577 lines
16 KiB
Fortran
577 lines
16 KiB
Fortran
BEGIN_PROVIDER [ double precision, ao_nucl_elec_integral, (ao_num_align,ao_num)]
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BEGIN_DOC
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! interaction nuclear electron
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END_DOC
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implicit none
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double precision :: alpha, beta, gama, delta
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integer :: i_c,num_A,num_B
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double precision :: A_center(3),B_center(3),C_center(3)
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integer :: power_A(3),power_B(3)
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integer :: i,j,k,l,n_pt_in,m
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double precision ::overlap_x,overlap_y,overlap_z,overlap,dx,NAI_pol_mult
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integer :: nucl_numC
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! Important for OpenMP
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ao_nucl_elec_integral = 0.d0
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!$OMP PARALLEL &
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!$OMP DEFAULT (NONE) &
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!$OMP PRIVATE (i,j,k,l,m,alpha,beta,A_center,B_center,C_center,power_A,power_B, &
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!$OMP num_A,num_B,Z,c,n_pt_in) &
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!$OMP SHARED (ao_num,ao_prim_num,ao_expo_ordered_transp,ao_power,ao_nucl,nucl_coord,ao_coef_normalized_ordered_transp, &
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!$OMP n_pt_max_integrals,ao_nucl_elec_integral,nucl_num,nucl_charge)
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n_pt_in = n_pt_max_integrals
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!$OMP DO SCHEDULE (guided)
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do j = 1, ao_num
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power_A(1)= ao_power(j,1)
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power_A(2)= ao_power(j,2)
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power_A(3)= ao_power(j,3)
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num_A = ao_nucl(j)
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A_center(1) = nucl_coord(num_A,1)
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A_center(2) = nucl_coord(num_A,2)
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A_center(3) = nucl_coord(num_A,3)
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do i = 1, ao_num
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power_B(1)= ao_power(i,1)
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power_B(2)= ao_power(i,2)
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power_B(3)= ao_power(i,3)
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num_B = ao_nucl(i)
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B_center(1) = nucl_coord(num_B,1)
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B_center(2) = nucl_coord(num_B,2)
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B_center(3) = nucl_coord(num_B,3)
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do l=1,ao_prim_num(j)
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alpha = ao_expo_ordered_transp(l,j)
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do m=1,ao_prim_num(i)
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beta = ao_expo_ordered_transp(m,i)
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c = 0.d0
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do k = 1, nucl_num
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double precision :: Z,c
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Z = nucl_charge(k)
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C_center(1) = nucl_coord(k,1)
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C_center(2) = nucl_coord(k,2)
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C_center(3) = nucl_coord(k,3)
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c = c+Z*NAI_pol_mult(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in)
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enddo
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ao_nucl_elec_integral(i,j) = ao_nucl_elec_integral(i,j) - &
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ao_coef_normalized_ordered_transp(l,j)*ao_coef_normalized_ordered_transp(m,i)*c
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enddo
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enddo
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enddo
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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END_PROVIDER
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BEGIN_PROVIDER [ double precision, ao_nucl_elec_integral_per_atom, (ao_num_align,ao_num,nucl_num)]
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BEGIN_DOC
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! ao_nucl_elec_integral_per_atom(i,j,k) = -<AO(i)|1/|r-Rk|AO(j)>
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! where Rk is the geometry of the kth atom
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END_DOC
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implicit none
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double precision :: alpha, beta, gama, delta
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integer :: i_c,num_A,num_B
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double precision :: A_center(3),B_center(3),C_center(3)
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integer :: power_A(3),power_B(3)
