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more cleaning in functionals
This commit is contained in:
Emmanuel Giner
parent
192854f771
commit
9d2d00f040
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@ -1,125 +0,0 @@
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subroutine give_all_stuffs_in_r_for_lyp_88(r,rho,rho_a,rho_b,grad_rho_a_2,grad_rho_b_2,grad_rho_2)
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implicit none
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double precision, intent(in) :: r(3)
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double precision, intent(out) :: rho_a(N_states),rho_b(N_states),grad_rho_a_2(N_states),grad_rho_b_2(N_states),grad_rho_2(N_states),rho(N_states)
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double precision :: grad_rho_a(3,N_states),grad_rho_b(3,N_states),grad_rho_a_b(N_states)
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double precision :: grad_aos_array(3,ao_num),aos_array(ao_num)
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call density_and_grad_alpha_beta_and_all_aos_and_grad_aos_at_r(r,rho_a,rho_b, grad_rho_a, grad_rho_b, aos_array, grad_aos_array)
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integer :: i,istate
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rho = rho_a + rho_b
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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 istate = 1, N_states
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do i = 1, 3
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grad_rho_a_2(istate) += grad_rho_a(i,istate) * grad_rho_a(i,istate)
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grad_rho_b_2(istate) += grad_rho_b(i,istate) * grad_rho_b(i,istate)
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grad_rho_a_b(istate) += grad_rho_a(i,istate) * grad_rho_b(i,istate)
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enddo
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enddo
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grad_rho_2 = grad_rho_a_2 + grad_rho_b_2 + 2.d0 * grad_rho_a_b
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end
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double precision function ec_lyp_88(rho,rho_a,rho_b,grad_rho_a_2,grad_rho_b_2,grad_rho_2)
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implicit none
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BEGIN_DOC
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! LYP functional of the Lee, Yan, Parr, Phys. Rev B 1988, Vol 37, page 785.
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! The expression used is the one by Miehlich, Savin, Stoll, Preuss, CPL, 1989 which gets rid of the laplacian of the density
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END_DOC
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include 'constants.include.F'
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! Input variables
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double precision, intent(in) :: rho,rho_a,rho_b,grad_rho_a_2,grad_rho_b_2,grad_rho_2
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! Local variables
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double precision :: a,b,c,d,c_f,omega,delta
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double precision :: rho_13,rho_inv_13,rho_83,rho_113,rho_inv_113,denom
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double precision :: thr,huge_num,rho_inv
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double precision :: cst_2_113,cst_8_3,rho_2,rho_a_2,rho_b_2
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double precision :: tmp1,tmp2,tmp3,tmp4
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double precision :: big1,big2,big3
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! Constants of the LYP correlation functional
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a = 0.04918d0
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b = 0.132d0
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c = 0.2533d0
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d = 0.349d0
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ec_lyp_88 = 0.d0
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thr = 1d-15
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huge_num = 1.d0/thr
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if(dabs(rho_a).lt.thr)then
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return
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endif
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if(dabs(rho_b).lt.thr)then
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return
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endif
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if(rho.lt.0.d0)then
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print*,'pb !! rho.lt.0.d0'
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stop
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endif
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rho_13 = rho**(1.d0/3.d0)
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rho_113 = rho**(11.d0/3.d0)
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if(dabs(rho_13) < thr) then
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rho_inv_13 = huge_num
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else
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rho_inv_13 = 1.d0/rho_13
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endif
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if (dabs(rho_113) < thr) then
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rho_inv_113 = huge_num
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else
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rho_inv_113 = 1.d0/rho_113
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endif
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if (dabs(rho) < thr) then
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rho_inv = huge_num
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else
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rho_inv = 1.d0/rho
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endif
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! Useful quantities to predefine
