BEGIN_PROVIDER [double precision, ecmd_pbe_ueg_eff_xi_mu_of_r, (N_states)] BEGIN_DOC ! ecmd_pbe_ueg_eff_xi_mu_of_r = multi-determinantal Ecmd within the PBE-UEG and effective spin polarization approximation with mu(r), ! ! see Eqs. 30 in ??????????? ! ! Based on the PBE-on-top functional (see Eqs. 26, 27 of J. Chem. Phys.150, 084103 (2019); doi: 10.1063/1.5082638) ! ! and replaces the approximation of the exact on-top pair density by the exact on-top of the UEG ! ! !!!! BUT !!!! with an EFFECTIVE SPIN POLARIZATION DEPENDING ON THE ON-TOP PAIR DENSITY ! ! See P. Perdew, A. Savin, and K. Burke, Phys. Rev. A 51, 4531 (1995). for original Ref., and Eq. 29 in ??????????? END_DOC implicit none double precision :: weight,density integer :: ipoint,istate double precision :: eps_c_md_PBE,mu,rho_a,rho_b,grad_rho_a(3),grad_rho_b(3),g0_UEG_mu_inf,on_top ecmd_pbe_ueg_eff_xi_mu_of_r = 0.d0 print*,'Providing ecmd_pbe_ueg_eff_xi_mu_of_r ...' call wall_time(wall0) 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) ! We use the effective spin density to define rho_a/rho_b rho_a = 0.5d0 * (density + effective_spin_dm(ipoint,istate)) rho_b = 0.5d0 * (density - effective_spin_dm(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) ! We take the on-top pair density of the UEG which is (1-zeta^2) rhoc^2 g0 = 4 rhoa * rhob * g0 ! with the effective rho_a and rho_b on_top = 4.d0 * rho_a * rho_b * g0_UEG_mu_inf(rho_a,rho_b) call ec_md_pbe_on_top_general(mu,rho_a,rho_b,grad_rho_a,grad_rho_b,on_top,eps_c_md_PBE) ecmd_pbe_ueg_eff_xi_mu_of_r(istate) += eps_c_md_PBE * weight enddo enddo double precision :: wall1, wall0 call wall_time(wall1) print*,'Time for the ecmd_pbe_ueg_eff_xi_mu_of_r:',wall1-wall0 END_PROVIDER BEGIN_PROVIDER [double precision, ecmd_lda_eff_xi_mu_of_r, (N_states)] BEGIN_DOC ! ecmd_lda_eff_xi_mu_of_r = multi-determinantal Ecmd within the LDA and effective spin polarization approximation with mu(r), ! ! corresponds to equation 40 in J. Chem. Phys. 149, 194301 (2018); https://doi.org/10.1063/1.5052714 ! ! !!!! BUT !!!! with an EFFECTIVE SPIN POLARIZATION DEPENDING ON THE ON-TOP PAIR DENSITY ! ! See P. Perdew, A. Savin, and K. Burke, Phys. Rev. A 51, 4531 (1995). for original Ref., and Eq. 29 in ??????????? END_DOC implicit none integer :: ipoint,istate double precision :: rho_a, rho_b, ec logical :: dospin double precision :: wall0,wall1,weight,mu,density dospin = .true. ! JT dospin have to be set to true for open shell print*,'Providing ecmd_lda_eff_xi_mu_of_r ...' ecmd_lda_eff_xi_mu_of_r = 0.d0 call wall_time(wall0) do istate = 1, N_states do ipoint = 1, n_points_final_grid mu = mu_of_r_prov(ipoint,istate) weight = final_weight_at_r_vector(ipoint) 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 = 0.5d0 * (density + effective_spin_dm(ipoint,istate)) rho_b = 0.5d0 * (density - effective_spin_dm(ipoint,istate)) call ESRC_MD_LDAERF (mu,rho_a,rho_b,dospin,ec) if(isnan(ec))then print*,'ec is nan' stop endif ecmd_lda_eff_xi_mu_of_r(istate) += weight * ec enddo enddo call wall_time(wall1) print*,'Time for ecmd_lda_eff_xi_mu_of_r :',wall1-wall0 END_PROVIDER