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184 lines
7.0 KiB
Fortran
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 ontop pair density


!


! +) the total density, density gradients


!


! +) the spin density


!


! Defined originally in Eq. (25) of JCP, 150, 084103 110 (2019) for RSDFT 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 ontop(r) where ontop(r) is supposed to be the exact ontop 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 ontop is done through the assymptotic expansion (in \mu) of the exact ontop pair density (see Eq. 29) but with a mu(r) instead of a constant mu


!


! Such an asymptotic expansion was introduced in P. GoriGiorgi 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 ontop of the CAS wave function which is computed with mu(r)


on_top = on_top_cas_mu_r(ipoint,istate)


else


! You take the ontop of the CAS wave function computed separately


on_top = total_cas_on_top_density(ipoint,istate)


endif


! We take the extrapolated ontop 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 ontop pair density


!


! +) the total density, density gradients


!


! +) !!!!! NO SPIN POLAIRIZATION !!!!!


!


! Defined originally in Eq. (25) of JCP, 150, 084103 110 (2019) for RSDFT 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 ontop(r) where ontop(r) is supposed to be the exact ontop 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 ontop is done through the assymptotic expansion (in \mu) of the exact ontop pair density (see Eq. 29) but with a mu(r) instead of a constant mu


!


! Such an asymptotic expansion was introduced in P. GoriGiorgi 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 ontop of the CAS wave function which is computed with mu(r)


on_top = on_top_cas_mu_r(ipoint,istate)


else


! You take the ontop of the CAS wave function computed separately


on_top = total_cas_on_top_density(ipoint,istate)


endif


! We take the extrapolated ontop 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 ontop pair density


!


! +) the total density, density gradients


!


! +) !!!!! NO SPIN POLAIRIZATION !!!!!


!


! Defined originally in Eq. (25) of JCP, 150, 084103 110 (2019) for RSDFT 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 ontop(r) where ontop(r) is supposed to be the exact ontop 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 ontop is done through the assymptotic expansion (in \mu) of the exact ontop pair density (see Eq. 29) but with a mu(r) instead of a constant mu


!


! Such an asymptotic expansion was introduced in P. GoriGiorgi 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 ontop of the CAS wave function which is computed with mu(r)


on_top = on_top_cas_mu_r(ipoint,istate)


else


! You take the ontop of the CAS wave function computed separately


on_top = total_cas_on_top_density(ipoint,istate)


endif


! We DO NOT take the extrapolated ontop 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