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denom = 1d0/(1d0 + d*rho_inv_13)
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omega = rho_inv_113*exp(-c*rho_inv_13)*denom
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delta = c*rho_inv_13 + d*rho_inv_13*denom
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c_f = 0.3d0*(3.d0*pi*pi)**(2.d0/3.d0)
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rho_2 = rho *rho
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rho_a_2 = rho_a*rho_a
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rho_b_2 = rho_b*rho_b
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cst_2_113 = 2.d0**(11.d0/3.d0)
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cst_8_3 = 8.d0/3.d0
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! first term in the equation (2) of Preuss CPL, 1989
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big1 = 4.d0*denom*rho_a*rho_b*rho_inv
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tmp1 = cst_2_113*c_f*(rho_a**cst_8_3 + rho_b**cst_8_3)
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tmp2 = (47.d0/18.d0 - 7.d0/18.d0*delta)*grad_rho_2
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tmp3 = - (5d0/2d0 - 1.d0/18d0*delta)*(grad_rho_a_2 + grad_rho_b_2)
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tmp4 = - (delta - 11d0)/9d0*(rho_a*rho_inv*grad_rho_a_2 + rho_b*rho_inv*grad_rho_b_2)
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big2 = rho_a*rho_b*(tmp1 + tmp2 + tmp3 + tmp4)
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tmp1 = -2d0/3d0*rho_2*grad_rho_2
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tmp2 = grad_rho_b_2*(2d0/3d0*rho_2 - rho_a_2)
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tmp3 = grad_rho_a_2*(2d0/3d0*rho_2 - rho_b_2)
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big3 = tmp1 + tmp2 + tmp3
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ec_lyp_88 = -a*big1 -a*b*omega*big2 -a*b*omega*big3
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end
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@ -1,28 +0,0 @@
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double precision function ec_lyp2(RhoA,RhoB,GA,GB,GAB)
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include 'constants.include.F'
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implicit none
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double precision, intent(in) :: RhoA,RhoB,GA,GB,GAB
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double precision :: Tol,caa,cab,cac,cad,cae,RA,RB,comega,cdelta,cLaa,cLbb,cLab,E
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ec_lyp2 = 0.d0
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Tol=1D-14
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E=2.718281828459045D0
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caa=0.04918D0
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cab=0.132D0
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cac=0.2533D0
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cad=0.349D0
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cae=(2D0**(11D0/3D0))*((3D0/10D0)*((3D0*(Pi**2D0))**(2D0/3D0)))
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RA = MAX(RhoA,0D0)
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RB = MAX(RhoB,0D0)
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IF ((RA.gt.Tol).OR.(RB.gt.Tol)) THEN
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IF ((RA.gt.Tol).AND.(RB.gt.Tol)) THEN
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comega = 1D0/(E**(cac/(RA+RB)**(1D0/3D0))*(RA+RB)**(10D0/3D0)*(cad+(RA+RB)**(1D0/3D0)))
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cdelta = (cac+cad+(cac*cad)/(RA+RB)**(1D0/3D0))/(cad+(RA+RB)**(1D0/3D0))
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cLaa = (cab*comega*RB*(RA-3D0*cdelta*RA-9D0*RB-((-11D0+cdelta)*RA**2D0)/(RA+RB)))/9D0
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cLbb = (cab*comega*RA*(-9D0*RA+(RB*(RA-3D0*cdelta*RA-4D0*(-3D0+cdelta)*RB))/(RA+RB)))/9D0
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cLab = cab*comega*(((47D0-7D0*cdelta)*RA*RB)/9D0-(4D0*(RA+RB)**2D0)/3D0)
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ec_lyp2 = -(caa*(cLaa*GA+cLab*GAB+cLbb*GB+cab*cae*comega*RA*RB*(RA**(8D0/3D0)+RB**(8D0/3D0))+(4D0*RA*RB)/(RA+RB+cad*(RA+RB)**(2D0/3D0))))
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endif
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endif
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end
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@ -1,99 +0,0 @@
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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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@ -1,100 +0,0 @@
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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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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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fc_alpha = dexp(-c_1c * alpha * inv_1alph) * step_f(cst_1alph) - d_c * dexp(c_2c * inv_1alph) * step_f(-cst_1alph)
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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
|
||||
|
||||
h0 = b_1c * dlog(1.d0 + w_0 * (1.d0 - g_inf))
|
||||
e_c_0 = (e_c_lsda0 + h0) * gc_xi
|
||||
|
||||
ec_scan = e_c_1 + fc_alpha * (e_c_0 - e_c_1)
|
||||
end
|
||||
|
||||
double precision function step_f(x)
|
||||
implicit none
|
||||
double precision, intent(in) :: x
|
||||
if(x.lt.0.d0)then
|
||||
step_f = 0.d0
|
||||
else
|
||||
step_f = 1.d0
|
||||
endif
|
||||
end
|
||||
|
||||
double precision function beta_rs(rs)
|
||||
implicit none
|
||||
double precision, intent(in) ::rs
|
||||
beta_rs = 0.066725d0 * (1.d0 + 0.1d0 * rs)/(1.d0 + 0.1778d0 * rs)
|
||||
|
||||
end
|
||||
|
|
@ -7,8 +7,11 @@
|
|||
! Effective_one_e_potential(i,j) = $\rangle i_{MO}| v_{H}^{sr} |j_{MO}\rangle + \rangle i_{MO}| h_{core} |j_{MO}\rangle + \rangle i_{MO}|v_{xc} |j_{MO}\rangle$
|
||||
!
|
||||
! on the |MO| basis
|
||||
!
|
||||
! Taking the expectation value does not provide any energy, but
|
||||
!
|
||||
! effective_one_e_potential(i,j) is the potential coupling DFT and WFT part to
|
||||
!
|
||||
! be used in any WFT calculation.
|
||||
!
