,nBas,nC,nO,nV,nR,nS,eGW,dipole_int,OmRPA,rho_RPA, &
call Bethe_Salpeter_dynamic_perturbation(dTDA,eta,nBas,nC,nO,nV,nR,nS,eW,eGW,dipole_int,OmRPA,rho_RPA, &
OmBSE(:,ispin),XpY_BSE(:,:,ispin),XmY_BSE(:,:,ispin))
end if
@ -127,7 +127,7 @@ subroutine Bethe_Salpeter(TDA_W,TDA,dBSE,dTDA,evDyn,singlet,triplet,eta,nBas,nC,
OmBSE(:,ispin),XpY_BSE(:,:,ispin),XmY_BSE(:,:,ispin))
else
call Bethe_Salpeter_dynamic_perturbation(dTDA,eta,nBas,nC,nO,nV,nR,nS,eGW,dipole_int,OmRPA,rho_RPA, &
call Bethe_Salpeter_dynamic_perturbation(dTDA,eta,nBas,nC,nO,nV,nR,nS,eW,eGW,dipole_int,OmRPA,rho_RPA, &
OmBSE(:,ispin),XpY_BSE(:,:,ispin),XmY_BSE(:,:,ispin))
end if

3
src/MBPT/Bethe_Salpeter_dynamic_perturbation.f90
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@ -1,4 +1,4 @@
subroutine Bethe_Salpeter_dynamic_perturbation(dTDA,eta,nBas,nC,nO,nV,nR,nS,eGW,dipole_int,OmRPA,rho_RPA,OmBSE,XpY,XmY)
subroutine Bethe_Salpeter_dynamic_perturbation(dTDA,eta,nBas,nC,nO,nV,nR,nS,eW,eGW,dipole_int,OmRPA,rho_RPA,OmBSE,XpY,XmY)
! Compute dynamical effects via perturbation theory for BSE
@ -16,6 +16,7 @@ subroutine Bethe_Salpeter_dynamic_perturbation(dTDA,eta,nBas,nC,nO,nV,nR,nS,eGW,
integer,intent(in) :: nR
integer,intent(in) :: nS
double precision,intent(in) :: eW(nBas)
double precision,intent(in) :: eGW(nBas)
double precision,intent(in) :: dipole_int(nBas,nBas,ncart)
double precision,intent(in) :: OmRPA(nS)

4
src/MBPT/qsUGW.f90
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@ -375,14 +375,14 @@ subroutine qsUGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,COHSEX,SOS
! Deallocate memory
deallocate(c,cp,P,F,Fp,J,K,SigC,SigCp,SigCm,Z,OmRPA,XpY_RPA,XmY_RPA,rho_RPA,error,error_diis,F_diis)
deallocate(cp,P,F,Fp,J,K,SigC,SigCp,SigCm,Z,OmRPA,XpY_RPA,XmY_RPA,rho_RPA,error,error_diis,F_diis)
! Perform BSE calculation
if(BSE) then
call unrestricted_Bethe_Salpeter(TDA_W,TDA,dBSE,dTDA,evDyn,spin_conserved,spin_flip,eta,nBas,nC,nO,nV,nR,nS, &
S,ERI_aaaa,ERI_aabb,ERI_bbbb,dipole_int_aa,dipole_int_bb,cHF,eGW,eGW,EcBSE)
S,ERI_aaaa,ERI_aabb,ERI_bbbb,dipole_int_aa,dipole_int_bb,c,eGW,eGW,EcBSE)
if(exchange_kernel) then

4
src/MBPT/unrestricted_Bethe_Salpeter.f90
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@ -112,7 +112,7 @@ subroutine unrestricted_Bethe_Salpeter(TDA_W,TDA,dBSE,dTDA,evDyn,spin_conserved,
if(dBSE) &
call unrestricted_Bethe_Salpeter_dynamic_perturbation(ispin,dTDA,eta,nBas,nC,nO,nV,nR,nS,nS_aa,nS_bb,nS_sc,nS_sc, &
eGW,ERI_aaaa,ERI_aabb,ERI_bbbb,dipole_int_aa,dipole_int_bb, &
eW,eGW,ERI_aaaa,ERI_aabb,ERI_bbbb,dipole_int_aa,dipole_int_bb, &
