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qp2/src/basis_correction/pbe_on_top.irp.f
Emmanuel Giner bef6175ee4 minor modifs
2020-04-15 17:00:15 +02:00

184 lines
7.0 KiB
Fortran

BEGIN_PROVIDER [double precision, ecmd_pbe_on_top_mu_of_r, (N_states)]
BEGIN_DOC
!
! Ecmd functional evaluated with mu(r) and depending on
! +) the on-top pair density
!
! +) the total density, density gradients
!
! +) the spin density
!
! Defined originally in Eq. (25) of JCP, 150, 084103 1-10 (2019) for RS-DFT calculations, but evaluated with mu(r).
!
! Such a functional is built by interpolating between two regimes :
!
! +) the large mu behaviour in cst/(\mu^3) \int dr on-top(r) where on-top(r) is supposed to be the exact on-top of the system
!
! +) mu= 0 with the usal ec_pbe(rho_a,rho_b,grad_rho_a,grad_rho_b)
!
! Here the approximation to the exact on-top is done through the assymptotic expansion (in \mu) of the exact on-top pair density (see Eq. 29) but with a mu(r) instead of a constant mu
!
! Such an asymptotic expansion was introduced in P. Gori-Giorgi and A. Savin, Phys. Rev. A73, 032506 (2006)
!
END_DOC
implicit none
double precision :: weight
double precision :: eps_c_md_on_top_PBE,on_top_extrap,mu_correction_of_on_top
integer :: ipoint,istate
double precision :: eps_c_md_PBE,mu,rho_a,rho_b,grad_rho_a(3),grad_rho_b(3),on_top
ecmd_pbe_on_top_mu_of_r = 0.d0
do istate = 1, N_states
do ipoint = 1, n_points_final_grid
weight = final_weight_at_r_vector(ipoint)
mu = mu_of_r_prov(ipoint,istate)
! depends on (rho_a, rho_b) <==> (rho_tot,spin_pol)
rho_a = one_e_dm_and_grad_alpha_in_r(4,ipoint,istate)
rho_b = one_e_dm_and_grad_beta_in_r(4,ipoint,istate)
grad_rho_a(1:3) = one_e_dm_and_grad_alpha_in_r(1:3,ipoint,istate)
grad_rho_b(1:3) = one_e_dm_and_grad_beta_in_r(1:3,ipoint,istate)
if(mu_of_r_potential == "cas_ful")then
! You take the on-top of the CAS wave function which is computed with mu(r)
on_top = on_top_cas_mu_r(ipoint,istate)
else
! You take the on-top of the CAS wave function computed separately
on_top = total_cas_on_top_density(ipoint,istate)
endif
! We take the extrapolated on-top pair density * 2 because of normalization
on_top_extrap = 2.d0 * mu_correction_of_on_top(mu,on_top)
call ec_md_pbe_on_top_general(mu,rho_a,rho_b,grad_rho_a,grad_rho_b,on_top_extrap,eps_c_md_on_top_PBE)
ecmd_pbe_on_top_mu_of_r(istate) += eps_c_md_on_top_PBE * weight
enddo
enddo
END_PROVIDER
BEGIN_PROVIDER [double precision, ecmd_pbe_on_top_su_mu_of_r, (N_states)]
BEGIN_DOC
!
! Ecmd functional evaluated with mu(r) and depending on
! +) the on-top pair density
!
! +) the total density, density gradients
!
! +) !!!!! NO SPIN POLAIRIZATION !!!!!
!
! Defined originally in Eq. (25) of JCP, 150, 084103 1-10 (2019) for RS-DFT calculations, but evaluated with mu(r).
!
! Such a functional is built by interpolating between two regimes :
!
! +) the large mu behaviour in cst/(\mu^3) \int dr on-top(r) where on-top(r) is supposed to be the exact on-top of the system
!
! +) mu= 0 with the usal ec_pbe(rho_a,rho_b,grad_rho_a,grad_rho_b)
!
! Here the approximation to the exact on-top is done through the assymptotic expansion (in \mu) of the exact on-top pair density (see Eq. 29) but with a mu(r) instead of a constant mu
!
! Such an asymptotic expansion was introduced in P. Gori-Giorgi and A. Savin, Phys. Rev. A73, 032506 (2006)
!
