mirror of
https://github.com/QuantumPackage/qp2.git
synced 2024-08-31 05:03:40 +02:00
195 lines
7.1 KiB
Fortran
195 lines
7.1 KiB
Fortran
![]() |
|
||
|
subroutine ecmd_pbe_ueg_at_r(mu,r,eps_c_md_PBE)
|
||
|
implicit none
|
||
|
BEGIN_DOC
|
||
|
! provides the integrand of Eq. (13) of Phys.Chem.Lett.2019, 10, 2931 2937
|
||
|
!
|
||
|
! !!! WARNING !!! This is the total integrand of Eq. (13), which is e_cmd * n
|
||
|
!
|
||
|
! such a function is based on the exact behaviour of the Ecmd at large mu
|
||
|
!
|
||
|
! but with the exact on-top estimated with that of the UEG
|
||
|
!
|
||
|
! You enter with r(3), you get out with eps_c_md_PBE(1:N_states)
|
||
|
END_DOC
|
||
|
double precision, intent(in) :: mu , r(3)
|
||
|
double precision, intent(out) :: eps_c_md_PBE(N_states)
|
||
|
double precision :: pi, e_PBE, beta
|
||
|
double precision :: aos_array(ao_num), grad_aos_array(3,ao_num)
|
||
|
double precision :: rho_a(N_states),rho_b(N_states)
|
||
|
double precision :: grad_rho_a(3,N_states),grad_rho_b(3,N_states)
|
||
|
double precision :: grad_rho_a_2(N_states),grad_rho_b_2(N_states),grad_rho_a_b(N_states)
|
||
|
double precision :: rhoc,rhoo,sigmacc,sigmaco,sigmaoo,vrhoc,vrhoo,vsigmacc,vsigmaco,vsigmaoo
|
||
|
double precision :: g0_UEG_mu_inf, denom
|
||
|
integer :: m, istate
|
||
|
|
||
|
pi = 4.d0 * datan(1.d0)
|
||
|
|
||
|
eps_c_md_PBE = 0.d0
|
||
|
call density_and_grad_alpha_beta_and_all_aos_and_grad_aos_at_r(r,rho_a,rho_b, grad_rho_a, grad_rho_b, aos_array, grad_aos_array)
|
||
|
grad_rho_a_2 = 0.d0
|
||
|
grad_rho_b_2 = 0.d0
|
||
|
grad_rho_a_b = 0.d0
|
||
|
do istate = 1, N_states
|
||
|
do m = 1, 3
|
||
|
grad_rho_a_2(istate) += grad_rho_a(m,istate)*grad_rho_a(m,istate)
|
||
|
grad_rho_b_2(istate) += grad_rho_b(m,istate)*grad_rho_b(m,istate)
|
||
|
grad_rho_a_b(istate) += grad_rho_a(m,istate)*grad_rho_b(m,istate)
|
||
|
enddo
|
||
|
enddo
|
||
|
do istate = 1, N_states
|
||
|
! convertion from (alpha,beta) formalism to (closed, open) formalism
|
||
|
call rho_ab_to_rho_oc(rho_a(istate),rho_b(istate),rhoo,rhoc)
|
||
|
call grad_rho_ab_to_grad_rho_oc(grad_rho_a_2(istate),grad_rho_b_2(istate),grad_rho_a_b(istate),sigmaoo,sigmacc,sigmaco)
|
||
|
call ec_pbe_only(0.d0,rhoc,rhoo,sigmacc,sigmaco,sigmaoo,e_PBE)
|
||
|
|
||
|
if(mu == 0.d0) then
|
||
|
eps_c_md_PBE(istate)=e_PBE
|
||
|
else
|
||
|
! note: the on-top pair density is (1-zeta^2) rhoc^2 g0 = 4 rhoa * rhob * g0
|
||
|
denom = (-2.d0+sqrt(2d0))*sqrt(2.d0*pi) * 4.d0*rho_a(istate)*rho_b(istate)*g0_UEG_mu_inf(rho_a(istate),rho_b(istate))
|
||
|
if (dabs(denom) > 1.d-12) then
|
||
|
beta = (3.d0*e_PBE)/denom
|
||
|
eps_c_md_PBE(istate)=e_PBE/(1.d0+beta*mu**3)
|
||
|
else
|
||
|
eps_c_md_PBE(istate)=0.d0
|
||
|
endif
|
||
|
endif
|
||
|
enddo
|
||
|
end
|
||
|
|
||
|
|
||
|
|
||
|
subroutine eps_c_md_PBE_from_density(mu,rho_a,rho_b, grad_rho_a, grad_rho_b,eps_c_md_PBE) ! EG
|
||
|
implicit none
|
||
|
BEGIN_DOC
|
||
|
! provides the integrand of Eq. (13) of Phys.Chem.Lett.2019, 10, 2931 2937
|
||
|
!