|
||||
END_DOC
|
||||
|
|
|
|||
264
src/dft_utils_one_e/garbage_func.irp.f
Normal file
264
src/dft_utils_one_e/garbage_func.irp.f
Normal file
|
|
@ -0,0 +1,264 @@
|
|||
|
||||
subroutine give_all_stuffs_in_r_for_lyp_88(r,rho,rho_a,rho_b,grad_rho_a_2,grad_rho_b_2,grad_rho_2)
|
||||
implicit none
|
||||
double precision, intent(in) :: r(3)
|
||||
double precision, intent(out) :: rho_a(N_states),rho_b(N_states),grad_rho_a_2(N_states),grad_rho_b_2(N_states),grad_rho_2(N_states),rho(N_states)
|
||||
double precision :: grad_rho_a(3,N_states),grad_rho_b(3,N_states),grad_rho_a_b(N_states)
|
||||
double precision :: grad_aos_array(3,ao_num),aos_array(ao_num)
|
||||
|
||||
call density_and_grad_alpha_beta_and_all_aos_and_grad_aos_at_r(r,rho_a,rho_b, grad_rho_a, grad_rho_b, aos_array, grad_aos_array)
|
||||
integer :: i,istate
|
||||
rho = rho_a + rho_b
|
||||
grad_rho_a_2 = 0.d0
|
||||
grad_rho_b_2 = 0.d0
|
||||
grad_rho_a_b = 0.d0
|
||||
do istate = 1, N_states
|
||||
do i = 1, 3
|
||||
grad_rho_a_2(istate) += grad_rho_a(i,istate) * grad_rho_a(i,istate)
|
||||
grad_rho_b_2(istate) += grad_rho_b(i,istate) * grad_rho_b(i,istate)
|
||||
grad_rho_a_b(istate) += grad_rho_a(i,istate) * grad_rho_b(i,istate)
|
||||
enddo
|
||||
enddo
|
||||
grad_rho_2 = grad_rho_a_2 + grad_rho_b_2 + 2.d0 * grad_rho_a_b
|
||||
|
||||
end
|
||||
|
||||
|
||||
double precision function ec_lyp_88(rho,rho_a,rho_b,grad_rho_a_2,grad_rho_b_2,grad_rho_2)
|
||||
|
||||
implicit none
|
||||
|
||||
BEGIN_DOC
|
||||
! LYP functional of the Lee, Yan, Parr, Phys. Rev B 1988, Vol 37, page 785.
|
||||
! The expression used is the one by Miehlich, Savin, Stoll, Preuss, CPL, 1989 which gets rid of the laplacian of the density
|
||||
END_DOC
|
||||
|
||||
include 'constants.include.F'
|
||||
|
||||
! Input variables
|
||||
double precision, intent(in) :: rho,rho_a,rho_b,grad_rho_a_2,grad_rho_b_2,grad_rho_2
|
||||
! Local variables
|
||||
double precision :: a,b,c,d,c_f,omega,delta
|
||||
double precision :: rho_13,rho_inv_13,rho_83,rho_113,rho_inv_113,denom
|
||||
double precision :: thr,huge_num,rho_inv
|
||||
double precision :: cst_2_113,cst_8_3,rho_2,rho_a_2,rho_b_2
|
||||
double precision :: tmp1,tmp2,tmp3,tmp4
|
||||
double precision :: big1,big2,big3
|
||||
|
||||
|
||||
! Constants of the LYP correlation functional
|
||||
|
||||
a = 0.04918d0
|
||||
b = 0.132d0
|
||||
c = 0.2533d0
|
||||
d = 0.349d0
|
||||
|
||||
ec_lyp_88 = 0.d0
|
||||
|
||||
thr = 1d-15
|
||||
huge_num = 1.d0/thr
|
||||
if(dabs(rho_a).lt.thr)then
|
||||
return
|
||||
endif
|
||||
|
||||
if(dabs(rho_b).lt.thr)then
|
||||
return
|
||||
endif
|
||||
|
||||
if(rho.lt.0.d0)then
|
||||
print*,'pb !! rho.lt.0.d0'
|
||||
stop
|
||||
endif
|
||||
|
||||
rho_13 = rho**(1.d0/3.d0)
|
||||
rho_113 = rho**(11.d0/3.d0)
|
||||
|
||||
if(dabs(rho_13) < thr) then
|
||||
rho_inv_13 = huge_num
|
||||
else
|
||||
rho_inv_13 = 1.d0/rho_13
|
||||
endif
|
||||
|
||||
if (dabs(rho_113) < thr) then
|
||||
rho_inv_113 = huge_num
|
||||
else
|
||||
rho_inv_113 = 1.d0/rho_113
|
||||
endif
|
||||
|
||||
if (dabs(rho) < thr) then
|
||||
rho_inv = huge_num
|
||||
else
|
||||
rho_inv = 1.d0/rho
|
||||
endif
|