END_DOC
implicit none
double precision :: weight
double precision :: eps_c_md_on_top_PBE,on_top_extrap,mu_correction_of_on_top
integer :: ipoint,istate
double precision :: eps_c_md_PBE,mu,rho_a,rho_b,grad_rho_a(3),grad_rho_b(3),on_top,density
ecmd_pbe_on_top_su_mu_of_r = 0.d0
do istate = 1, N_states
do ipoint = 1, n_points_final_grid
weight = final_weight_at_r_vector(ipoint)
mu = mu_of_r_prov(ipoint,istate)
density = one_e_dm_and_grad_alpha_in_r(4,ipoint,istate) + one_e_dm_and_grad_beta_in_r(4,ipoint,istate)
! rho_a = rho_b = rho_tot/2 ==> NO SPIN POLARIZATION
rho_a = 0.5d0 * density
rho_b = 0.5d0 * density
grad_rho_a(1:3) = one_e_dm_and_grad_alpha_in_r(1:3,ipoint,istate)
grad_rho_b(1:3) = one_e_dm_and_grad_beta_in_r(1:3,ipoint,istate)
if(mu_of_r_potential == "cas_ful")then
! You take the on-top of the CAS wave function which is computed with mu(r)
on_top = on_top_cas_mu_r(ipoint,istate)
else
! You take the on-top of the CAS wave function computed separately
on_top = total_cas_on_top_density(ipoint,istate)
endif
! We take the extrapolated on-top pair density * 2 because of normalization
on_top_extrap = 2.d0 * mu_correction_of_on_top(mu,on_top)
call ec_md_pbe_on_top_general(mu,rho_a,rho_b,grad_rho_a,grad_rho_b,on_top_extrap,eps_c_md_on_top_PBE)
ecmd_pbe_on_top_su_mu_of_r(istate) += eps_c_md_on_top_PBE * weight
enddo
enddo
END_PROVIDER
BEGIN_PROVIDER [double precision, ecmd_pbe_on_top_no_extrap_su_mu_of_r, (N_states)]
BEGIN_DOC
!
! Ecmd functional evaluated with mu(r) and depending on
! +) the on-top pair density
!
! +) the total density, density gradients
!
! +) !!!!! NO SPIN POLAIRIZATION !!!!!
!
! Defined originally in Eq. (25) of JCP, 150, 084103 1-10 (2019) for RS-DFT calculations, but evaluated with mu(r).
!
! Such a functional is built by interpolating between two regimes :
!
! +) the large mu behaviour in cst/(\mu^3) \int dr on-top(r) where on-top(r) is supposed to be the exact on-top of the system
!
! +) mu= 0 with the usal ec_pbe(rho_a,rho_b,grad_rho_a,grad_rho_b)
!
! Here the approximation to the exact on-top is done through the assymptotic expansion (in \mu) of the exact on-top pair density (see Eq. 29) but with a mu(r) instead of a constant mu
!
! Such an asymptotic expansion was introduced in P. Gori-Giorgi and A. Savin, Phys. Rev. A73, 032506 (2006)
!
END_DOC
implicit none
double precision :: weight
double precision :: eps_c_md_on_top_PBE,on_top_extrap,mu_correction_of_on_top
integer :: ipoint,istate
double precision :: eps_c_md_PBE,mu,rho_a,rho_b,grad_rho_a(3),grad_rho_b(3),on_top,density
ecmd_pbe_on_top_no_extrap_su_mu_of_r = 0.d0
do istate = 1, N_states
do ipoint = 1, n_points_final_grid
weight = final_weight_at_r_vector(ipoint)
mu = mu_of_r_prov(ipoint,istate)
density = one_e_dm_and_grad_alpha_in_r(4,ipoint,istate) + one_e_dm_and_grad_beta_in_r(4,ipoint,istate)
! rho_a = rho_b = rho_tot/2 ==> NO SPIN POLARIZATION
rho_a = 0.5d0 * density
rho_b = 0.5d0 * density
grad_rho_a(1:3) = one_e_dm_and_grad_alpha_in_r(1:3,ipoint,istate)
grad_rho_b(1:3) = one_e_dm_and_grad_beta_in_r(1:3,ipoint,istate)
if(mu_of_r_potential == "cas_ful")then
! You take the on-top of the CAS wave function which is computed with mu(r)
on_top = on_top_cas_mu_r(ipoint,istate)
else
! You take the on-top of the CAS wave function computed separately
on_top = total_cas_on_top_density(ipoint,istate)
endif
! We DO NOT take the extrapolated on-top pair density, but there is * 2 because of normalization
on_top_extrap = 2.d0 * on_top
call ec_md_pbe_on_top_general(mu,rho_a,rho_b,grad_rho_a,grad_rho_b,on_top_extrap,eps_c_md_on_top_PBE)
ecmd_pbe_on_top_no_extrap_su_mu_of_r(istate) += eps_c_md_on_top_PBE * weight
enddo
enddo
END_PROVIDER