2020-04-07 11:03:19 +02:00
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subroutine ec_md_pbe_on_top_general(mu,rho_a,rho_b,grad_rho_a,grad_rho_b,on_top,eps_c_md_on_top_PBE)
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implicit none
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BEGIN_DOC
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!
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! General e_cmd functional interpolating between :
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!
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! +) the large mu behaviour in cst/(\mu^3) on-top
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!
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! +) mu= 0 with the usal ec_pbe at
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!
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! Depends on : mu, the density (rho_a,rho_b), the square of the density gradient (grad_rho_a,grad_rho_b)
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!
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! the flavour of on-top densiyt (on_top) you fill in: in principle it should be the exact on-top
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!
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! The form of the functional was originally introduced in JCP, 150, 084103 1-10 (2019)
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!
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END_DOC
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double precision, intent(in) :: mu,rho_a,rho_b,grad_rho_a(3),grad_rho_b(3),on_top
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double precision, intent(out) :: eps_c_md_on_top_PBE
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double precision :: pi, e_pbe,beta,denom
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double precision :: grad_rho_a_2,grad_rho_b_2,grad_rho_a_b
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double precision :: rhoc,rhoo,sigmacc,sigmaco,sigmaoo,vrhoc,vrhoo,vsigmacc,vsigmaco,vsigmaoo
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integer :: m
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pi = 4.d0 * datan(1.d0)
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eps_c_md_on_top_PBE = 0.d0
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2020-04-23 12:42:06 +02:00
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! convertion from (alpha,beta) formalism to (closed, open) formalism for the density
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call rho_ab_to_rho_oc(rho_a,rho_b,rhoo,rhoc)
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if(rhoc.lt.1.d-10)then
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return
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else if(on_top/(rhoc**2) .lt. 1.d-6)then
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return
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endif
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2020-04-07 11:03:19 +02:00
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grad_rho_a_2 = 0.d0
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grad_rho_b_2 = 0.d0
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grad_rho_a_b = 0.d0
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do m = 1, 3
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grad_rho_a_2 += grad_rho_a(m)*grad_rho_a(m)
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grad_rho_b_2 += grad_rho_b(m)*grad_rho_b(m)
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grad_rho_a_b += grad_rho_a(m)*grad_rho_b(m)
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enddo
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2020-04-23 12:42:06 +02:00
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! same same for gradients : convertion from (alpha,beta) formalism to (closed, open) formalism
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2020-04-07 11:03:19 +02:00
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call grad_rho_ab_to_grad_rho_oc(grad_rho_a_2,grad_rho_b_2,grad_rho_a_b,sigmaoo,sigmacc,sigmaco)
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! usual PBE correlation energy using the density, spin polarization and density gradients for alpha/beta electrons
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call ec_pbe_only(0.d0,rhoc,rhoo,sigmacc,sigmaco,sigmaoo,e_PBE)
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denom = (-2.d0+sqrt(2d0))*sqrt(2.d0*pi)* on_top
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if (dabs(denom) > 1.d-12) then
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! quantity of Eq. (26)
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beta = (3.d0*e_PBE)/denom
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eps_c_md_on_top_PBE = e_PBE/(1.d0+beta*mu**3)
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else
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eps_c_md_on_top_PBE =0.d0
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endif
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end
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