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_full")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 on_top_extrap = 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_full")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 on_top_extrap = 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_full")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 on_top_extrap = 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