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qp2/plugins/local/ao_tc_eff_map/two_e_ints_gauss.irp.f

328 lines
11 KiB
Fortran

double precision function ao_tc_sym_two_e_pot(i,j,k,l)
implicit none
BEGIN_DOC
! integral of the AO basis <ik|jl> or (ij|kl)
! i(r1) j(r1) (tc_pot(r12,mu)) k(r2) l(r2)
!
! where (tc_pot(r12,mu)) is the scalar part of the potential EXCLUDING the term erf(mu r12)/r12.
!
! See Eq. (32) of JCP 154, 084119 (2021).
END_DOC
integer,intent(in) :: i,j,k,l
integer :: p,q,r,s
double precision :: I_center(3),J_center(3),K_center(3),L_center(3)
integer :: num_i,num_j,num_k,num_l,dim1,I_power(3),J_power(3),K_power(3),L_power(3)
double precision :: integral
include 'utils/constants.include.F'
double precision :: P_new(0:max_dim,3),P_center(3),fact_p,pp
double precision :: Q_new(0:max_dim,3),Q_center(3),fact_q,qq
integer :: iorder_p(3), iorder_q(3)
double precision, allocatable :: schwartz_kl(:,:)
double precision :: schwartz_ij
double precision :: scw_gauss_int,general_primitive_integral_gauss
dim1 = n_pt_max_integrals
num_i = ao_nucl(i)
num_j = ao_nucl(j)
num_k = ao_nucl(k)
num_l = ao_nucl(l)
ao_tc_sym_two_e_pot = 0.d0
double precision :: thr
thr = ao_integrals_threshold*ao_integrals_threshold
allocate(schwartz_kl(0:ao_prim_num(l),0:ao_prim_num(k)))
double precision :: coef3
double precision :: coef2
double precision :: p_inv,q_inv
double precision :: coef1
double precision :: coef4
do p = 1, 3
I_power(p) = ao_power(i,p)
J_power(p) = ao_power(j,p)
K_power(p) = ao_power(k,p)
L_power(p) = ao_power(l,p)
I_center(p) = nucl_coord(num_i,p)
J_center(p) = nucl_coord(num_j,p)
K_center(p) = nucl_coord(num_k,p)
L_center(p) = nucl_coord(num_l,p)
enddo
schwartz_kl(0,0) = 0.d0
do r = 1, ao_prim_num(k)
coef1 = ao_coef_normalized_ordered_transp(r,k)*ao_coef_normalized_ordered_transp(r,k)
schwartz_kl(0,r) = 0.d0
do s = 1, ao_prim_num(l)
coef2 = coef1 * ao_coef_normalized_ordered_transp(s,l) * ao_coef_normalized_ordered_transp(s,l)
call give_explicit_poly_and_gaussian(Q_new,Q_center,qq,fact_q,iorder_q,&
ao_expo_ordered_transp(r,k),ao_expo_ordered_transp(s,l), &
K_power,L_power,K_center,L_center,dim1)
q_inv = 1.d0/qq
scw_gauss_int = general_primitive_integral_gauss(dim1, &
Q_new,Q_center,fact_q,qq,q_inv,iorder_q, &
Q_new,Q_center,fact_q,qq,q_inv,iorder_q)
schwartz_kl(s,r) = dabs(scw_gauss_int * coef2)
schwartz_kl(0,r) = max(schwartz_kl(0,r),schwartz_kl(s,r))
enddo
schwartz_kl(0,0) = max(schwartz_kl(0,r),schwartz_kl(0,0))
enddo
do p = 1, ao_prim_num(i)
coef1 = ao_coef_normalized_ordered_transp(p,i)
do q = 1, ao_prim_num(j)
coef2 = coef1*ao_coef_normalized_ordered_transp(q,j)
call give_explicit_poly_and_gaussian(P_new,P_center,pp,fact_p,iorder_p,&
ao_expo_ordered_transp(p,i),ao_expo_ordered_transp(q,j), &
I_power,J_power,I_center,J_center,dim1)
p_inv = 1.d0/pp
scw_gauss_int = general_primitive_integral_gauss(dim1, &
P_new,P_center,fact_p,pp,p_inv,iorder_p, &
P_new,P_center,fact_p,pp,p_inv,iorder_p)
schwartz_ij = dabs(scw_gauss_int * coef2*coef2)
if (schwartz_kl(0,0)*schwartz_ij < thr) then
cycle
endif
do r = 1, ao_prim_num(k)