OmRPA,rho_RPA,OmBSE_sc,XpY_BSE_sc,XmY_BSE_sc)
deallocate(OmBSE_sc,XpY_BSE_sc,XmY_BSE_sc)
@ -148,7 +148,7 @@ subroutine unrestricted_Bethe_Salpeter(TDA_W,TDA,dBSE,dTDA,evDyn,spin_conserved,
if(dBSE) &
call unrestricted_Bethe_Salpeter_dynamic_perturbation(ispin,dTDA,eta,nBas,nC,nO,nV,nR,nS,nS_ab,nS_ba,nS_sf,nS_sc, &
eGW,ERI_aaaa,ERI_aabb,ERI_bbbb,dipole_int_aa,dipole_int_bb, &
eW,eGW,ERI_aaaa,ERI_aabb,ERI_bbbb,dipole_int_aa,dipole_int_bb, &
OmRPA,rho_RPA,OmBSE_sf,XpY_BSE_sf,XmY_BSE_sf)
deallocate(OmBSE_sf,XpY_BSE_sf,XmY_BSE_sf)

5
src/MBPT/unrestricted_Bethe_Salpeter_dynamic_perturbation.f90
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@ -1,5 +1,5 @@
subroutine unrestricted_Bethe_Salpeter_dynamic_perturbation(ispin,dTDA,eta,nBas,nC,nO,nV,nR,nS,nSa,nSb,nSt,nS_sc,eGW, &
ERI_aaaa,ERI_aabb,ERI_bbbb,dipole_int_aa,dipole_int_bb, &
subroutine unrestricted_Bethe_Salpeter_dynamic_perturbation(ispin,dTDA,eta,nBas,nC,nO,nV,nR,nS,nSa,nSb,nSt,nS_sc,eW,eGW, &
ERI_aaaa,ERI_aabb,ERI_bbbb,dipole_int_aa,dipole_int_bb, &
OmRPA,rho_RPA,OmBSE,XpY_BSE,XmY_BSE)
! Compute dynamical effects via perturbation theory for BSE
@ -23,6 +23,7 @@ subroutine unrestricted_Bethe_Salpeter_dynamic_perturbation(ispin,dTDA,eta,nBas,
integer,intent(in) :: nSt
integer,intent(in) :: nS_sc
double precision,intent(in) :: eW(nBas,nspin)
double precision,intent(in) :: eGW(nBas,nspin)
double precision,intent(in) :: ERI_aaaa(nBas,nBas,nBas,nBas)
double precision,intent(in) :: ERI_aabb(nBas,nBas,nBas,nBas)

137
src/eDFT/UVWN3_lda_correlation_energy.f90 Normal file
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@ -0,0 +1,137 @@
subroutine UVWN3_lda_correlation_energy(nGrid,weight,rho,Ec)
! Compute unrestricted VWN3 LDA 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)
! Local variables
integer :: iG
double precision :: ra,rb,r,rs,x,z
double precision :: a_p,x0_p,xx0_p,b_p,c_p,x_p,q_p
double precision :: a_f,x0_f,xx0_f,b_f,c_f,x_f,q_f
double precision :: a_a,x0_a,xx0_a,b_a,c_a,x_a,q_a
double precision :: ec_z,ec_p,ec_f,ec_a
double precision :: fz,d2fz
! Output variables
double precision :: Ec(nsp)
! Parameters of the functional
a_p = +0.0621814d0/2d0
x0_p = -0.409286d0
b_p = +13.0720d0
c_p = +42.7198d0
a_f = +0.0621814d0/4d0
x0_f = -0.743294d0
b_f = +20.1231d0
c_f = +101.578d0
a_a = -1d0/(6d0*pi**2)
x0_a = -0.0047584D0
b_a = 1.13107d0
c_a = 13.0045d0
! Initialization
Ec(:) = 0d0
do iG=1,nGrid
ra = max(0d0,rho(iG,1))
rb = max(0d0,rho(iG,2))
! alpha-alpha contribution
if(ra > threshold) then
rs = (4d0*pi*ra/3d0)**(-1d0/3d0)
