.. _ao_two_e_ints: .. program:: ao_two_e_ints .. default-role:: option ================== ao_two_e_ints ================== Here, all two-electron integrals (:math:`1/r_{12}`) are computed. As they have 4 indices and many are zero, they are stored in a map, as defined in :file:`utils/map_module.f90`. To fetch an |AO| integral, use the `get_ao_two_e_integral(i,j,k,l,ao_integrals_map)` function. The conventions are: * For |AO| integrals : (ij|kl) = (11|22) = = <12|12> EZFIO parameters ---------------- .. option:: io_ao_two_e_integrals Read/Write |AO| integrals from/to disk [ Write | Read | None ] Default: None .. option:: ao_integrals_threshold If | (pq|rs) | < `ao_integrals_threshold` then (pq|rs) is zero Default: 1.e-15 .. option:: do_direct_integrals Compute integrals on the fly (very slow, only for debugging) Default: False Providers --------- .. c:var:: ao_integrals_cache .. code:: text double precision, allocatable :: ao_integrals_cache (0:64*64*64*64) File: :file:`map_integrals.irp.f` Cache of AO integrals for fast access .. c:var:: ao_integrals_cache_max .. code:: text integer :: ao_integrals_cache_min integer :: ao_integrals_cache_max File: :file:`map_integrals.irp.f` Min and max values of the AOs for which the integrals are in the cache .. c:var:: ao_integrals_cache_min .. code:: text integer :: ao_integrals_cache_min integer :: ao_integrals_cache_max File: :file:`map_integrals.irp.f` Min and max values of the AOs for which the integrals are in the cache .. c:var:: ao_integrals_map .. code:: text type(map_type) :: ao_integrals_map File: :file:`map_integrals.irp.f` AO integrals .. c:var:: ao_two_e_integral_schwartz .. code:: text double precision, allocatable :: ao_two_e_integral_schwartz (ao_num,ao_num) File: :file:`two_e_integrals.irp.f` Needed to compute Schwartz inequalities .. c:var:: ao_two_e_integrals_in_map .. code:: text logical :: ao_two_e_integrals_in_map File: :file:`two_e_integrals.irp.f` Map of Atomic integrals i(r1) j(r2) 1/r12 k(r1) l(r2) .. c:var:: gauleg_t2 .. code:: text double precision, allocatable :: gauleg_t2 (n_pt_max_integrals,n_pt_max_integrals/2) double precision, allocatable :: gauleg_w (n_pt_max_integrals,n_pt_max_integrals/2) File: :file:`gauss_legendre.irp.f` t_w(i,1,k) = w(i) t_w(i,2,k) = t(i) .. c:var:: gauleg_w .. code:: text double precision, allocatable :: gauleg_t2 (n_pt_max_integrals,n_pt_max_integrals/2) double precision, allocatable :: gauleg_w (n_pt_max_integrals,n_pt_max_integrals/2) File: :file:`gauss_legendre.irp.f` t_w(i,1,k) = w(i) t_w(i,2,k) = t(i) .. c:var:: general_primitive_integral .. code:: text double precision function general_primitive_integral(dim, & P_new,P_center,fact_p,p,p_inv,iorder_p, & Q_new,Q_center,fact_q,q,q_inv,iorder_q) File: :file:`two_e_integrals.irp.f` Computes the integral where p,q,r,s are Gaussian primitives .. c:var:: i_x1_new .. code:: text recursive subroutine I_x1_new(a,c,B_10,B_01,B_00,res,n_pt) File: :file:`two_e_integrals.irp.f` recursive function involved in the two-electron integral .. c:var:: i_x1_pol_mult_a1 .. code:: text recursive subroutine I_x1_pol_mult_a1(c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in) File: :file:`two_e_integrals.irp.f` recursive function involved in the two-electron integral .. c:var:: i_x1_pol_mult_a2 .. code:: text recursive