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integer :: i,j,k,l,n_pt_in,m
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double precision ::overlap_x,overlap_y,overlap_z,overlap,dx,NAI_pol_mult
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integer :: nucl_numC
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! Important for OpenMP
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ao_nucl_elec_integral_per_atom = 0.d0
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do k = 1, nucl_num
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C_center(1) = nucl_coord(k,1)
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C_center(2) = nucl_coord(k,2)
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C_center(3) = nucl_coord(k,3)
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!$OMP PARALLEL &
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!$OMP DEFAULT (NONE) &
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!$OMP PRIVATE (i,j,l,m,alpha,beta,A_center,B_center,power_A,power_B, &
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!$OMP num_A,num_B,c,n_pt_in) &
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!$OMP SHARED (k,ao_num,ao_prim_num,ao_expo_ordered_transp,ao_power,ao_nucl,nucl_coord,ao_coef_normalized_ordered_transp, &
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!$OMP n_pt_max_integrals,ao_nucl_elec_integral_per_atom,nucl_num,C_center)
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n_pt_in = n_pt_max_integrals
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!$OMP DO SCHEDULE (guided)
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double precision :: c
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do j = 1, ao_num
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power_A(1)= ao_power(j,1)
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power_A(2)= ao_power(j,2)
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power_A(3)= ao_power(j,3)
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num_A = ao_nucl(j)
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A_center(1) = nucl_coord(num_A,1)
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A_center(2) = nucl_coord(num_A,2)
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A_center(3) = nucl_coord(num_A,3)
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do i = 1, ao_num
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power_B(1)= ao_power(i,1)
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power_B(2)= ao_power(i,2)
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power_B(3)= ao_power(i,3)
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num_B = ao_nucl(i)
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B_center(1) = nucl_coord(num_B,1)
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B_center(2) = nucl_coord(num_B,2)
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B_center(3) = nucl_coord(num_B,3)
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c = 0.d0
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do l=1,ao_prim_num(j)
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alpha = ao_expo_ordered_transp(l,j)
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do m=1,ao_prim_num(i)
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beta = ao_expo_ordered_transp(m,i)
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c = c + NAI_pol_mult(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in) &
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* ao_coef_normalized_ordered_transp(l,j)*ao_coef_normalized_ordered_transp(m,i)
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enddo
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enddo
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ao_nucl_elec_integral_per_atom(i,j,k) = -c
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enddo
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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enddo
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END_PROVIDER
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double precision function NAI_pol_mult(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in)
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! function that calculate the folowing integral :
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! int{dr} of (x-A_x)^ax (x-B_X)^bx exp(-alpha (x-A_x)^2 - beta (x-B_x)^2 ) 1/(r-R_c)
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implicit none
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double precision,intent(in) :: C_center(3),A_center(3),B_center(3),alpha,beta
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integer :: power_A(3),power_B(3)
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integer :: i,j,k,l,n_pt
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double precision :: P_center(3)
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double precision :: d(0:n_pt_in),pouet,coeff,rho,dist,const,pouet_2,p,p_inv,factor
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double precision :: I_n_special_exact,integrate_bourrin,I_n_bibi
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double precision :: V_e_n,const_factor,dist_integral,tmp
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include 'constants.F'
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if ( (A_center(1)/=B_center(1)).or. &
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(A_center(2)/=B_center(2)).or. &
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(A_center(3)/=B_center(3)).or. &
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(A_center(1)/=C_center(1)).or. &
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(A_center(2)/=C_center(2)).or. &
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(A_center(3)/=C_center(3))) then