x = sqrt(rs)
x_f = x*x + b_f*x + c_f
xx0_f = x0_f*x0_f + b_f*x0_f + c_f
q_f = sqrt(4d0*c_f - b_f*b_f)
ec_f = a_f*( log(x**2/x_f) + 2d0*b_f/q_f*atan(q_f/(2d0*x + b_f)) &
- b_f*x0_f/xx0_f*( log((x - x0_f)**2/x_f) + 2d0*(b_f + 2d0*x0_f)/q_f*atan(q_f/(2d0*x + b_f)) ) )
Ec(1) = Ec(1) + weight(iG)*ec_f*ra
end if
! alpha-beta contribution
if(ra > threshold .or. rb > threshold) then
r = ra + rb
rs = (4d0*pi*r/3d0)**(-1d0/3d0)
z = (ra - rb)/r
x = sqrt(rs)
fz = (1d0 + z)**(4d0/3d0) + (1d0 - z)**(4d0/3d0) - 2d0
fz = fz/(2d0*(2d0**(1d0/3d0) - 1d0))
d2fz = 4d0/(9d0*(2**(1d0/3d0) - 1d0))
x_p = x*x + b_p*x + c_p
x_f = x*x + b_f*x + c_f
x_a = x*x + b_a*x + c_a
xx0_p = x0_p*x0_p + b_p*x0_p + c_p
xx0_f = x0_f*x0_f + b_f*x0_f + c_f
xx0_a = x0_a*x0_a + b_a*x0_a + c_a
q_p = sqrt(4d0*c_p - b_p*b_p)
q_f = sqrt(4d0*c_f - b_f*b_f)
q_a = sqrt(4d0*c_a - b_a*b_a)
ec_p = a_p*( log(x**2/x_p) + 2d0*b_p/q_p*atan(q_p/(2d0*x + b_p)) &
- b_p*x0_p/xx0_p*( log((x - x0_p)**2/x_p) + 2d0*(b_p + 2d0*x0_p)/q_p*atan(q_p/(2d0*x + b_p)) ) )
ec_f = a_f*( log(x**2/x_f) + 2d0*b_f/q_f*atan(q_f/(2d0*x + b_f)) &
- b_f*x0_f/xx0_f*( log((x - x0_f)**2/x_f) + 2d0*(b_f + 2d0*x0_f)/q_f*atan(q_f/(2d0*x + b_f)) ) )
ec_a = a_a*( log(x**2/x_a) + 2d0*b_a/q_a*atan(q_a/(2d0*x + b_a)) &
- b_a*x0_a/xx0_a*( log((x - x0_a)**2/x_a) + 2d0*(b_a + 2d0*x0_a)/q_a*atan(q_a/(2d0*x + b_a)) ) )
ec_z = ec_p + ec_a*fz/d2fz*(1d0-z**4) + (ec_f - ec_p)*fz*z**4
Ec(2) = Ec(2) + weight(iG)*ec_z*r
end if
! beta-beta contribution
if(rb > threshold) then
rs = (4d0*pi*rb/3d0)**(-1d0/3d0)
x = sqrt(rs)
x_f = x*x + b_f*x + c_f
xx0_f = x0_f*x0_f + b_f*x0_f + c_f
q_f = sqrt(4d0*c_f - b_f*b_f)
ec_f = a_f*( log(x**2/x_f) + 2d0*b_f/q_f*atan(q_f/(2d0*x + b_f)) &
- b_f*x0_f/xx0_f*( log((x - x0_f)**2/x_f) + 2d0*(b_f + 2d0*x0_f)/q_f*atan(q_f/(2d0*x + b_f)) ) )
Ec(3) = Ec(3) + weight(iG)*ec_f*rb
end if
end do
Ec(2) = Ec(2) - Ec(1) - Ec(3)
end subroutine UVWN3_lda_correlation_energy

202
src/eDFT/UVWN3_lda_correlation_individual_energy.f90 Normal file
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@ -0,0 +1,202 @@
subroutine UVWN3_lda_correlation_individual_energy(nGrid,weight,rhow,rho,Ec)
! Compute VWN3 LDA correlation potential
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: nGrid
double precision,intent(in) :: weight(nGrid)
double precision,intent(in) :: rhow(nGrid,nspin)
double precision,intent(in) :: rho(nGrid,nspin)
! Local variables
integer :: iG
double precision :: ra,rb,r,raI,rbI,rI,rs,x,z
double precision :: a_p,x0_p,xx0_p,b_p,c_p,x_p,q_p
double precision :: a_f,x0_f,xx0_f,b_f,c_f,x_f,q_f