if (schwartz_kl(0,r)*schwartz_ij < thr) then
cycle
endif
coef3 = coef2*ao_coef_normalized_ordered_transp(r,k)
do s = 1, ao_prim_num(l)
if (schwartz_kl(s,r)*schwartz_ij < thr) then
cycle
endif
coef4 = coef3*ao_coef_normalized_ordered_transp(s,l)
call give_explicit_poly_and_gaussian(Q_new,Q_center,qq,fact_q,iorder_q, &
ao_expo_ordered_transp(r,k),ao_expo_ordered_transp(s,l), &
K_power,L_power,K_center,L_center,dim1)
q_inv = 1.d0/qq
integral = general_primitive_integral_gauss(dim1, &
P_new,P_center,fact_p,pp,p_inv,iorder_p, &
Q_new,Q_center,fact_q,qq,q_inv,iorder_q)
ao_tc_sym_two_e_pot = ao_tc_sym_two_e_pot + coef4 * integral
enddo ! s
enddo ! r
enddo ! q
enddo ! p
deallocate (schwartz_kl)
end
double precision function general_primitive_integral_gauss(dim, &
P_new,P_center,fact_p,p,p_inv,iorder_p, &
Q_new,Q_center,fact_q,q,q_inv,iorder_q)
implicit none
BEGIN_DOC
! Computes the integral <pq|rs> where p,q,r,s are Gaussian primitives
END_DOC
integer,intent(in) :: dim
include 'utils/constants.include.F'
double precision, intent(in) :: P_new(0:max_dim,3),P_center(3),fact_p,p,p_inv
double precision, intent(in) :: Q_new(0:max_dim,3),Q_center(3),fact_q,q,q_inv
integer, intent(in) :: iorder_p(3)
integer, intent(in) :: iorder_q(3)
double precision :: r_cut,gama_r_cut,rho,dist
double precision :: dx(0:max_dim),Ix_pol(0:max_dim),dy(0:max_dim),Iy_pol(0:max_dim),dz(0:max_dim),Iz_pol(0:max_dim)
integer :: n_Ix,n_Iy,n_Iz,nx,ny,nz
double precision :: bla
integer :: ix,iy,iz,jx,jy,jz,i
double precision :: a,b,c,d,e,f,accu,pq,const
double precision :: pq_inv, p10_1, p10_2, p01_1, p01_2,pq_inv_2
integer :: n_pt_tmp,n_pt_out, iorder
double precision :: d1(0:max_dim),d_poly(0:max_dim),rint,d1_screened(0:max_dim)
double precision :: thr
thr = ao_integrals_threshold
general_primitive_integral_gauss = 0.d0
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: dx,Ix_pol,dy,Iy_pol,dz,Iz_pol
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: d1, d_poly
! Gaussian Product
! ----------------
pq = p_inv*0.5d0*q_inv
pq_inv = 0.5d0/(p+q)
p10_1 = q*pq ! 1/(2p)
p01_1 = p*pq ! 1/(2q)
pq_inv_2 = pq_inv+pq_inv
p10_2 = pq_inv_2 * p10_1*q !0.5d0*q/(pq + p*p)
p01_2 = pq_inv_2 * p01_1*p !0.5d0*p/(q*q + pq)
accu = 0.d0
iorder = iorder_p(1)+iorder_q(1)+iorder_p(1)+iorder_q(1)
do ix=0,iorder
Ix_pol(ix) = 0.d0
enddo
n_Ix = 0
do ix = 0, iorder_p(1)
if (abs(P_new(ix,1)) < thr) cycle
a = P_new(ix,1)
do jx = 0, iorder_q(1)
d = a*Q_new(jx,1)
if (abs(d) < thr) cycle
!DIR$ FORCEINLINE
call give_polynom_mult_center_x(P_center(1),Q_center(1),ix,jx,p,q,iorder,pq_inv,pq_inv_2,p10_1,p01_1,p10_2,p01_2,dx,nx)
!DIR$ FORCEINLINE
call add_poly_multiply(dx,nx,d,Ix_pol,n_Ix)
enddo
enddo
if (n_Ix == -1) then
return
endif
iorder = iorder_p(2)+iorder_q(2)+iorder_p(2)+iorder_q(2)
do ix=0, iorder
Iy_pol(ix) = 0.d0
enddo
n_Iy = 0
do iy = 0, iorder_p(2)
if (abs(P_new(iy,2)) > thr) then
b = P_new(iy,2)
do jy = 0, iorder_q(2)
e = b*Q_new(jy,2)
if (abs(e) < thr) cycle
!DIR$ FORCEINLINE
call give_polynom_mult_center_x(P_center(2),Q_center(2),iy,jy,p,q,iorder,pq_inv,pq_inv_2,p10_1,p01_1,p10_2,p01_2,dy,ny)
!DIR$ FORCEINLINE
