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