double precision :: a_a,x0_a,xx0_a,b_a,c_a,x_a,q_a
double precision :: dfzdz,dxdrs,dxdx_p,dxdx_f,dxdx_a,decdx_p,decdx_f,decdx_a
double precision :: dzdra,dfzdra,drsdra,decdra_p,decdra_f,decdra_a,decdra
double precision :: dzdrb,dfzdrb,drsdrb,decdrb_p,decdrb_f,decdrb_a,decdrb
double precision :: ec_z,ec_p,ec_f,ec_a
double precision :: fz,d2fz
! Output variables
double precision :: Ec(nsp)
! Parameters of the functional
a_p = +0.0621814d0/2d0
x0_p = -0.409286d0
b_p = +13.0720d0
c_p = +42.7198d0
a_f = +0.0621814d0/4d0
x0_f = -0.743294d0
b_f = +20.1231d0
c_f = +101.578d0
a_a = -1d0/(6d0*pi**2)
x0_a = -0.0047584D0
b_a = +1.13107d0
c_a = +13.0045d0
! Initialization
Ec(:) = 0d0
do iG=1,nGrid
ra = max(0d0,rhow(iG,1))
rb = max(0d0,rhow(iG,2))
raI = max(0d0,rho(iG,1))
rbI = max(0d0,rho(iG,2))
! spin-up contribution
if(ra > threshold .or. raI > threshold) then
r = ra
rI = raI
rs = (4d0*pi*r/3d0)**(-1d0/3d0)
x = sqrt(rs)
x_f = x*x + b_f*x + c_f
xx0_f = x0_f*x0_f + b_f*x0_f + c_f
q_f = sqrt(4d0*c_f - b_f*b_f)
ec_f = a_f*( log(x**2/x_f) + 2d0*b_f/q_f*atan(q_f/(2d0*x + b_f)) &
- b_f*x0_f/xx0_f*( log((x - x0_f)**2/x_f) + 2d0*(b_f + 2d0*x0_f)/q_f*atan(q_f/(2d0*x + b_f)) ) )
drsdra = - (36d0*pi)**(-1d0/3d0)*r**(-4d0/3d0)
dxdrs = 0.5d0/sqrt(rs)
dxdx_f = 2d0*x + b_f
decdx_f = a_f*( 2d0/x - 4d0*b_f/( (b_f+2d0*x)**2 + q_f**2) - dxdx_f/x_f &
- b_f*x0_f/xx0_f*( 2/(x-x0_f) - 4d0*(b_f+2d0*x0_f)/( (b_f+2d0*x)**2 + q_f**2) - dxdx_f/x_f ) )
decdra_f = drsdra*dxdrs*decdx_f
Ec(1) = Ec(1) + weight(iG)*(ec_f + decdra_f*r)*rI
end if
! up-down contribution
if(ra > threshold .or. raI > threshold) then
r = ra + rb
rI = raI + rbI
rs = (4d0*pi*r/3d0)**(-1d0/3d0)
z = (ra - rb)/r
x = sqrt(rs)
fz = (1d0 + z)**(4d0/3d0) + (1d0 - z)**(4d0/3d0) - 2d0
fz = fz/(2d0*(2d0**(1d0/3d0) - 1d0))
d2fz = 4d0/(9d0*(2**(1d0/3d0) - 1d0))
x_p = x*x + b_p*x + c_p
x_f = x*x + b_f*x + c_f
x_a = x*x + b_a*x + c_a
xx0_p = x0_p*x0_p + b_p*x0_p + c_p
xx0_f = x0_f*x0_f + b_f*x0_f + c_f
xx0_a = x0_a*x0_a + b_a*x0_a + c_a
q_p = sqrt(4d0*c_p - b_p*b_p)
q_f = sqrt(4d0*c_f - b_f*b_f)
q_a = sqrt(4d0*c_a - b_a*b_a)
ec_p = a_p*( log(x**2/x_p) + 2d0*b_p/q_p*atan(q_p/(2d0*x + b_p)) &
- b_p*x0_p/xx0_p*( log((x - x0_p)**2/x_p) + 2d0*(b_p + 2d0*x0_p)/q_p*atan(q_p/(2d0*x + b_p)) ) )
ec_f = a_f*( log(x**2/x_f) + 2d0*b_f/q_f*atan(q_f/(2d0*x + b_f)) &
- b_f*x0_f/xx0_f*( log((x - x0_f)**2/x_f) + 2d0*(b_f + 2d0*x0_f)/q_f*atan(q_f/(2d0*x + b_f)) ) )
ec_a = a_a*( log(x**2/x_a) + 2d0*b_a/q_a*atan(q_a/(2d0*x + b_a)) &
- b_a*x0_a/xx0_a*( log((x - x0_a)**2/x_a) + 2d0*(b_a + 2d0*x0_a)/q_a*atan(q_a/(2d0*x + b_a)) ) )