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continue
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else
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NAI_pol_mult = V_e_n(power_A(1),power_A(2),power_A(3),power_B(1),power_B(2),power_B(3),alpha,beta)
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return
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endif
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p = alpha + beta
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! print*, "a"
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p_inv = 1.d0/p
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rho = alpha * beta * p_inv
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dist = 0.d0
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dist_integral = 0.d0
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do i = 1, 3
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P_center(i) = (alpha * A_center(i) + beta * B_center(i)) * p_inv
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dist += (A_center(i) - B_center(i))*(A_center(i) - B_center(i))
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dist_integral += (P_center(i) - C_center(i))*(P_center(i) - C_center(i))
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enddo
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const_factor = dist*rho
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const = p * dist_integral
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if(const_factor.ge.80.d0)then
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NAI_pol_mult = 0.d0
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return
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endif
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factor = dexp(-const_factor)
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coeff = dtwo_pi * factor * p_inv
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lmax = 20
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! print*, "b"
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do i = 0, n_pt_in
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d(i) = 0.d0
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enddo
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n_pt = 2 * ( (power_A(1) + power_B(1)) +(power_A(2) + power_B(2)) +(power_A(3) + power_B(3)) )
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if (n_pt == 0) then
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epsilo = 1.d0
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pouet = rint(0,const)
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NAI_pol_mult = coeff * pouet
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return
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endif
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call give_polynom_mult_center_mono_elec(A_center,B_center,alpha,beta,power_A,power_B,C_center,n_pt_in,d,n_pt_out)
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if(n_pt_out<0)then
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NAI_pol_mult = 0.d0
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return
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endif
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double precision :: accu,epsilo,rint
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integer :: n_pt_in,n_pt_out,lmax
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accu = 0.d0
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! 1/r1 standard attraction integral
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epsilo = 1.d0
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! sum of integrals of type : int {t,[0,1]} exp-(rho.(P-Q)^2 * t^2) * t^i
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do i =0 ,n_pt_out,2
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accu += d(i) * rint(i/2,const)
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enddo
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NAI_pol_mult = accu * coeff
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end
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subroutine give_polynom_mult_center_mono_elec(A_center,B_center,alpha,beta,power_A,power_B,C_center,n_pt_in,d,n_pt_out)
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!!!! subroutine that returns the explicit polynom in term of the "t" variable of the following polynomw ::
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!!!! I_x1(a_x, d_x,p,q) * I_x1(a_y, d_y,p,q) * I_x1(a_z, d_z,p,q)
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!!!! it is for the nuclear electron atraction
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implicit none
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integer, intent(in) :: n_pt_in
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integer,intent(out) :: n_pt_out
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double precision, intent(in) :: A_center(3), B_center(3),C_center(3)
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double precision, intent(in) :: alpha,beta
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integer, intent(in) :: power_A(3), power_B(3)
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integer :: a_x,b_x,a_y,b_y,a_z,b_z
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double precision :: d(0:n_pt_in)
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double precision :: d1(0:n_pt_in)
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double precision :: d2(0:n_pt_in)
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double precision :: d3(0:n_pt_in)
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double precision :: accu, pq_inv, p10_1, p10_2, p01_1, p01_2
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double precision :: p,P_center(3),rho,p_inv,p_inv_2
