100 lines
3.1 KiB
Fortran
100 lines
3.1 KiB
Fortran
double precision function ec_scan(rho_a,rho_b,tau,grad_rho_2)
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include 'constants.include.F'
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implicit none
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double precision, intent(in) :: rho_a,rho_b,tau,grad_rho_2
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double precision :: cst_13,cst_23,cst_43,cst_53,rho_inv,cst_18,cst_3pi2
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double precision :: thr,nup,ndo,xi,s,spin_d,drho,drho2,rho,inv_1alph,e_c_lsda1,h0
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double precision :: rs,t_w,t_unif,ds_xi,alpha,fc_alpha,step_f,cst_1alph,beta_inf
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double precision :: c_1c,c_2c,d_c,e_c_ldsa1,h1,phi,t,beta_rs,gama,a,w_1,g_at2,phi_3,e_c_1
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double precision :: b_1c,b_2c,b_3c,dx_xi,gc_xi,e_c_lsda0,w_0,g_inf,cx_xi,x_inf,f0,e_c_0
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thr = 1.d-12
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nup = max(rho_a,thr)
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ndo = max(rho_b,thr)
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rho = nup + ndo
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ec_scan = 0.d0
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if((rho).lt.thr)return
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! constants ...
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rho_inv = 1.d0/rho
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cst_13 = 1.d0/3.d0
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cst_23 = 2.d0 * cst_13
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cst_43 = 4.d0 * cst_13
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cst_53 = 5.d0 * cst_13
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cst_18 = 1.d0/8.d0
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cst_3pi2 = 3.d0 * pi*pi
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drho2 = max(grad_rho_2,thr)
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drho = dsqrt(drho2)
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if((nup-ndo).gt.0.d0)then
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spin_d = max(nup-ndo,thr)
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else
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spin_d = min(nup-ndo,-thr)
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endif
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c_1c = 0.64d0
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c_2c = 1.5d0
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d_c = 0.7d0
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b_1c = 0.0285764d0
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b_2c = 0.0889d0
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b_3c = 0.125541d0
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gama = 0.031091d0
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! correlation energy lsda1
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call ec_only_lda_sr(0.d0,nup,ndo,e_c_lsda1)
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! correlation energy per particle
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e_c_lsda1 = e_c_lsda1/rho
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xi = spin_d/rho
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rs = (cst_43 * pi * rho)**(-cst_13)
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s = drho/( 2.d0 * cst_3pi2**(cst_13) * rho**cst_43 )
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t_w = drho2 * cst_18 * rho_inv
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ds_xi = 0.5d0 * ( (1.d0+xi)**cst_53 + (1.d0 - xi)**cst_53)
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t_unif = 0.3d0 * (cst_3pi2)**cst_23 * rho**cst_53*ds_xi
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t_unif = max(t_unif,thr)
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alpha = (tau - t_w)/t_unif
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cst_1alph= 1.d0 - alpha
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if(cst_1alph.gt.0.d0)then
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cst_1alph= max(cst_1alph,thr)
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else
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cst_1alph= min(cst_1alph,-thr)
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endif
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inv_1alph= 1.d0/cst_1alph
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phi = 0.5d0 * ( (1.d0+xi)**cst_23 + (1.d0 - xi)**cst_23)
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phi_3 = phi*phi*phi
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t = (cst_3pi2/16.d0)**cst_13 * s / (phi * rs**0.5d0)
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w_1 = dexp(-e_c_lsda1/(gama * phi_3)) - 1.d0
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a = beta_rs(rs) /(gama * w_1)
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g_at2 = 1.d0/(1.d0 + 4.d0 * a*t*t)**0.25d0
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h1 = gama * phi_3 * dlog(1.d0 + w_1 * (1.d0 - g_at2))
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! interpolation function
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if(cst_1alph.gt.0.d0)then
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fc_alpha = dexp(-c_1c * alpha * inv_1alph)
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else
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fc_alpha = - d_c * dexp(c_2c * inv_1alph)
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endif
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! first part of the correlation energy
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e_c_1 = e_c_lsda1 + h1
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dx_xi = 0.5d0 * ( (1.d0+xi)**cst_43 + (1.d0 - xi)**cst_43)
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gc_xi = (1.d0 - 2.3631d0 * (dx_xi - 1.d0) ) * (1.d0 - xi**12.d0)
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e_c_lsda0= - b_1c / (1.d0 + b_2c * rs**0.5d0 + b_3c * rs)
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w_0 = dexp(-e_c_lsda0/b_1c) - 1.d0
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beta_inf = 0.066725d0 * 0.1d0 / 0.1778d0
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cx_xi = -3.d0/(4.d0*pi) * (9.d0 * pi/4.d0)**cst_13 * dx_xi
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x_inf = 0.128026d0
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f0 = -0.9d0
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g_inf = 1.d0/(1.d0 + 4.d0 * x_inf * s*s)**0.25d0
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h0 = b_1c * dlog(1.d0 + w_0 * (1.d0 - g_inf))
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e_c_0 = (e_c_lsda0 + h0) * gc_xi
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ec_scan = e_c_1 + fc_alpha * (e_c_0 - e_c_1)
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end
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double precision function beta_rs(rs)
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implicit none
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double precision, intent(in) ::rs
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beta_rs = 0.066725d0 * (1.d0 + 0.1d0 * rs)/(1.d0 + 0.1778d0 * rs)
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end
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