ec_z = ec_p + ec_a*fz/d2fz*(1d0-z**4) + (ec_f - ec_p)*fz*z**4
dzdra = (1d0 - z)/r
dfzdz = (4d0/3d0)*((1d0 + z)**(1d0/3d0) - (1d0 - z)**(1d0/3d0))/(2d0*(2d0**(1d0/3d0) - 1d0))
dfzdra = dzdra*dfzdz
drsdra = - (36d0*pi)**(-1d0/3d0)*r**(-4d0/3d0)
dxdrs = 0.5d0/sqrt(rs)
dxdx_p = 2d0*x + b_p
dxdx_f = 2d0*x + b_f
dxdx_a = 2d0*x + b_a
decdx_p = a_p*( 2d0/x - 4d0*b_p/( (b_p+2d0*x)**2 + q_p**2) - dxdx_p/x_p &
- b_p*x0_p/xx0_p*( 2/(x-x0_p) - 4d0*(b_p+2d0*x0_p)/( (b_p+2d0*x)**2 + q_p**2) - dxdx_p/x_p ) )
decdx_f = a_f*( 2d0/x - 4d0*b_f/( (b_f+2d0*x)**2 + q_f**2) - dxdx_f/x_f &
- b_f*x0_f/xx0_f*( 2/(x-x0_f) - 4d0*(b_f+2d0*x0_f)/( (b_f+2d0*x)**2 + q_f**2) - dxdx_f/x_f ) )
decdx_a = a_a*( 2d0/x - 4d0*b_a/( (b_a+2d0*x)**2 + q_a**2) - dxdx_a/x_a &
- b_a*x0_a/xx0_a*( 2/(x-x0_a) - 4d0*(b_a+2d0*x0_a)/( (b_a+2d0*x)**2 + q_a**2) - dxdx_a/x_a ) )
decdra_p = drsdra*dxdrs*decdx_p
decdra_f = drsdra*dxdrs*decdx_f
decdra_a = drsdra*dxdrs*decdx_a
decdra = decdra_p + decdra_a*fz/d2fz*(1d0-z**4) + ec_a*dfzdra/d2fz*(1d0-z**4) - 4d0*ec_a*fz/d2fz*dzdra*z**3 &
+ (decdra_f - decdra_p)*fz*z**4 + (ec_f - ec_p)*dfzdra*z**4 + 4d0*(ec_f - ec_p)*fz*dzdra*z**3
Ec(2) = Ec(2) + weight(iG)*(ec_z + decdra*r)*rI
end if
! spin-down contribution
if(rb > threshold .or. rbI > threshold) then
r = rb
rI = rbI
rs = (4d0*pi*r/3d0)**(-1d0/3d0)
x = sqrt(rs)
x_f = x*x + b_f*x + c_f
xx0_f = x0_f*x0_f + b_f*x0_f + c_f
q_f = sqrt(4d0*c_f - b_f*b_f)
ec_f = a_f*( log(x**2/x_f) + 2d0*b_f/q_f*atan(q_f/(2d0*x + b_f)) &
- b_f*x0_f/xx0_f*( log((x - x0_f)**2/x_f) + 2d0*(b_f + 2d0*x0_f)/q_f*atan(q_f/(2d0*x + b_f)) ) )
drsdra = - (36d0*pi)**(-1d0/3d0)*r**(-4d0/3d0)
dxdrs = 0.5d0/sqrt(rs)
dxdx_f = 2d0*x + b_f
decdx_f = a_f*( 2d0/x - 4d0*b_f/( (b_f+2d0*x)**2 + q_f**2) - dxdx_f/x_f &
- b_f*x0_f/xx0_f*( 2/(x-x0_f) - 4d0*(b_f+2d0*x0_f)/( (b_f+2d0*x)**2 + q_f**2) - dxdx_f/x_f ) )
decdra_f = drsdra*dxdrs*decdx_f
Ec(3) = Ec(3) + weight(iG)*(ec_f + decdra_f*r)*rI
end if
end do
Ec(2) = Ec(2) - Ec(1) - Ec(3)
end subroutine UVWN3_lda_correlation_individual_energy

202
src/eDFT/UVWN3_lda_correlation_potential.f90 Normal file
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@ -0,0 +1,202 @@
subroutine UVWN3_lda_correlation_potential(nGrid,weight,nBas,AO,rho,Fc)
! Compute unrestricted VWN3 LDA 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) :: rho(nGrid,nspin)
! Local variables
integer :: mu,nu,iG
double precision :: ra,rb,r,rs,x,z
double precision :: a_p,x0_p,xx0_p,b_p,c_p,x_p,q_p
double precision :: a_f,x0_f,xx0_f,b_f,c_f,x_f,q_f