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!print*,'n_pt_in = ',n_pt_in
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accu = 0.d0
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!COMPTEUR irp_rdtsc1 = irp_rdtsc()
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ASSERT (n_pt_in > 1)
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p = alpha+beta
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p_inv = 1.d0/p
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p_inv_2 = 0.5d0/p
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do i =1, 3
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P_center(i) = (alpha * A_center(i) + beta * B_center(i)) * p_inv
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enddo
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! print*,'passed the P_center'
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double precision :: R1x(0:2), B01(0:2), R1xp(0:2),R2x(0:2)
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R1x(0) = (P_center(1) - A_center(1))
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R1x(1) = 0.d0
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R1x(2) = -(P_center(1) - C_center(1))
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! R1x = (P_x - A_x) - (P_x - C_x) t^2
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R1xp(0) = (P_center(1) - B_center(1))
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R1xp(1) = 0.d0
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R1xp(2) =-(P_center(1) - C_center(1))
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!R1xp = (P_x - B_x) - (P_x - C_x) t^2
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R2x(0) = p_inv_2
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R2x(1) = 0.d0
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R2x(2) = -p_inv_2
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!R2x = 0.5 / p - 0.5/p t^2
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do i = 0,n_pt_in
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d(i) = 0.d0
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enddo
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do i = 0,n_pt_in
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d1(i) = 0.d0
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enddo
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do i = 0,n_pt_in
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d2(i) = 0.d0
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enddo
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do i = 0,n_pt_in
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d3(i) = 0.d0
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enddo
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integer :: n_pt1,n_pt2,n_pt3,dim,i
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n_pt1 = n_pt_in
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n_pt2 = n_pt_in
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n_pt3 = n_pt_in
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a_x = power_A(1)
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b_x = power_B(1)
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call I_x1_pol_mult_mono_elec(a_x,b_x,R1x,R1xp,R2x,d1,n_pt1,n_pt_in)
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! print*,'passed the first I_x1'
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if(n_pt1<0)then
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n_pt_out = -1
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do i = 0,n_pt_in
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d(i) = 0.d0
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enddo
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return
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endif
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R1x(0) = (P_center(2) - A_center(2))
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R1x(1) = 0.d0
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R1x(2) = -(P_center(2) - C_center(2))
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! R1x = (P_x - A_x) - (P_x - C_x) t^2
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R1xp(0) = (P_center(2) - B_center(2))
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R1xp(1) = 0.d0
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R1xp(2) =-(P_center(2) - C_center(2))
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!R1xp = (P_x - B_x) - (P_x - C_x) t^2
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a_y = power_A(2)
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b_y = power_B(2)
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call I_x1_pol_mult_mono_elec(a_y,b_y,R1x,R1xp,R2x,d2,n_pt2,n_pt_in)
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! print*,'passed the second I_x1'
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if(n_pt2<0)then
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n_pt_out = -1
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do i = 0,n_pt_in
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d(i) = 0.d0
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enddo
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return
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endif
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R1x(0) = (P_center(3) - A_center(3))
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R1x(1) = 0.d0
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R1x(2) = -(P_center(3) - C_center(3))
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! R1x = (P_x - A_x) - (P_x - C_x) t^2
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R1xp(0) = (P_center(3) - B_center(3))
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R1xp(1) = 0.d0
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R1xp(2) =-(P_center(3) - C_center(3))