||||
|
||||
! Useful quantities to predefine
|
||||
|
||||
denom = 1d0/(1d0 + d*rho_inv_13)
|
||||
omega = rho_inv_113*exp(-c*rho_inv_13)*denom
|
||||
delta = c*rho_inv_13 + d*rho_inv_13*denom
|
||||
c_f = 0.3d0*(3.d0*pi*pi)**(2.d0/3.d0)
|
||||
|
||||
rho_2 = rho *rho
|
||||
rho_a_2 = rho_a*rho_a
|
||||
rho_b_2 = rho_b*rho_b
|
||||
|
||||
cst_2_113 = 2.d0**(11.d0/3.d0)
|
||||
cst_8_3 = 8.d0/3.d0
|
||||
|
||||
! first term in the equation (2) of Preuss CPL, 1989
|
||||
|
||||
big1 = 4.d0*denom*rho_a*rho_b*rho_inv
|
||||
|
||||
tmp1 = cst_2_113*c_f*(rho_a**cst_8_3 + rho_b**cst_8_3)
|
||||
tmp2 = (47.d0/18.d0 - 7.d0/18.d0*delta)*grad_rho_2
|
||||
tmp3 = - (5d0/2d0 - 1.d0/18d0*delta)*(grad_rho_a_2 + grad_rho_b_2)
|
||||
tmp4 = - (delta - 11d0)/9d0*(rho_a*rho_inv*grad_rho_a_2 + rho_b*rho_inv*grad_rho_b_2)
|
||||
big2 = rho_a*rho_b*(tmp1 + tmp2 + tmp3 + tmp4)
|
||||
|
||||
tmp1 = -2d0/3d0*rho_2*grad_rho_2
|
||||
tmp2 = grad_rho_b_2*(2d0/3d0*rho_2 - rho_a_2)
|
||||
tmp3 = grad_rho_a_2*(2d0/3d0*rho_2 - rho_b_2)
|
||||
big3 = tmp1 + tmp2 + tmp3
|
||||
|
||||
ec_lyp_88 = -a*big1 -a*b*omega*big2 -a*b*omega*big3
|
||||
|
||||
end
|
||||
|
||||
double precision function ec_lyp2(RhoA,RhoB,GA,GB,GAB)
|
||||
include 'constants.include.F'
|
||||
implicit none
|
||||
double precision, intent(in) :: RhoA,RhoB,GA,GB,GAB
|
||||
double precision :: Tol,caa,cab,cac,cad,cae,RA,RB,comega,cdelta,cLaa,cLbb,cLab,E
|
||||
ec_lyp2 = 0.d0
|
||||
Tol=1D-14
|
||||
E=2.718281828459045D0
|
||||
caa=0.04918D0
|
||||
cab=0.132D0
|
||||
cac=0.2533D0
|
||||
cad=0.349D0
|
||||
cae=(2D0**(11D0/3D0))*((3D0/10D0)*((3D0*(Pi**2D0))**(2D0/3D0)))
|
||||
|
||||
|
||||
RA = MAX(RhoA,0D0)
|
||||
RB = MAX(RhoB,0D0)
|
||||
IF ((RA.gt.Tol).OR.(RB.gt.Tol)) THEN
|
||||
IF ((RA.gt.Tol).AND.(RB.gt.Tol)) THEN
|
||||
comega = 1D0/(E**(cac/(RA+RB)**(1D0/3D0))*(RA+RB)**(10D0/3D0)*(cad+(RA+RB)**(1D0/3D0)))
|
||||
cdelta = (cac+cad+(cac*cad)/(RA+RB)**(1D0/3D0))/(cad+(RA+RB)**(1D0/3D0))
|
||||
cLaa = (cab*comega*RB*(RA-3D0*cdelta*RA-9D0*RB-((-11D0+cdelta)*RA**2D0)/(RA+RB)))/9D0
|
||||
cLbb = (cab*comega*RA*(-9D0*RA+(RB*(RA-3D0*cdelta*RA-4D0*(-3D0+cdelta)*RB))/(RA+RB)))/9D0
|
||||
cLab = cab*comega*(((47D0-7D0*cdelta)*RA*RB)/9D0-(4D0*(RA+RB)**2D0)/3D0)
|
||||
ec_lyp2 = -(caa*(cLaa*GA+cLab*GAB+cLbb*GB+cab*cae*comega*RA*RB*(RA**(8D0/3D0)+RB**(8D0/3D0))+(4D0*RA*RB)/(RA+RB+cad*(RA+RB)**(2D0/3D0))))
|
||||
endif
|
||||
endif
|
||||
end
|
||||
|
||||
double precision function ec_scan(rho_a,rho_b,tau,grad_rho_2)
|
||||
include 'constants.include.F'
|
||||
implicit none
|
||||
double precision, intent(in) :: rho_a,rho_b,tau,grad_rho_2
|
||||
double precision :: cst_13,cst_23,cst_43,cst_53,rho_inv,cst_18,cst_3pi2
|
||||
double precision :: thr,nup,ndo,xi,s,spin_d,drho,drho2,rho,inv_1alph,e_c_lsda1,h0
|
||||
double precision :: rs,t_w,t_unif,ds_xi,alpha,fc_alpha,step_f,cst_1alph,beta_inf
|
||||
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
|
||||
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
|
||||
thr = 1.d-12
|
||||
nup = max(rho_a,thr)
|
||||
ndo = max(rho_b,thr)
|
||||
rho = nup + ndo
|
||||
ec_scan = 0.d0
|
||||
if((rho).lt.thr)return
|
||||
! constants ...