double precision :: a_a,x0_a,xx0_a,b_a,c_a,x_a,q_a
double precision :: dfzdz,dxdrs,dxdx_p,dxdx_f,dxdx_a,decdx_p,decdx_f,decdx_a
double precision :: dzdra,dfzdra,drsdra,decdra_p,decdra_f,decdra_a,decdra
double precision :: dzdrb,dfzdrb,drsdrb,decdrb_p,decdrb_f,decdrb_a,decdrb
double precision :: ec_z,ec_p,ec_f,ec_a
double precision :: fz,d2fz
! Output variables
double precision :: Fc(nBas,nBas,nspin)
! Parameters of the functional
a_p = +0.0621814d0/2d0
x0_p = -0.409286d0
b_p = +13.0720d0
c_p = +42.7198d0
a_f = +0.0621814d0/4d0
x0_f = -0.743294d0
b_f = +20.1231d0
c_f = +101.578d0
a_a = -1d0/(6d0*pi**2)
x0_a = -0.0047584D0
b_a = +1.13107d0
c_a = +13.0045d0
! Initialization
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))
! spin-up contribution
if(ra > threshold) then
r = ra + rb
rs = (4d0*pi*r/3d0)**(-1d0/3d0)
z = (ra - rb)/r
x = sqrt(rs)
fz = (1d0 + z)**(4d0/3d0) + (1d0 - z)**(4d0/3d0) - 2d0
fz = fz/(2d0*(2d0**(1d0/3d0) - 1d0))
d2fz = 4d0/(9d0*(2**(1d0/3d0) - 1d0))
x_p = x*x + b_p*x + c_p
x_f = x*x + b_f*x + c_f
x_a = x*x + b_a*x + c_a
xx0_p = x0_p*x0_p + b_p*x0_p + c_p
xx0_f = x0_f*x0_f + b_f*x0_f + c_f
xx0_a = x0_a*x0_a + b_a*x0_a + c_a
q_p = sqrt(4d0*c_p - b_p*b_p)
q_f = sqrt(4d0*c_f - b_f*b_f)
q_a = sqrt(4d0*c_a - b_a*b_a)
ec_p = a_p*( log(x**2/x_p) + 2d0*b_p/q_p*atan(q_p/(2d0*x + b_p)) &
- b_p*x0_p/xx0_p*( log((x - x0_p)**2/x_p) + 2d0*(b_p + 2d0*x0_p)/q_p*atan(q_p/(2d0*x + b_p)) ) )
ec_f = a_f*( log(x**2/x_f) + 2d0*b_f/q_f*atan(q_f/(2d0*x + b_f)) &
- b_f*x0_f/xx0_f*( log((x - x0_f)**2/x_f) + 2d0*(b_f + 2d0*x0_f)/q_f*atan(q_f/(2d0*x + b_f)) ) )
ec_a = a_a*( log(x**2/x_a) + 2d0*b_a/q_a*atan(q_a/(2d0*x + b_a)) &
- b_a*x0_a/xx0_a*( log((x - x0_a)**2/x_a) + 2d0*(b_a + 2d0*x0_a)/q_a*atan(q_a/(2d0*x + b_a)) ) )
ec_z = ec_p + ec_a*fz/d2fz*(1d0-z**4) + (ec_f - ec_p)*fz*z**4
dzdra = (1d0 - z)/r
dfzdz = (4d0/3d0)*((1d0 + z)**(1d0/3d0) - (1d0 - z)**(1d0/3d0))/(2d0*(2d0**(1d0/3d0) - 1d0))
dfzdra = dzdra*dfzdz
drsdra = - (36d0*pi)**(-1d0/3d0)*r**(-4d0/3d0)
dxdrs = 0.5d0/sqrt(rs)
dxdx_p = 2d0*x + b_p
dxdx_f = 2d0*x + b_f
dxdx_a = 2d0*x + b_a
decdx_p = a_p*( 2d0/x - 4d0*b_p/( (b_p+2d0*x)**2 + q_p**2) - dxdx_p/x_p &
- b_p*x0_p/xx0_p*( 2/(x-x0_p) - 4d0*(b_p+2d0*x0_p)/( (b_p+2d0*x)**2 + q_p**2) - dxdx_p/x_p ) )
decdx_f = a_f*( 2d0/x - 4d0*b_f/( (b_f+2d0*x)**2 + q_f**2) - dxdx_f/x_f &
- b_f*x0_f/xx0_f*( 2/(x-x0_f) - 4d0*(b_f+2d0*x0_f)/( (b_f+2d0*x)**2 + q_f**2) - dxdx_f/x_f ) )
decdx_a = a_a*( 2d0/x - 4d0*b_a/( (b_a+2d0*x)**2 + q_a**2) - dxdx_a/x_a &
- b_a*x0_a/xx0_a*( 2/(x-x0_a) - 4d0*(b_a+2d0*x0_a)/( (b_a+2d0*x)**2 + q_a**2) - dxdx_a/x_a ) )