call add_poly_multiply(dy,ny,e,Iy_pol,n_Iy)
enddo
endif
enddo
if (n_Iy == -1) then
return
endif
iorder = iorder_p(3)+iorder_q(3)+iorder_p(3)+iorder_q(3)
do ix=0,iorder
Iz_pol(ix) = 0.d0
enddo
n_Iz = 0
do iz = 0, iorder_p(3)
if (abs(P_new(iz,3)) > thr) then
c = P_new(iz,3)
do jz = 0, iorder_q(3)
f = c*Q_new(jz,3)
if (abs(f) < thr) cycle
!DIR$ FORCEINLINE
call give_polynom_mult_center_x(P_center(3),Q_center(3),iz,jz,p,q,iorder,pq_inv,pq_inv_2,p10_1,p01_1,p10_2,p01_2,dz,nz)
!DIR$ FORCEINLINE
call add_poly_multiply(dz,nz,f,Iz_pol,n_Iz)
enddo
endif
enddo
if (n_Iz == -1) then
return
endif
rho = p*q *pq_inv_2
dist = (P_center(1) - Q_center(1))*(P_center(1) - Q_center(1)) + &
(P_center(2) - Q_center(2))*(P_center(2) - Q_center(2)) + &
(P_center(3) - Q_center(3))*(P_center(3) - Q_center(3))
const = dist*rho
n_pt_tmp = n_Ix+n_Iy
do i=0,n_pt_tmp
d_poly(i)=0.d0
enddo
!DIR$ FORCEINLINE
call multiply_poly(Ix_pol,n_Ix,Iy_pol,n_Iy,d_poly,n_pt_tmp)
if (n_pt_tmp == -1) then
return
endif
n_pt_out = n_pt_tmp+n_Iz
do i=0,n_pt_out
d1(i)=0.d0
enddo
!DIR$ FORCEINLINE
call multiply_poly(d_poly ,n_pt_tmp ,Iz_pol,n_Iz,d1,n_pt_out)
double precision :: aa,c_a,t_a,rho_old,w_a,pi_3,prefactor,inv_pq_3_2
double precision :: gauss_int
integer :: m
gauss_int = 0.d0
pi_3 = pi*pi*pi
inv_pq_3_2 = (p_inv * q_inv)**(1.5d0)
rho_old = (p*q)/(p+q)
prefactor = pi_3 * inv_pq_3_2 * fact_p * fact_q
do i = 1, n_gauss_eff_pot ! browse the gaussians with different expo/coef
!do i = 1, n_gauss_eff_pot-1
aa = expo_gauss_eff_pot(i)
c_a = coef_gauss_eff_pot(i)
t_a = dsqrt( aa /(rho_old + aa) )
w_a = dexp(-t_a*t_a*rho_old*dist)
accu = 0.d0
! evaluation of the polynom Ix(t_a) * Iy(t_a) * Iz(t_a)
do m = 0, n_pt_out,2
accu += d1(m) * (t_a)**(dble(m))
enddo
! equation A8 of PRA-70-062505 (2004) of Toul. Col. Sav.
gauss_int = gauss_int + c_a * prefactor * (1.d0 - t_a*t_a)**(1.5d0) * w_a * accu
enddo
general_primitive_integral_gauss = gauss_int
end
subroutine compute_ao_integrals_gauss_jl(j,l,n_integrals,buffer_i,buffer_value)
implicit none
use map_module
BEGIN_DOC
! Parallel client for AO integrals
END_DOC
integer, intent(in) :: j,l
integer,intent(out) :: n_integrals
integer(key_kind),intent(out) :: buffer_i(ao_num*ao_num)
real(integral_kind),intent(out) :: buffer_value(ao_num*ao_num)
integer :: i,k
double precision :: cpu_1,cpu_2, wall_1, wall_2
double precision :: integral, wall_0
double precision :: thr,ao_tc_sym_two_e_pot
integer :: kk, m, j1, i1
logical, external :: ao_two_e_integral_zero
thr = ao_integrals_threshold
n_integrals = 0
j1 = j+ishft(l*l-l,-1)
do k = 1, ao_num ! r1
i1 = ishft(k*k-k,-1)
if (i1 > j1) then
exit
endif
do i = 1, k
i1 += 1
if (i1 > j1) then
exit
endif
! if (ao_two_e_integral_zero(i,j,k,l)) then
if (.False.) then
cycle
endif
if (ao_two_e_integral_erf_schwartz(i,k)*ao_two_e_integral_erf_schwartz(j,l) < thr ) then
cycle
endif
!DIR$ FORCEINLINE
integral = ao_tc_sym_two_e_pot(i,k,j,l) ! i,k : r1 j,l : r2
if (abs(integral) < thr) then
cycle
endif
n_integrals += 1
!DIR$ FORCEINLINE
call two_e_integrals_index(i,j,k,l,buffer_i(n_integrals))
buffer_value(n_integrals) = integral
enddo
enddo
end