184 lines
6.9 KiB
Fortran
184 lines
6.9 KiB
Fortran
BEGIN_PROVIDER [double precision, ecmd_pbe_on_top_mu_of_r, (N_states)]
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BEGIN_DOC
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!
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! Ecmd functional evaluated with mu(r) and depending on
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! +) the on-top pair density
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!
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! +) the total density, density gradients
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!
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! +) the spin density
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!
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! Defined originally in Eq. (25) of JCP, 150, 084103 1-10 (2019) for RS-DFT calculations, but evaluated with mu(r).
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!
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! Such a functional is built by interpolating between two regimes :
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!
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! +) 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
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!
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! +) mu= 0 with the usal ec_pbe(rho_a,rho_b,grad_rho_a,grad_rho_b)
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!
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! 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
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!
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! Such an asymptotic expansion was introduced in P. Gori-Giorgi and A. Savin, Phys. Rev. A73, 032506 (2006)
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!
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END_DOC
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implicit none
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double precision :: weight
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double precision :: eps_c_md_on_top_PBE,on_top_extrap,mu_correction_of_on_top
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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),on_top
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ecmd_pbe_on_top_mu_of_r = 0.d0
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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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! depends on (rho_a, rho_b) <==> (rho_tot,spin_pol)
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rho_a = one_e_dm_and_grad_alpha_in_r(4,ipoint,istate)
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rho_b = one_e_dm_and_grad_beta_in_r(4,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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if(mu_of_r_potential == "cas_ful")then
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! You take the on-top of the CAS wave function which is computed with mu(r)
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on_top = on_top_cas_mu_r(ipoint,istate)
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else
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! You take the on-top of the CAS wave function computed separately
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on_top = total_cas_on_top_density(ipoint,istate)
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endif
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! We take the extrapolated on-top pair density
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on_top_extrap = mu_correction_of_on_top(mu,on_top)
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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)
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ecmd_pbe_on_top_mu_of_r(istate) += eps_c_md_on_top_PBE * weight
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enddo
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enddo
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END_PROVIDER
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BEGIN_PROVIDER [double precision, ecmd_pbe_on_top_su_mu_of_r, (N_states)]
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BEGIN_DOC
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!
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! Ecmd functional evaluated with mu(r) and depending on
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! +) the on-top pair density
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!
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! +) the total density, density gradients
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!
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! +) !!!!! NO SPIN POLAIRIZATION !!!!!
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!
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! Defined originally in Eq. (25) of JCP, 150, 084103 1-10 (2019) for RS-DFT calculations, but evaluated with mu(r).
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!
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! Such a functional is built by interpolating between two regimes :
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!
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! +) 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
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!
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! +) mu= 0 with the usal ec_pbe(rho_a,rho_b,grad_rho_a,grad_rho_b)
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!
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! 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
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!
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! Such an asymptotic expansion was introduced in P. Gori-Giorgi and A. Savin, Phys. Rev. A73, 032506 (2006)
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!
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END_DOC
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implicit none
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double precision :: weight
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double precision :: eps_c_md_on_top_PBE,on_top_extrap,mu_correction_of_on_top
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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),on_top,density
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ecmd_pbe_on_top_su_mu_of_r = 0.d0
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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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! rho_a = rho_b = rho_tot/2 ==> NO SPIN POLARIZATION
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rho_a = 0.5d0 * density
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rho_b = 0.5d0 * density
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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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if(mu_of_r_potential == "cas_ful")then
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! You take the on-top of the CAS wave function which is computed with mu(r)
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on_top = on_top_cas_mu_r(ipoint,istate)
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else
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! You take the on-top of the CAS wave function computed separately
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on_top = total_cas_on_top_density(ipoint,istate)
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endif
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! We take the extrapolated on-top pair density
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on_top_extrap = mu_correction_of_on_top(mu,on_top)
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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)
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ecmd_pbe_on_top_su_mu_of_r(istate) += eps_c_md_on_top_PBE * weight
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enddo
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enddo
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END_PROVIDER
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BEGIN_PROVIDER [double precision, ecmd_pbe_on_top_no_extrap_su_mu_of_r, (N_states)]
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BEGIN_DOC
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!
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! Ecmd functional evaluated with mu(r) and depending on
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! +) the on-top pair density
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!
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! +) the total density, density gradients
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!
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! +) !!!!! NO SPIN POLAIRIZATION !!!!!
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!
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! Defined originally in Eq. (25) of JCP, 150, 084103 1-10 (2019) for RS-DFT calculations, but evaluated with mu(r).
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!
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! Such a functional is built by interpolating between two regimes :
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!
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! +) 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
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!
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! +) mu= 0 with the usal ec_pbe(rho_a,rho_b,grad_rho_a,grad_rho_b)
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!
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! 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
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!
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! Such an asymptotic expansion was introduced in P. Gori-Giorgi and A. Savin, Phys. Rev. A73, 032506 (2006)
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!
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END_DOC
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implicit none
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double precision :: weight
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double precision :: eps_c_md_on_top_PBE,on_top_extrap,mu_correction_of_on_top
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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),on_top,density
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ecmd_pbe_on_top_no_extrap_su_mu_of_r = 0.d0
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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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! rho_a = rho_b = rho_tot/2 ==> NO SPIN POLARIZATION
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rho_a = 0.5d0 * density
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rho_b = 0.5d0 * density
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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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if(mu_of_r_potential == "cas_ful")then
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! You take the on-top of the CAS wave function which is computed with mu(r)
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on_top = on_top_cas_mu_r(ipoint,istate)
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else
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! You take the on-top of the CAS wave function computed separately
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on_top = total_cas_on_top_density(ipoint,istate)
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endif
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! We DO NOT take the extrapolated on-top pair density
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on_top_extrap = on_top
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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)
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ecmd_pbe_on_top_no_extrap_su_mu_of_r(istate) += eps_c_md_on_top_PBE * weight
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enddo
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enddo
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END_PROVIDER
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