decdra_p = drsdra*dxdrs*decdx_p
decdra_f = drsdra*dxdrs*decdx_f
decdra_a = drsdra*dxdrs*decdx_a
decdra = decdra_p + decdra_a*fz/d2fz*(1d0-z**4) + ec_a*dfzdra/d2fz*(1d0-z**4) - 4d0*ec_a*fz/d2fz*dzdra*z**3 &
+ (decdra_f - decdra_p)*fz*z**4 + (ec_f - ec_p)*dfzdra*z**4 + 4d0*(ec_f - ec_p)*fz*dzdra*z**3
Fc(mu,nu,1) = Fc(mu,nu,1) + weight(iG)*AO(mu,iG)*AO(nu,iG)*(ec_z + decdra*r)
end if
! spin-down contribution
if(rb > threshold) then
r = ra + rb
rs = (4d0*pi*r/3d0)**(-1d0/3d0)
z = (ra - rb)/r
x = sqrt(rs)
fz = (1d0 + z)**(4d0/3d0) + (1d0 - z)**(4d0/3d0) - 2d0
fz = fz/(2d0*(2d0**(1d0/3d0) - 1d0))
d2fz = 4d0/(9d0*(2**(1d0/3d0) - 1d0))
x_p = x*x + b_p*x + c_p
x_f = x*x + b_f*x + c_f
x_a = x*x + b_a*x + c_a
xx0_p = x0_p*x0_p + b_p*x0_p + c_p
xx0_f = x0_f*x0_f + b_f*x0_f + c_f
xx0_a = x0_a*x0_a + b_a*x0_a + c_a
q_p = sqrt(4d0*c_p - b_p*b_p)
q_f = sqrt(4d0*c_f - b_f*b_f)
q_a = sqrt(4d0*c_a - b_a*b_a)
ec_p = a_p*( log(x**2/x_p) + 2d0*b_p/q_p*atan(q_p/(2d0*x + b_p)) &
- b_p*x0_p/xx0_p*( log((x - x0_p)**2/x_p) + 2d0*(b_p + 2d0*x0_p)/q_p*atan(q_p/(2d0*x + b_p)) ) )
ec_f = a_f*( log(x**2/x_f) + 2d0*b_f/q_f*atan(q_f/(2d0*x + b_f)) &
- b_f*x0_f/xx0_f*( log((x - x0_f)**2/x_f) + 2d0*(b_f + 2d0*x0_f)/q_f*atan(q_f/(2d0*x + b_f)) ) )
ec_a = a_a*( log(x**2/x_a) + 2d0*b_a/q_a*atan(q_a/(2d0*x + b_a)) &
- b_a*x0_a/xx0_a*( log((x - x0_a)**2/x_a) + 2d0*(b_a + 2d0*x0_a)/q_a*atan(q_a/(2d0*x + b_a)) ) )
ec_z = ec_p + ec_a*fz/d2fz*(1d0-z**4) + (ec_f - ec_p)*fz*z**4
dzdrb = - (1d0 + z)/r
dfzdz = (4d0/3d0)*((1d0 + z)**(1d0/3d0) - (1d0 - z)**(1d0/3d0))/(2d0*(2d0**(1d0/3d0) - 1d0))
dfzdrb = dzdrb*dfzdz
drsdrb = - (36d0*pi)**(-1d0/3d0)*r**(-4d0/3d0)
dxdrs = 0.5d0/sqrt(rs)
dxdx_p = 2d0*x + b_p
dxdx_f = 2d0*x + b_f
dxdx_a = 2d0*x + b_a
decdx_p = a_p*( 2d0/x - 4d0*b_p/( (b_p+2d0*x)**2 + q_p**2) - dxdx_p/x_p &
- b_p*x0_p/xx0_p*( 2/(x-x0_p) - 4d0*(b_p+2d0*x0_p)/( (b_p+2d0*x)**2 + q_p**2) - dxdx_p/x_p ) )
decdx_f = a_f*( 2d0/x - 4d0*b_f/( (b_f+2d0*x)**2 + q_f**2) - dxdx_f/x_f &
- b_f*x0_f/xx0_f*( 2/(x-x0_f) - 4d0*(b_f+2d0*x0_f)/( (b_f+2d0*x)**2 + q_f**2) - dxdx_f/x_f ) )
decdx_a = a_a*( 2d0/x - 4d0*b_a/( (b_a+2d0*x)**2 + q_a**2) - dxdx_a/x_a &
- b_a*x0_a/xx0_a*( 2/(x-x0_a) - 4d0*(b_a+2d0*x0_a)/( (b_a+2d0*x)**2 + q_a**2) - dxdx_a/x_a ) )
decdrb_p = drsdrb*dxdrs*decdx_p
decdrb_f = drsdrb*dxdrs*decdx_f
decdrb_a = drsdrb*dxdrs*decdx_a
decdrb = decdrb_p + decdrb_a*fz/d2fz*(1d0-z**4) + ec_a*dfzdrb/d2fz*(1d0-z**4) - 4d0*ec_a*fz/d2fz*dzdrb*z**3 &
+ (decdrb_f - decdrb_p)*fz*z**4 + (ec_f - ec_p)*dfzdrb*z**4 + 4d0*(ec_f - ec_p)*fz*dzdrb*z**3