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!R2x = 0.5 / p - 0.5/p t^2
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a_z = power_A(3)
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b_z = power_B(3)
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! print*,'a_z = ',a_z
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! print*,'b_z = ',b_z
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call I_x1_pol_mult_mono_elec(a_z,b_z,R1x,R1xp,R2x,d3,n_pt3,n_pt_in)
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! print*,'passed the third I_x1'
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if(n_pt3<0)then
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n_pt_out = -1
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do i = 0,n_pt_in
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d(i) = 0.d0
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enddo
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return
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endif
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integer :: n_pt_tmp
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n_pt_tmp = 0
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call multiply_poly(d1,n_pt1,d2,n_pt2,d,n_pt_tmp)
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do i = 0,n_pt_tmp
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d1(i) = 0.d0
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enddo
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n_pt_out = 0
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call multiply_poly(d ,n_pt_tmp ,d3,n_pt3,d1,n_pt_out)
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do i = 0, n_pt_out
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d(i) = d1(i)
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enddo
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end
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recursive subroutine I_x1_pol_mult_mono_elec(a,c,R1x,R1xp,R2x,d,nd,n_pt_in)
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!!!! recursive function involved in the electron nucleus potential
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implicit none
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integer , intent(in) :: n_pt_in
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double precision,intent(inout) :: d(0:n_pt_in)
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integer,intent(inout) :: nd
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integer, intent(in):: a,c
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double precision, intent(in) :: R1x(0:2),R1xp(0:2),R2x(0:2)
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include 'constants.F'
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double precision :: X(0:max_dim)
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double precision :: Y(0:max_dim)
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!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: X, Y
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integer :: nx, ix,dim,iy,ny
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dim = n_pt_in
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! print*,'a,c = ',a,c
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! print*,'nd_in = ',nd
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if( (a==0) .and. (c==0))then
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nd = 0
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d(0) = 1.d0
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return
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elseif( (c<0).or.(nd<0) )then
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nd = -1
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return
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else if ((a==0).and.(c.ne.0)) then
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call I_x2_pol_mult_mono_elec(c,R1x,R1xp,R2x,d,nd,n_pt_in)
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! print*,'nd 0,c',nd
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else if (a==1) then
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nx = nd
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do ix=0,n_pt_in
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X(ix) = 0.d0
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Y(ix) = 0.d0
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enddo
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call I_x2_pol_mult_mono_elec(c-1,R1x,R1xp,R2x,X,nx,n_pt_in)
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do ix=0,nx
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X(ix) *= c
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enddo
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call multiply_poly(X,nx,R2x,2,d,nd)
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ny=0
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call I_x2_pol_mult_mono_elec(c,R1x,R1xp,R2x,Y,ny,n_pt_in)
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call multiply_poly(Y,ny,R1x,2,d,nd)
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else
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do ix=0,n_pt_in
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X(ix) = 0.d0
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Y(ix) = 0.d0
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enddo
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nx = 0
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call I_x1_pol_mult_mono_elec(a-2,c,R1x,R1xp,R2x,X,nx,n_pt_in)
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! print*,'nx a-2,c= ',nx
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do ix=0,nx
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X(ix) *= a-1
