diff --git a/input/dft b/input/dft index 3d705c5..c783a3f 100644 --- a/input/dft +++ b/input/dft @@ -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 diff --git a/input/methods b/input/methods index 1fb9bee..94ad703 100644 --- a/input/methods +++ b/input/methods @@ -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 diff --git a/input/options b/input/options index 24bc7ba..f2afee0 100644 --- a/input/options +++ b/input/options @@ -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 diff --git a/src/MBPT/Bethe_Salpeter.f90 b/src/MBPT/Bethe_Salpeter.f90 index 8ca6757..4d8621d 100644 --- a/src/MBPT/Bethe_Salpeter.f90 +++ b/src/MBPT/Bethe_Salpeter.f90 @@ -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 diff --git a/src/MBPT/Bethe_Salpeter_dynamic_perturbation.f90 b/src/MBPT/Bethe_Salpeter_dynamic_perturbation.f90 index c960a75..88dcc08 100644 --- a/src/MBPT/Bethe_Salpeter_dynamic_perturbation.f90 +++ b/src/MBPT/Bethe_Salpeter_dynamic_perturbation.f90 @@ -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) diff --git a/src/MBPT/qsUGW.f90 b/src/MBPT/qsUGW.f90 index 2128d0f..09d8cef 100644 --- a/src/MBPT/qsUGW.f90 +++ b/src/MBPT/qsUGW.f90 @@ -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 diff --git a/src/MBPT/unrestricted_Bethe_Salpeter.f90 b/src/MBPT/unrestricted_Bethe_Salpeter.f90 index 5b0436b..a483c0e 100644 --- a/src/MBPT/unrestricted_Bethe_Salpeter.f90 +++ b/src/MBPT/unrestricted_Bethe_Salpeter.f90 @@ -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) diff --git a/src/MBPT/unrestricted_Bethe_Salpeter_dynamic_perturbation.f90 b/src/MBPT/unrestricted_Bethe_Salpeter_dynamic_perturbation.f90 index 4bb3cd7..56a8ed9 100644 --- a/src/MBPT/unrestricted_Bethe_Salpeter_dynamic_perturbation.f90 +++ b/src/MBPT/unrestricted_Bethe_Salpeter_dynamic_perturbation.f90 @@ -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) diff --git a/src/eDFT/UVWN3_lda_correlation_energy.f90 b/src/eDFT/UVWN3_lda_correlation_energy.f90 new file mode 100644 index 0000000..161f1ad --- /dev/null +++ b/src/eDFT/UVWN3_lda_correlation_energy.f90 @@ -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 diff --git a/src/eDFT/UVWN3_lda_correlation_individual_energy.f90 b/src/eDFT/UVWN3_lda_correlation_individual_energy.f90 new file mode 100644 index 0000000..2448381 --- /dev/null +++ b/src/eDFT/UVWN3_lda_correlation_individual_energy.f90 @@ -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 diff --git a/src/eDFT/UVWN3_lda_correlation_potential.f90 b/src/eDFT/UVWN3_lda_correlation_potential.f90 new file mode 100644 index 0000000..47f8cd9 --- /dev/null +++ b/src/eDFT/UVWN3_lda_correlation_potential.f90 @@ -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 diff --git a/src/eDFT/unrestricted_hybrid_correlation_energy.f90 b/src/eDFT/unrestricted_hybrid_correlation_energy.f90 index 4a3413e..e8a286b 100644 --- a/src/eDFT/unrestricted_hybrid_correlation_energy.f90 +++ b/src/eDFT/unrestricted_hybrid_correlation_energy.f90 @@ -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(:)) diff --git a/src/eDFT/unrestricted_hybrid_correlation_potential.f90 b/src/eDFT/unrestricted_hybrid_correlation_potential.f90 index 96a9935..4b37441 100644 --- a/src/eDFT/unrestricted_hybrid_correlation_potential.f90 +++ b/src/eDFT/unrestricted_hybrid_correlation_potential.f90 @@ -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(:,:,:)) diff --git a/src/eDFT/unrestricted_lda_correlation_energy.f90 b/src/eDFT/unrestricted_lda_correlation_energy.f90 index 938ec59..4837f1e 100644 --- a/src/eDFT/unrestricted_lda_correlation_energy.f90 +++ b/src/eDFT/unrestricted_lda_correlation_energy.f90 @@ -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) diff --git a/src/eDFT/unrestricted_lda_correlation_individual_energy.f90 b/src/eDFT/unrestricted_lda_correlation_individual_energy.f90 index 1db2a25..6cdb3b9 100644 --- a/src/eDFT/unrestricted_lda_correlation_individual_energy.f90 +++ b/src/eDFT/unrestricted_lda_correlation_individual_energy.f90 @@ -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) diff --git a/src/eDFT/unrestricted_lda_correlation_potential.f90 b/src/eDFT/unrestricted_lda_correlation_potential.f90 index 549bc55..e66b357 100644 --- a/src/eDFT/unrestricted_lda_correlation_potential.f90 +++ b/src/eDFT/unrestricted_lda_correlation_potential.f90 @@ -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(:,:,:))