Fc(mu,nu,2) = Fc(mu,nu,2) + weight(iG)*AO(mu,iG)*AO(nu,iG)*(ec_z + decdrb*r)
end if
end do
end do
end do
end subroutine UVWN3_lda_correlation_potential

2
src/eDFT/unrestricted_hybrid_correlation_energy.f90
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@ -35,7 +35,7 @@ subroutine unrestricted_hybrid_correlation_energy(DFA,nEns,wEns,nGrid,weight,rho
aC = 0.81d0
call unrestricted_lda_correlation_energy('VWN5 ',nEns,wEns,nGrid,weight,rho,EcLDA)
call unrestricted_lda_correlation_energy('VWN3 ',nEns,wEns,nGrid,weight,rho,EcLDA)
call unrestricted_gga_correlation_energy('LYP ',nEns,wEns,nGrid,weight,rho,drho,EcGGA)
Ec(:) = EcLDA(:) + aC*(EcGGA(:) - EcLDA(:))

2
src/eDFT/unrestricted_hybrid_correlation_potential.f90
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@ -42,7 +42,7 @@ subroutine unrestricted_hybrid_correlation_potential(DFA,nEns,wEns,nGrid,weight,
aC = 0.81d0
call unrestricted_lda_correlation_potential('VWN5 ',nEns,wEns,nGrid,weight,nBas,AO,rho,FcLDA)
call unrestricted_lda_correlation_potential('VWN3 ',nEns,wEns,nGrid,weight,nBas,AO,rho,FcLDA)
call unrestricted_gga_correlation_potential('LYP ',nEns,wEns,nGrid,weight,nBas,AO,dAO,rho,drho,FcGGA)
Fc(:,:,:) = FcLDA(:,:,:) + aC*(FcGGA(:,:,:) - FcLDA(:,:,:))

4
src/eDFT/unrestricted_lda_correlation_energy.f90
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@ -34,6 +34,10 @@ subroutine unrestricted_lda_correlation_energy(DFA,nEns,wEns,nGrid,weight,rho,Ec
! Vosko, Wilk and Nusair's functional V: Can. J. Phys. 58 (1980) 1200
case ('VWN3')
call UVWN3_lda_correlation_energy(nGrid,weight,rho,Ec)
case ('VWN5')
call UVWN5_lda_correlation_energy(nGrid,weight,rho,Ec)

4
src/eDFT/unrestricted_lda_correlation_individual_energy.f90
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@ -26,6 +26,10 @@ subroutine unrestricted_lda_correlation_individual_energy(DFA,LDA_centered,nEns,
! Vosko, Wilk and Nusair's functional V: Can. J. Phys. 58 (1980) 1200
case ('VWN3')
call UVWN3_lda_correlation_individual_energy(nGrid,weight,rhow,rho,Ec)
case ('VWN5')
call UVWN5_lda_correlation_individual_energy(nGrid,weight,rhow,rho,Ec)

4
src/eDFT/unrestricted_lda_correlation_potential.f90
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@ -38,6 +38,10 @@ include 'parameters.h'
! Vosko, Wilk and Nusair's functional V: Can. J. Phys. 58 (1980) 1200
case ('VWN3')
call UVWN3_lda_correlation_potential(nGrid,weight(:),nBas,AO(:,:),rho(:,:),Fc(:,:,:))
case ('VWN5')
call UVWN5_lda_correlation_potential(nGrid,weight(:),nBas,AO(:,:),rho(:,:),Fc(:,:,:))