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enddo
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call multiply_poly(X,nx,R2x,2,d,nd)
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! print*,'nd out = ',nd
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|
|
|
nx = nd
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|
do ix=0,n_pt_in
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|
X(ix) = 0.d0
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|
enddo
|
|
call I_x1_pol_mult_mono_elec(a-1,c-1,R1x,R1xp,R2x,X,nx,n_pt_in)
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|
! print*,'nx a-1,c-1 = ',nx
|
|
do ix=0,nx
|
|
X(ix) *= c
|
|
enddo
|
|
call multiply_poly(X,nx,R2x,2,d,nd)
|
|
ny=0
|
|
call I_x1_pol_mult_mono_elec(a-1,c,R1x,R1xp,R2x,Y,ny,n_pt_in)
|
|
call multiply_poly(Y,ny,R1x,2,d,nd)
|
|
endif
|
|
end
|
|
|
|
recursive subroutine I_x2_pol_mult_mono_elec(c,R1x,R1xp,R2x,d,nd,dim)
|
|
implicit none
|
|
integer , intent(in) :: dim
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|
include 'constants.F'
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|
double precision :: d(0:max_dim)
|
|
integer,intent(inout) :: nd
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|
integer, intent(in):: c
|
|
double precision, intent(in) :: R1x(0:2),R1xp(0:2),R2x(0:2)
|
|
integer :: i
|
|
!print*,'X2,c = ',c
|
|
!print*,'nd_in = ',nd
|
|
|
|
if(c==0) then
|
|
nd = 0
|
|
d(0) = 1.d0
|
|
! print*,'nd IX2 = ',nd
|
|
return
|
|
elseif ((nd<0).or.(c<0))then
|
|
nd = -1
|
|
return
|
|
else
|
|
integer :: nx, ix,ny
|
|
double precision :: X(0:max_dim),Y(0:max_dim)
|
|
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: X, Y
|
|
do ix=0,dim
|
|
X(ix) = 0.d0
|
|
Y(ix) = 0.d0
|
|
enddo
|
|
nx = 0
|
|
call I_x1_pol_mult_mono_elec(0,c-2,R1x,R1xp,R2x,X,nx,dim)
|
|
! print*,'nx 0,c-2 = ',nx
|
|
do ix=0,nx
|
|
X(ix) *= c-1
|
|
enddo
|
|
call multiply_poly(X,nx,R2x,2,d,nd)
|
|
! print*,'nd = ',nd
|
|
ny = 0
|
|
do ix=0,dim
|
|
Y(ix) = 0.d0
|
|
enddo
|
|
|
|
call I_x1_pol_mult_mono_elec(0,c-1,R1x,R1xp,R2x,Y,ny,dim)
|
|
! print*,'ny = ',ny
|
|
! do ix=0,ny
|
|
! print*,'Y(ix) = ',Y(ix)
|
|
! enddo
|
|
if(ny.ge.0)then
|
|
call multiply_poly(Y,ny,R1xp,2,d,nd)
|
|
endif
|
|
endif
|
|
end
|
|
|
|
double precision function V_e_n(a_x,a_y,a_z,b_x,b_y,b_z,alpha,beta)
|
|
implicit none
|
|
!!! primitve nuclear attraction between the two primitves centered on the same atom ::
|
|
!!!! primitive_1 = x**(a_x) y**(a_y) z**(a_z) exp(-alpha * r**2)
|
|
!!!! primitive_2 = x**(b_x) y**(b_y) z**(b_z) exp(- beta * r**2)
|
|
integer :: a_x,a_y,a_z,b_x,b_y,b_z
|
|
double precision :: alpha,beta
|
|
double precision :: V_r, V_phi, V_theta
|
|
if(iand((a_x+b_x),1)==1.or.iand(a_y+b_y,1)==1.or.iand((a_z+b_z),1)==1)then
|
|
V_e_n = 0.d0
|
|
else
|
|
V_e_n = V_r(a_x+b_x+a_y+b_y+a_z+b_z+1,alpha+beta) &
|
|
& * V_phi(a_x+b_x,a_y+b_y) &
|
|
& * V_theta(a_z+b_z,a_x+b_x+a_y+b_y+1)
|
|
endif
|
|
|
|
end
|
|
|
|
|
|
double precision function int_gaus_pol(alpha,n)
|
|
!!!! calculate the integral of
|
|
!! integral on "x" with boundaries (- infinity; + infinity) of [ x**n exp(-alpha * x**2) ]
|
|
implicit none
|
|
double precision :: alpha
|
|
integer :: n
|
|
double precision :: dble_fact
|
|
include 'constants.F'
|
|
|
|
!if(iand(n,1).eq.1)then
|
|
! int_gaus_pol= 0.d0
|
|
!else
|
|
! int_gaus_pol = dsqrt(pi/alpha) * dble_fact(n -1)/(alpha+alpha)**(n/2)
|
|
!endif
|
|
|
|
int_gaus_pol = 0.d0
|
|
if(iand(n,1).eq.0)then
|
|
int_gaus_pol = dsqrt(alpha/pi)
|
|
double precision :: two_alpha
|
|
two_alpha = alpha+alpha
|
|
integer :: i
|
|
do i=1,n,2
|
|
int_gaus_pol = int_gaus_pol * two_alpha
|
|
enddo
|
|
int_gaus_pol = dble_fact(n -1) / int_gaus_pol
|
|
endif
|
|
|
|
end
|
|
|
|
double precision function V_r(n,alpha)
|
|
!!!! calculate the radial part of the nuclear attraction integral which is the following integral :
|
|
!! integral on "r" with boundaries ( 0 ; + infinity) of [ r**n exp(-alpha * r**2) ]
|
|
!!! CAUTION :: this function requires the constant sqpi = dsqrt(pi)
|
|
implicit none
|
|
double precision :: alpha, fact
|
|
integer :: n
|
|
include 'constants.F'
|
|
if(iand(n,1).eq.1)then
|
|
V_r = 0.5d0 * fact(ishft(n,-1)) / (alpha ** (ishft(n,-1) + 1))
|
|
else
|
|
V_r = sqpi * fact(n) / fact(ishft(n,-1)) * (0.5d0/sqrt(alpha)) ** (n+1)
|
|
endif
|
|
end
|
|
|
|
|
|
double precision function V_phi(n,m)
|
|
implicit none
|
|
!!!! calculate the angular "phi" part of the nuclear attraction integral wich is the following integral :
|
|
!! integral on "phi" with boundaries ( 0 ; 2 pi) of [ cos(phi) **n sin(phi) **m ]
|
|
integer :: n,m, i
|
|
double precision :: prod, Wallis
|
|
prod = 1.d0
|
|
do i = 0,ishft(n,-1)-1
|
|
prod = prod/ (1.d0 + dfloat(m+1)/dfloat(n-i-i-1))
|
|
enddo
|
|
V_phi = 4.d0 * prod * Wallis(m)
|
|
end
|
|
|
|
double precision function V_theta(n,m)
|
|
implicit none
|
|
!!!! calculate the angular "theta" part of the nuclear attraction integral wich is the following integral :
|
|
!! integral on "theta" with boundaries ( 0 ; pi) of [ cos(theta) **n sin(theta) **m ]
|
|
integer :: n,m,i
|
|
double precision :: Wallis, prod
|
|
include 'constants.F'
|
|
V_theta = 0.d0
|
|
prod = 1.d0
|
|
do i = 0,ishft(n,-1)-1
|
|
prod = prod / (1.d0 + dfloat(m+1)/dfloat(n-i-i-1))
|
|
enddo
|
|
V_theta = (prod+prod) * Wallis(m)
|
|
end
|
|
|
|
|
|
double precision function Wallis(n)
|
|
!!!! calculate the Wallis integral :
|
|
!! integral on "theta" with boundaries ( 0 ; pi/2) of [ cos(theta) **n ]
|
|
implicit none
|
|
double precision :: fact
|
|
integer :: n,p
|
|
include 'constants.F'
|
|
if(iand(n,1).eq.0)then
|
|
Wallis = fact(ishft(n,-1))
|
|
Wallis = pi * fact(n) / (dble(ibset(0_8,n)) * (Wallis+Wallis)*Wallis)
|
|
else
|
|
p = ishft(n,-1)
|
|
Wallis = fact(p)
|
|
Wallis = dble(ibset(0_8,p+p)) * Wallis*Wallis / fact(p+p+1)
|
|
endif
|
|
|
|
end
|
|
|
|
|