|
||||
rho_inv = 1.d0/rho
|
||||
cst_13 = 1.d0/3.d0
|
||||
cst_23 = 2.d0 * cst_13
|
||||
cst_43 = 4.d0 * cst_13
|
||||
cst_53 = 5.d0 * cst_13
|
||||
cst_18 = 1.d0/8.d0
|
||||
cst_3pi2 = 3.d0 * pi*pi
|
||||
drho2 = max(grad_rho_2,thr)
|
||||
drho = dsqrt(drho2)
|
||||
if((nup-ndo).gt.0.d0)then
|
||||
spin_d = max(nup-ndo,thr)
|
||||
else
|
||||
spin_d = min(nup-ndo,-thr)
|
||||
endif
|
||||
c_1c = 0.64d0
|
||||
c_2c = 1.5d0
|
||||
d_c = 0.7d0
|
||||
b_1c = 0.0285764d0
|
||||
b_2c = 0.0889d0
|
||||
b_3c = 0.125541d0
|
||||
gama = 0.031091d0
|
||||
! correlation energy lsda1
|
||||
call ec_only_lda_sr(0.d0,nup,ndo,e_c_lsda1)
|
||||
|
||||
! correlation energy per particle
|
||||
e_c_lsda1 = e_c_lsda1/rho
|
||||
xi = spin_d/rho
|
||||
rs = (cst_43 * pi * rho)**(-cst_13)
|
||||
s = drho/( 2.d0 * cst_3pi2**(cst_13) * rho**cst_43 )
|
||||
t_w = drho2 * cst_18 * rho_inv
|
||||
ds_xi = 0.5d0 * ( (1.d0+xi)**cst_53 + (1.d0 - xi)**cst_53)
|
||||
t_unif = 0.3d0 * (cst_3pi2)**cst_23 * rho**cst_53*ds_xi
|
||||
t_unif = max(t_unif,thr)
|
||||
alpha = (tau - t_w)/t_unif
|
||||
cst_1alph= 1.d0 - alpha
|
||||
if(cst_1alph.gt.0.d0)then
|
||||
cst_1alph= max(cst_1alph,thr)
|
||||
else
|
||||
cst_1alph= min(cst_1alph,-thr)
|
||||
endif
|
||||
inv_1alph= 1.d0/cst_1alph
|
||||
phi = 0.5d0 * ( (1.d0+xi)**cst_23 + (1.d0 - xi)**cst_23)
|
||||
phi_3 = phi*phi*phi
|
||||
t = (cst_3pi2/16.d0)**cst_13 * s / (phi * rs**0.5d0)
|
||||
w_1 = dexp(-e_c_lsda1/(gama * phi_3)) - 1.d0
|
||||
a = beta_rs(rs) /(gama * w_1)
|
||||
g_at2 = 1.d0/(1.d0 + 4.d0 * a*t*t)**0.25d0
|
||||
h1 = gama * phi_3 * dlog(1.d0 + w_1 * (1.d0 - g_at2))
|
||||
! interpolation function
|
||||
|
||||
if(cst_1alph.gt.0.d0)then
|
||||
fc_alpha = dexp(-c_1c * alpha * inv_1alph)
|
||||
else
|
||||
fc_alpha = - d_c * dexp(c_2c * inv_1alph)
|
||||
endif
|
||||
! first part of the correlation energy
|
||||
e_c_1 = e_c_lsda1 + h1
|
||||
|
||||
dx_xi = 0.5d0 * ( (1.d0+xi)**cst_43 + (1.d0 - xi)**cst_43)
|
||||
gc_xi = (1.d0 - 2.3631d0 * (dx_xi - 1.d0) ) * (1.d0 - xi**12.d0)
|
||||
e_c_lsda0= - b_1c / (1.d0 + b_2c * rs**0.5d0 + b_3c * rs)
|
||||
w_0 = dexp(-e_c_lsda0/b_1c) - 1.d0
|
||||
beta_inf = 0.066725d0 * 0.1d0 / 0.1778d0
|
||||
cx_xi = -3.d0/(4.d0*pi) * (9.d0 * pi/4.d0)**cst_13 * dx_xi
|
||||
|
||||
x_inf = 0.128026d0
|
||||
f0 = -0.9d0
|
||||
g_inf = 1.d0/(1.d0 + 4.d0 * x_inf * s*s)**0.25d0
|
||||
|
||||
h0 = b_1c * dlog(1.d0 + w_0 * (1.d0 - g_inf))
|
||||
e_c_0 = (e_c_lsda0 + h0) * gc_xi
|
||||
|
||||
ec_scan = e_c_1 + fc_alpha * (e_c_0 - e_c_1)
|