subroutine I_x1_pol_mult_a2(c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in) File: :file:`two_e_integrals.irp.f` recursive function involved in the two-electron integral .. c:var:: i_x1_pol_mult_recurs .. code:: text recursive subroutine I_x1_pol_mult_recurs(a,c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in) File: :file:`two_e_integrals.irp.f` recursive function involved in the two-electron integral .. c:var:: i_x2_new .. code:: text recursive subroutine I_x2_new(c,B_10,B_01,B_00,res,n_pt) File: :file:`two_e_integrals.irp.f` recursive function involved in the two-electron integral .. c:var:: i_x2_pol_mult .. code:: text recursive subroutine I_x2_pol_mult(c,B_10,B_01,B_00,C_00,D_00,d,nd,dim) File: :file:`two_e_integrals.irp.f` recursive function involved in the two-electron integral Subroutines / functions ----------------------- .. c:function:: ao_l4 .. code:: text integer function ao_l4(i,j,k,l) File: :file:`two_e_integrals.irp.f` Computes the product of l values of i,j,k,and l .. c:function:: ao_two_e_integral .. code:: text double precision function ao_two_e_integral(i,j,k,l) File: :file:`two_e_integrals.irp.f` integral of the AO basis or (ij|kl) i(r1) j(r1) 1/r12 k(r2) l(r2) .. c:function:: ao_two_e_integral_schwartz_accel .. code:: text double precision function ao_two_e_integral_schwartz_accel(i,j,k,l) File: :file:`two_e_integrals.irp.f` integral of the AO basis or (ij|kl) i(r1) j(r1) 1/r12 k(r2) l(r2) .. c:function:: ao_two_e_integrals_in_map_collector .. code:: text subroutine ao_two_e_integrals_in_map_collector(zmq_socket_pull) File: :file:`integrals_in_map_slave.irp.f` Collects results from the AO integral calculation .. c:function:: ao_two_e_integrals_in_map_slave .. code:: text subroutine ao_two_e_integrals_in_map_slave(thread,iproc) File: :file:`integrals_in_map_slave.irp.f` Computes a buffer of integrals .. c:function:: ao_two_e_integrals_in_map_slave_inproc .. code:: text subroutine ao_two_e_integrals_in_map_slave_inproc(i) File: :file:`integrals_in_map_slave.irp.f` Computes a buffer of integrals. i is the ID of the current thread. .. c:function:: ao_two_e_integrals_in_map_slave_tcp .. code:: text subroutine ao_two_e_integrals_in_map_slave_tcp(i) File: :file:`integrals_in_map_slave.irp.f` Computes a buffer of integrals. i is the ID of the current thread. .. c:function:: clear_ao_map .. code:: text subroutine clear_ao_map File: :file:`map_integrals.irp.f` Frees the memory of the AO map .. c:function:: compute_ao_integrals_jl .. code:: text subroutine compute_ao_integrals_jl(j,l,n_integrals,buffer_i,buffer_value) File: :file:`two_e_integrals.irp.f` Parallel client for AO integrals .. c:function:: compute_ao_two_e_integrals .. code:: text subroutine compute_ao_two_e_integrals(j,k,l,sze,buffer_value) File: :file:`two_e_integrals.irp.f` Compute AO 1/r12 integrals for all i and fixed j,k,l .. c:function:: dump_ao_integrals .. code:: text subroutine dump_ao_integrals(filename) File: :file:`map_integrals.irp.f` Save to disk the |AO| integrals .. c:function:: eri .. code:: text double precision function ERI(alpha,beta,delta,gama,a_x,b_x,c_x,d_x,a_y,b_y,c_y,d_y,a_z,b_z,c_z,d_z) File: :file:`two_e_integrals.irp.f` ATOMIC PRIMTIVE two-electron integral between the 4 primitives :: primitive_1 = x1**(a_x) y1**(a_y) z1**(a_z) exp(-alpha * r1**2) primitive_2 = x1**(b_x) y1**(b_y) z1**(b_z) exp(- beta * r1**2) primitive_3 = x2**(c_x) y2**(c_y) z2**(c_z) exp(-delta * r2**2) primitive_4 = x2**(d_x) y2**(d_y) z2**(d_z) exp(- gama * r2**2) .. c:function:: gauleg .. code:: text subroutine gauleg(x1,x2,x,w,n) File: :file:`gauss_legendre.irp.f` Gauss-Legendre .. c:function:: get_ao_map_size .. code:: text function get_ao_map_size() File: :file:`map_integrals.irp.f` Returns the number of elements in the AO map .. c:function:: get_ao_two_e_integral .. code:: text double precision function get_ao_two_e_integral(i,j,k,l,map) result(result) File: :file:`map_integrals.irp.f` Gets one AO bi-electronic integral from the AO map .. c:function:: get_ao_two_e_integrals .. code:: text subroutine get_ao_two_e_integrals(j,k,l,sze,out_val) File: :file:`map_integrals.irp.f` Gets multiple AO bi-electronic integral from the AO map . All i are retrieved for j,k,l fixed. .. c:function:: get_ao_two_e_integrals_non_zero .. code:: text subroutine get_ao_two_e_integrals_non_zero(j,k,l,sze,out_val,out_val_index,non_zero_int) File: :file:`map_integrals.irp.f` Gets multiple AO bi-electronic integral from the AO map . All non-zero i are retrieved for j,k,l fixed. .. c:function:: give_polynom_mult_center_x .. code:: text subroutine give_polynom_mult_center_x(P_center,Q_center,a_x,d_x,p,q,n_pt_in,pq_inv,pq_inv_2,p10_1,p01_1,p10_2,p01_2,d,n_pt_out) File: :file:`two_e_integrals.irp.f` subroutine that returns the explicit polynom in term of the "t" variable of the following polynomw : I_x1(a_x, d_x,p,q) * I_x1(a_y, d_y,p,q) * I_x1(a_z, d_z,p,q) .. c:function:: i_x1_pol_mult .. code:: text subroutine I_x1_pol_mult(a,c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in) File: :file:`two_e_integrals.irp.f` recursive function involved in the two-electron integral .. c:function:: insert_into_ao_integrals_map .. code:: text subroutine insert_into_ao_integrals_map(n_integrals,buffer_i, buffer_values) File: :file:`map_integrals.irp.f` Create new entry into AO map .. c:function:: integrale_new .. code:: text subroutine integrale_new(I_f,a_x,b_x,c_x,d_x,a_y,b_y,c_y,d_y,a_z,b_z,c_z,d_z,p,q,n_pt) File: :file:`two_e_integrals.irp.f` calculate the integral of the polynom :: I_x1(a_x+b_x, c_x+d_x,p,q) * I_x1(a_y+b_y, c_y+d_y,p,q) * I_x1(a_z+b_z, c_z+d_z,p,q) between ( 0 ; 1) .. c:function:: load_ao_integrals .. code:: text integer function load_ao_integrals(filename) File: :file:`map_integrals.irp.f` Read from disk the |AO| integrals .. c:function:: n_pt_sup .. code:: text integer function n_pt_sup(a_x,b_x,c_x,d_x,a_y,b_y,c_y,d_y,a_z,b_z,c_z,d_z) File: :file:`two_e_integrals.irp.f` Returns the upper boundary of the degree of the polynomial involved in the bielctronic integral : Ix(a_x,b_x,c_x,d_x) * Iy(a_y,b_y,c_y,d_y) * Iz(a_z,b_z,c_z,d_z) .. c:function:: push_integrals .. code:: text subroutine push_integrals(zmq_socket_push, n_integrals, buffer_i, buffer_value, task_id) File: :file:`integrals_in_map_slave.irp.f` Push integrals in the push socket .. c:function:: two_e_integrals_index .. code:: text subroutine two_e_integrals_index(i,j,k,l,i1) File: :file:`map_integrals.irp.f` .. c:function:: two_e_integrals_index_reverse .. code:: text subroutine two_e_integrals_index_reverse(i,j,k,l,i1) File: :file:`map_integrals.irp.f`