|
||
|
! !!! WARNING !!! This is the total integrand of Eq. (13), which is e_cmd * n
|
||
|
!
|
||
|
! such a function is based on the exact behaviour of the Ecmd at large mu
|
||
|
!
|
||
|
! but with the exact on-top estimated with that of the UEG
|
||
|
!
|
||
|
! You enter with the alpha/beta density and density gradients
|
||
|
!
|
||
|
! You get out with eps_c_md_PBE(1:N_states)
|
||
|
END_DOC
|
||
|
double precision, intent(in) :: mu(N_states) , rho_a(N_states),rho_b(N_states), grad_rho_a(3,N_states),grad_rho_b(3,N_states)
|
||
|
double precision, intent(out) :: eps_c_md_PBE(N_states)
|
||
|
double precision :: pi, e_PBE, beta
|
||
|
double precision :: aos_array(ao_num), grad_aos_array(3,ao_num)
|
||
|
double precision :: grad_rho_a_2(N_states),grad_rho_b_2(N_states),grad_rho_a_b(N_states)
|
||
|
double precision :: rhoc,rhoo,sigmacc,sigmaco,sigmaoo,vrhoc,vrhoo,vsigmacc,vsigmaco,vsigmaoo
|
||
|
double precision :: g0_UEG_mu_inf, denom
|
||
|
integer :: m, istate
|
||
|
|
||
|
pi = 4.d0 * datan(1.d0)
|
||
|
|
||
|
eps_c_md_PBE = 0.d0
|
||
|
grad_rho_a_2 = 0.d0
|
||
|
grad_rho_b_2 = 0.d0
|
||
|
grad_rho_a_b = 0.d0
|
||
|
do istate = 1, N_states
|
||
|
do m = 1, 3
|
||
|
grad_rho_a_2(istate) += grad_rho_a(m,istate)*grad_rho_a(m,istate)
|
||
|
grad_rho_b_2(istate) += grad_rho_b(m,istate)*grad_rho_b(m,istate)
|
||
|
grad_rho_a_b(istate) += grad_rho_a(m,istate)*grad_rho_b(m,istate)
|
||
|
enddo
|
||
|
enddo
|
||
|
do istate = 1, N_states
|
||
|
! convertion from (alpha,beta) formalism to (closed, open) formalism
|
||
|
call rho_ab_to_rho_oc(rho_a(istate),rho_b(istate),rhoo,rhoc)
|
||
|
call grad_rho_ab_to_grad_rho_oc(grad_rho_a_2(istate),grad_rho_b_2(istate),grad_rho_a_b(istate),sigmaoo,sigmacc,sigmaco)
|
||
|
call ec_pbe_only(0.d0,rhoc,rhoo,sigmacc,sigmaco,sigmaoo,e_PBE)
|
||
|
|
||
|
if(mu(istate) == 0.d0) then
|
||
|
eps_c_md_PBE(istate)=e_PBE
|
||
|
else
|
||
|
! note: the on-top pair density is (1-zeta^2) rhoc^2 g0 = 4 rhoa * rhob * g0
|
||
|
denom = (-2.d0+sqrt(2d0))*sqrt(2.d0*pi) * 4.d0*rho_a(istate)*rho_b(istate)*g0_UEG_mu_inf(rho_a(istate),rho_b(istate))
|
||
|
if (dabs(denom) > 1.d-12) then
|
||
|
beta = (3.d0*e_PBE)/denom
|
||
|
eps_c_md_PBE(istate)=e_PBE/(1.d0+beta*mu(istate)**3)
|
||
|
else
|
||
|
eps_c_md_PBE(istate)=0.d0
|
||
|
endif
|
||
|
endif
|
||
|
enddo
|
||
|
end
|
||
|
|
||
|
|
||
|
|
||
|
|
||
|
|
||
|
subroutine eps_c_md_PBE_at_grid_pt(mu,i_point,eps_c_md_PBE)
|
||
|
implicit none
|
||
|
BEGIN_DOC
|
||
|
! provides the integrand of Eq. (13) of Phys.Chem.Lett.2019, 10, 2931 2937
|
||
|
!