||||
end
|
||||
|
||||
|
||||
double precision function beta_rs(rs)
|
||||
implicit none
|
||||
double precision, intent(in) ::rs
|
||||
beta_rs = 0.066725d0 * (1.d0 + 0.1d0 * rs)/(1.d0 + 0.1778d0 * rs)
|
||||
|
||||
end
|
||||
|
||||
|
||||
double precision function step_f(x)
|
||||
implicit none
|
||||
double precision, intent(in) :: x
|
||||
if(x.lt.0.d0)then
|
||||
step_f = 0.d0
|
||||
else
|
||||
step_f = 1.d0
|
||||
endif
|
||||
end
|
||||
|
|
@ -1,5 +1,10 @@
|
|||
subroutine rho_ab_to_rho_oc(rho_a,rho_b,rho_o,rho_c)
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! convert rho_alpha, rho_beta to rho_c, rho_o
|
||||
!
|
||||
! rho_c = total density, rho_o spin density
|
||||
END_DOC
|
||||
double precision, intent(in) :: rho_a,rho_b
|
||||
double precision, intent(out) :: rho_o,rho_c
|
||||
rho_c=rho_a+rho_b
|
||||
|
|
@ -8,6 +13,11 @@ end
|
|||
|
||||
subroutine rho_oc_to_rho_ab(rho_o,rho_c,rho_a,rho_b)
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! convert rho_c, rho_o to rho_alpha, rho_beta
|
||||
!
|
||||
! rho_c = total density, rho_o spin density
|
||||
END_DOC
|
||||
double precision, intent(in) :: rho_o,rho_c
|
||||
double precision, intent(out) :: rho_a,rho_b
|
||||
rho_a= 0.5d0*(rho_c+rho_o)
|
||||
|
|
@ -18,6 +28,13 @@ end
|
|||
|
||||
subroutine grad_rho_ab_to_grad_rho_oc(grad_rho_a_2,grad_rho_b_2,grad_rho_a_b,grad_rho_o_2,grad_rho_c_2,grad_rho_o_c)
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! convert (grad_rho_a_2, grad_rho_b_2, grad_rho_a.grad_rho_b, )
|
||||
!
|
||||
! to (grad_rho_c_2, grad_rho_o_2, grad_rho_o.grad_rho_c)
|
||||
!
|
||||
! rho_c = total density, rho_o spin density
|
||||
END_DOC
|
||||
double precision, intent(in) :: grad_rho_a_2,grad_rho_b_2,grad_rho_a_b
|
||||
double precision, intent(out) :: grad_rho_o_2,grad_rho_c_2,grad_rho_o_c
|
||||
grad_rho_c_2 = grad_rho_a_2 + grad_rho_b_2 + 2d0*grad_rho_a_b
|
||||
|
|
@ -28,6 +45,11 @@ end
|
|||
|
||||
|
||||
subroutine v_rho_ab_to_v_rho_oc(v_rho_a,v_rho_b,v_rho_o,v_rho_c)
|
||||
BEGIN_DOC
|
||||
! convert v_rho_alpha, v_rho_beta to v_rho_c, v_rho_o
|
||||
!
|
||||
! rho_c = total density, rho_o spin density
|
||||
END_DOC
|
||||
implicit none
|
||||
double precision, intent(in) :: v_rho_a,v_rho_b
|
||||
double precision, intent(out) :: v_rho_o,v_rho_c
|
||||
|
|
@ -37,6 +59,11 @@ end
|
|||
|
||||
subroutine v_rho_oc_to_v_rho_ab(v_rho_o,v_rho_c,v_rho_a,v_rho_b)
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! convert v_rho_alpha, v_rho_beta to v_rho_c, v_rho_o
|
||||
!
