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 ! Output variables ! Constants of the LYP correlation functional a = 0.04918d0 b = 0.132d0 c = 0.2533d0 d = 0.349d0 thr = 1d-10 huge_num = 1.d0/thr if(rho.lt.0.d0)then print*,'pb !! rho.lt.0.d0' stop endif rho_13 = rho**(1d0/3d0) rho_113 = rho**(11d0/3d0) 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 = 1d0/rho_113 endif if (dabs(rho) < thr) then rho_inv = huge_num else rho_inv = 1d0/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*(3d0*pi*pi)**(2d0/3d0) rho_2 = rho *rho rho_a_2 = rho_a*rho_a rho_b_2 = rho_b*rho_b cst_2_113 = 2d0**(11d0/3d0) cst_8_3 = 8d0/3d0 ! first term in the equation (2) of Preuss CPL, 1989 big1 = 4d0*denom*rho_a*rho_b*rho_inv tmp1 = cst_2_113*c_f*(rho_a**cst_8_3 + rho_b**cst_8_3) tmp2 = (47d0/18d0 - 7d0/18d0*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