|
||
|
! !!! WARNING !!! This is the total integrand of Eq. (13), which is e_cmd * n
|
||
|
!
|
||
|
! such a function is based on the exact behaviour of the Ecmd at large mu
|
||
|
!
|
||
|
! but with the exact on-top estimated with that of the UEG
|
||
|
!
|
||
|
! You enter with the alpha/beta density and density gradients
|
||
|
!
|
||
|
! You get out with eps_c_md_PBE(1:N_states)
|
||
|
END_DOC
|
||
|
double precision, intent(in) :: mu
|
||
|
double precision, intent(out) :: eps_c_md_PBE(N_states)
|
||
|
integer, intent(in) :: i_point
|
||
|
double precision :: two_dm, pi, e_pbe,beta,mu_correction_of_on_top
|
||
|
double precision :: grad_rho_a(3),grad_rho_b(3)
|
||
|
double precision :: grad_rho_a_2,grad_rho_b_2,grad_rho_a_b
|
||
|
double precision :: rhoc,rhoo,ec_pbe_88
|
||
|
double precision :: delta,two_dm_corr,rho_a,rho_b
|
||
|
double precision :: grad_rho_2,denom,g0_UEG_mu_inf
|
||
|
double precision :: sigmacc,sigmaco,sigmaoo
|
||
|
integer :: m, istate
|
||
|
|
||
|
pi = 4.d0 * datan(1.d0)
|
||
|
|
||
|
eps_c_md_PBE = 0.d0
|
||
|
do istate = 1, N_states
|
||
|
! total and spin density
|
||
|
rhoc = one_e_dm_and_grad_alpha_in_r(4,i_point,istate) + one_e_dm_and_grad_beta_in_r(4,i_point,istate)
|
||
|
rhoo = one_e_dm_and_grad_alpha_in_r(4,i_point,istate) - one_e_dm_and_grad_beta_in_r(4,i_point,istate)
|
||
|
! gradients of the effective spin density
|
||
|
grad_rho_a_2 = 0.D0
|
||
|
grad_rho_b_2 = 0.D0
|
||
|
grad_rho_a_b = 0.D0
|
||
|
do m = 1, 3
|
||
|
grad_rho_a_2 += one_e_dm_and_grad_alpha_in_r(m,i_point,istate)**2.d0
|
||
|
grad_rho_b_2 += one_e_dm_and_grad_beta_in_r(m,i_point,istate) **2.d0
|
||
|
grad_rho_a_b += one_e_dm_and_grad_alpha_in_r(m,i_point,istate) * one_e_dm_and_grad_beta_in_r(m,i_point,istate)
|
||
|
enddo
|
||
|
sigmacc = grad_rho_a_2 + grad_rho_b_2 + 2.d0 * grad_rho_a_b
|
||
|
sigmaco = 0.d0
|
||
|
sigmaoo = 0.d0
|
||
|
rho_a = one_e_dm_and_grad_alpha_in_r(4,i_point,istate)
|
||
|
rho_b = one_e_dm_and_grad_beta_in_r(4,i_point,istate)
|
||
|
|
||
|
call ec_pbe_only(0.d0,rhoc,rhoo,sigmacc,sigmaco,sigmaoo,e_PBE)
|
||
|
if(e_PBE.gt.0.d0)then
|
||
|
print*,'PBE gt 0 with regular dens'
|
||
|
endif
|
||
|
if(mu == 0.d0) then
|
||
|
eps_c_md_PBE(istate)=e_PBE
|
||
|
else
|
||
|
! note: the on-top pair density is (1-zeta^2) rhoc^2 g0 = 4 rhoa * rhob * g0
|
||
|
denom = (-2.d0+dsqrt(2d0))*sqrt(2.d0*pi) * 4.d0*rho_a*rho_b*g0_UEG_mu_inf(rho_a,rho_b)
|
||
|
if (dabs(denom) > 1.d-12) then
|
||
|
beta = (3.d0*e_PBE)/denom
|
||
|
! Ecmd functional with the UEG ontop pair density when mu -> infty
|
||
|
! and the usual PBE correlation energy when mu = 0
|
||
|
eps_c_md_PBE(istate)=e_PBE/(1.d0+beta*mu**3)
|
||
|
else
|
||
|
eps_c_md_PBE(istate)=0.d0
|
||
|
endif
|
||
|
endif
|
||
|
enddo
|
||
|
end
|
||
|
|