|
||||
! rho_c = total density, rho_o spin density
|
||||
END_DOC
|
||||
double precision, intent(in) :: v_rho_o,v_rho_c
|
||||
double precision, intent(out) :: v_rho_a,v_rho_b
|
||||
v_rho_a = v_rho_c + v_rho_o
|
||||
|
|
@ -47,6 +74,13 @@ end
|
|||
|
||||
subroutine v_grad_rho_oc_to_v_grad_rho_ab(v_grad_rho_o_2,v_grad_rho_c_2,v_grad_rho_o_c,v_grad_rho_a_2,v_grad_rho_b_2,v_grad_rho_a_b)
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! convert (v_grad_rho_c_2, v_grad_rho_o_2, v_grad_rho_o.grad_rho_c)
|
||||
!
|
||||
! to (v_grad_rho_a_2, v_grad_rho_b_2, v_grad_rho_a.grad_rho_b)
|
||||
!
|
||||
! rho_c = total density, rho_o spin density
|
||||
END_DOC
|
||||
double precision, intent(in) :: v_grad_rho_o_2,v_grad_rho_c_2,v_grad_rho_o_c
|
||||
double precision, intent(out) :: v_grad_rho_a_2,v_grad_rho_b_2,v_grad_rho_a_b
|
||||
v_grad_rho_a_2 = v_grad_rho_o_2 + v_grad_rho_c_2 + v_grad_rho_o_c
|
||||
|
|
|
|||
|
|
@ -189,16 +189,27 @@ end
|
|||
subroutine ex_pbe_sr(mu,rho_a,rho_b,grd_rho_a_2,grd_rho_b_2,grd_rho_a_b,ex,vx_rho_a,vx_rho_b,vx_grd_rho_a_2,vx_grd_rho_b_2,vx_grd_rho_a_b)
|
||||
BEGIN_DOC
|
||||
!mu = range separation parameter
|
||||
!
|
||||
!rho_a = density alpha
|
||||
!
|
||||
!rho_b = density beta
|
||||
!
|
||||
!grd_rho_a_2 = (gradient rho_a)^2
|
||||
!
|
||||
!grd_rho_b_2 = (gradient rho_b)^2
|
||||
!
|
||||
!grd_rho_a_b = (gradient rho_a).(gradient rho_b)
|
||||
!
|
||||
!ex = exchange energy density at the density and corresponding gradients of the density
|
||||
!
|
||||
!vx_rho_a = d ex / d rho_a
|
||||
!
|
||||
!vx_rho_b = d ex / d rho_b
|
||||
!
|
||||
!vx_grd_rho_a_2 = d ex / d grd_rho_a_2
|
||||
!
|
||||
!vx_grd_rho_b_2 = d ex / d grd_rho_b_2
|
||||
!
|
||||
!vx_grd_rho_a_b = d ex / d grd_rho_a_b
|
||||
END_DOC
|
||||
|
||||
|
|
@ -313,10 +324,15 @@ END_DOC
|
|||
subroutine ex_pbe_sr_only(mu,rho_a,rho_b,grd_rho_a_2,grd_rho_b_2,grd_rho_a_b,ex)
|
||||
BEGIN_DOC
|
||||
!rho_a = density alpha
|
||||
!
|
||||
!rho_b = density beta
|
||||
!
|
||||
!grd_rho_a_2 = (gradient rho_a)^2
|
||||
!
|
||||
!grd_rho_b_2 = (gradient rho_b)^2
|
||||
!
|
||||
!grd_rho_a_b = (gradient rho_a).(gradient rho_b)
|
||||
!
|
||||
!ex = exchange energy density at point r
|
||||
END_DOC
|
||||
|
||||
|
|
@ -1,86 +0,0 @@
|
|||
|
||||
|
||||
BEGIN_PROVIDER[double precision, energy_sr_x_lda, (N_states) ]
|
||||
&BEGIN_PROVIDER[double precision, energy_sr_c_lda, (N_states) ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! exchange/correlation energy with the short range lda functional
|
||||
END_DOC
|
||||
integer :: istate,i,j
|
||||
double precision :: r(3)
|
||||
double precision :: mu,weight
|
||||
double precision :: e_c,vc_a,vc_b,e_x,vx_a,vx_b
|
||||
double precision, allocatable :: rhoa(:),rhob(:)
|
||||
allocate(rhoa(N_states), rhob(N_states))
|
||||
energy_sr_x_lda = 0.d0
|
||||
energy_sr_c_lda = 0.d0
|
||||
do istate = 1, N_states
|
||||
do i = 1, n_points_final_grid
|
||||
r(1) = final_grid_points(1,i)
|
||||
r(2) = final_grid_points(2,i)
|
||||
r(3) = final_grid_points(3,i)
|
||||
weight = final_weight_at_r_vector(i)
|
||||
rhoa(istate) = one_e_dm_and_grad_alpha_in_r(4,i,istate)
|
||||
rhob(istate) = one_e_dm_and_grad_beta_in_r(4,i,istate)
|
||||
call ec_lda_sr(mu_erf_dft,rhoa(istate),rhob(istate),e_c,vc_a,vc_b)
|
||||
call ex_lda_sr(mu_erf_dft,rhoa(istate),rhob(istate),e_x,vx_a,vx_b)
|
||||
energy_sr_x_lda(istate) += weight * e_x
|
||||
energy_sr_c_lda(istate) += weight * e_c
|
||||
enddo
|
||||
enddo
|
||||
|
||||
END_PROVIDER
|
||||
|
||||
BEGIN_PROVIDER[double precision, energy_sr_x_pbe, (N_states) ]
|
||||
&BEGIN_PROVIDER[double precision, energy_sr_c_pbe, (N_states) ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! exchange/correlation energy with the short range pbe functional
|
||||
END_DOC
|
||||
integer :: istate,i,j,m
|
||||
double precision :: r(3)
|
||||
double precision :: mu,weight
|
||||
double precision, allocatable :: ex(:), ec(:)
|
||||
double precision, allocatable :: rho_a(:),rho_b(:),grad_rho_a(:,:),grad_rho_b(:,:),grad_rho_a_2(:),grad_rho_b_2(:),grad_rho_a_b(:)
|
||||
double precision, allocatable :: contrib_grad_xa(:,:),contrib_grad_xb(:,:),contrib_grad_ca(:,:),contrib_grad_cb(:,:)
|
||||
double precision, allocatable :: vc_rho_a(:), vc_rho_b(:), vx_rho_a(:), vx_rho_b(:)
|
||||
double precision, allocatable :: vx_grad_rho_a_2(:), vx_grad_rho_b_2(:), vx_grad_rho_a_b(:), vc_grad_rho_a_2(:), vc_grad_rho_b_2(:), vc_grad_rho_a_b(:)
|
||||
allocate(vc_rho_a(N_states), vc_rho_b(N_states), vx_rho_a(N_states), vx_rho_b(N_states))
|
||||
allocate(vx_grad_rho_a_2(N_states), vx_grad_rho_b_2(N_states), vx_grad_rho_a_b(N_states), vc_grad_rho_a_2(N_states), vc_grad_rho_b_2(N_states), vc_grad_rho_a_b(N_states))
|
||||
|
||||
|
||||
allocate(rho_a(N_states), rho_b(N_states),grad_rho_a(3,N_states),grad_rho_b(3,N_states))
|
||||
allocate(grad_rho_a_2(N_states),grad_rho_b_2(N_states),grad_rho_a_b(N_states), ex(N_states), ec(N_states))
|
||||
energy_sr_x_pbe = 0.d0
|
||||
energy_sr_c_pbe = 0.d0
|
||||
do istate = 1, N_states
|
||||
do i = 1, n_points_final_grid
|
||||
r(1) = final_grid_points(1,i)
|
||||
r(2) = final_grid_points(2,i)
|
||||
r(3) = final_grid_points(3,i)
|
||||
weight = final_weight_at_r_vector(i)
|
||||
rho_a(istate) = one_e_dm_and_grad_alpha_in_r(4,i,istate)
|
||||
rho_b(istate) = one_e_dm_and_grad_beta_in_r(4,i,istate)
|
||||
grad_rho_a(1:3,istate) = one_e_dm_and_grad_alpha_in_r(1:3,i,istate)
|
||||
grad_rho_b(1:3,istate) = one_e_dm_and_grad_beta_in_r(1:3,i,istate)
|
||||
grad_rho_a_2 = 0.d0
|
||||
grad_rho_b_2 = 0.d0
|
||||
grad_rho_a_b = 0.d0
|
||||
do m = 1, 3
|
||||
grad_rho_a_2(istate) += grad_rho_a(m,istate) * grad_rho_a(m,istate)
|
||||
grad_rho_b_2(istate) += grad_rho_b(m,istate) * grad_rho_b(m,istate)
|
||||
grad_rho_a_b(istate) += grad_rho_a(m,istate) * grad_rho_b(m,istate)
|
||||
enddo
|
||||
|
||||
! inputs
|
||||
call GGA_sr_type_functionals(r,rho_a,rho_b,grad_rho_a_2,grad_rho_b_2,grad_rho_a_b, & ! outputs exchange
|
||||
ex,vx_rho_a,vx_rho_b,vx_grad_rho_a_2,vx_grad_rho_b_2,vx_grad_rho_a_b, & ! outputs correlation
|
||||
ec,vc_rho_a,vc_rho_b,vc_grad_rho_a_2,vc_grad_rho_b_2,vc_grad_rho_a_b )
|
||||
energy_sr_x_pbe += ex * weight
|
||||
energy_sr_c_pbe += ec * weight
|
||||
enddo
|
||||
enddo
|
||||
|
||||
|
||||
END_PROVIDER
|
||||
|
||||
Loading…
Reference in New Issue
Block a user