ao_two_e_ints

Here, all two-electron integrals (\(1/r_{12}\)) are computed. As they have 4 indices and many are zero, they are stored in a map, as defined in 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) = <ik|jl> = <12|12>

EZFIO parameters

io_ao_two_e_integrals

Read/Write AO integrals from/to disk [ Write | Read | None ]

Default: None

ao_integrals_threshold

If | (pq|rs) | < ao_integrals_threshold then (pq|rs) is zero

Default: 1.e-15

do_direct_integrals

Compute integrals on the fly (very slow, only for debugging)

Default: False

Providers

ao_integrals_cache

File : ao_two_e_ints/map_integrals.irp.f

double precision, allocatable   :: ao_integrals_cache   (0:64*64*64*64)

Cache of AO integrals for fast access

Needs:

ao_integrals_cache_min

ao_integrals_map

ao_two_e_integrals_in_map

ao_integrals_cache_max

File : ao_two_e_ints/map_integrals.irp.f

integer :: ao_integrals_cache_min
integer :: ao_integrals_cache_max

Min and max values of the AOs for which the integrals are in the cache

Needs:

ao_num

Needed by:

ao_integrals_cache

ao_integrals_cache_min

File : ao_two_e_ints/map_integrals.irp.f

integer :: ao_integrals_cache_min
integer :: ao_integrals_cache_max

Min and max values of the AOs for which the integrals are in the cache

Needs:

ao_num

Needed by:

ao_integrals_cache

ao_integrals_map

File : ao_two_e_ints/map_integrals.irp.f

type(map_type)  :: ao_integrals_map

AO integrals

Needs:

ao_num

Needed by:

ao_integrals_cache ao_two_e_integral_alpha

ao_two_e_integrals_in_map mo_two_e_integral_jj_from_ao

mo_two_e_integrals_vv_from_ao

ao_two_e_integral_schwartz

File : ao_two_e_ints/two_e_integrals.irp.f

double precision, allocatable   :: ao_two_e_integral_schwartz   (ao_num,ao_num)

Needed to compute Schwartz inequalities

Needs:

ao_coef_normalized_ordered_transp ao_expo_ordered_transp ao_nucl

ao_num ao_power ao_prim_num

n_pt_max_integrals nucl_coord

Needed by:

ao_two_e_integral_alpha

mo_two_e_integral_jj_from_ao

mo_two_e_integrals_vv_from_ao

ao_two_e_integrals_in_map

File : ao_two_e_ints/two_e_integrals.irp.f

logical :: ao_two_e_integrals_in_map

Map of Atomic integrals

i(r1) j(r2) 1/r12 k(r1) l(r2)

Needs:

ao_coef_normalized_ordered_transp ao_expo_ordered_transp ao_integrals_map ao_nucl ao_num ao_power

ao_prim_num ezfio_filename io_ao_two_e_integrals mpi_master n_pt_max_integrals nproc

nucl_coord read_ao_two_e_integrals zmq_context zmq_socket_pull_tcp_address zmq_state

Needed by:

ao_integrals_cache ao_two_e_integral_alpha

mo_two_e_integral_jj_from_ao mo_two_e_integrals_erf_in_map

mo_two_e_integrals_in_map mo_two_e_integrals_vv_from_ao

gauleg_t2

File : ao_two_e_ints/gauss_legendre.irp.f

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)

t_w(i,1,k) = w(i) t_w(i,2,k) = t(i)

Needs:

n_pt_max_integrals

gauleg_w

File : ao_two_e_ints/gauss_legendre.irp.f

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)

t_w(i,1,k) = w(i) t_w(i,2,k) = t(i)

Needs:

n_pt_max_integrals

general_primitive_integral:()

File : ao_two_e_ints/two_e_integrals.irp.f

  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)

Computes the integral <pq|rs> where p,q,r,s are Gaussian primitives

Calls:

add_poly_multiply()

give_polynom_mult_center_x()

multiply_poly()

i_x1_new:()

File : ao_two_e_ints/two_e_integrals.irp.f

recursive subroutine I_x1_new(a,c,B_10,B_01,B_00,res,n_pt)

recursive function involved in the two-electron integral

Needs:

n_pt_max_integrals

Called by:

i_x1_new() i_x2_new()

integrale_new()

integrale_new_erf()

Calls:

i_x1_new()

i_x2_new()

i_x1_pol_mult_a1:()

File : ao_two_e_ints/two_e_integrals.irp.f

recursive subroutine I_x1_pol_mult_a1(c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in)

recursive function involved in the two-electron integral

Called by:

i_x1_pol_mult()

i_x1_pol_mult_a2()

i_x1_pol_mult_recurs()

Calls:

i_x2_pol_mult()

multiply_poly()

i_x1_pol_mult_a2:()

File : ao_two_e_ints/two_e_integrals.irp.f

recursive subroutine I_x1_pol_mult_a2(c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in)

recursive function involved in the two-electron integral

Called by:

i_x1_pol_mult()

i_x1_pol_mult_recurs()

Calls:

i_x1_pol_mult_a1()

i_x2_pol_mult()

multiply_poly()

i_x1_pol_mult_recurs:()

File : ao_two_e_ints/two_e_integrals.irp.f

recursive subroutine I_x1_pol_mult_recurs(a,c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in)

recursive function involved in the two-electron integral

Called by:

i_x1_pol_mult()

i_x1_pol_mult_recurs()

Calls:

i_x1_pol_mult_a1() i_x1_pol_mult_a2()

i_x1_pol_mult_recurs()

multiply_poly()

i_x2_new:()

File : ao_two_e_ints/two_e_integrals.irp.f

recursive subroutine I_x2_new(c,B_10,B_01,B_00,res,n_pt)

recursive function involved in the two-electron integral

Needs:

n_pt_max_integrals

Called by:

i_x1_new()

Calls:

i_x1_new()

i_x2_pol_mult:()

File : ao_two_e_ints/two_e_integrals.irp.f

recursive subroutine I_x2_pol_mult(c,B_10,B_01,B_00,C_00,D_00,d,nd,dim)

recursive function involved in the two-electron integral

Called by:

i_x1_pol_mult() i_x1_pol_mult_a1()

i_x1_pol_mult_a2()

i_x2_pol_mult()

Calls:

i_x2_pol_mult()

multiply_poly()

Subroutines / functions

ao_l4:()

File : ao_two_e_ints/two_e_integrals.irp.f

integer function ao_l4(i,j,k,l)

Computes the product of l values of i,j,k,and l

Needs:

ao_l

ao_two_e_integral:()

File : ao_two_e_ints/two_e_integrals.irp.f

double precision function ao_two_e_integral(i,j,k,l)

integral of the AO basis <ik|jl> or (ij|kl)

i(r1) j(r1) 1/r12 k(r2) l(r2)

Needs:

n_pt_max_integrals ao_coef_normalized_ordered_transp ao_power

ao_expo_ordered_transp ao_prim_num

ao_nucl nucl_coord

Calls:

give_explicit_poly_and_gaussian()

ao_two_e_integral_schwartz_accel:()

File : ao_two_e_ints/two_e_integrals.irp.f

double precision function ao_two_e_integral_schwartz_accel(i,j,k,l)

integral of the AO basis <ik|jl> or (ij|kl)

i(r1) j(r1) 1/r12 k(r2) l(r2)

Needs:

n_pt_max_integrals ao_integrals_threshold ao_coef_normalized_ordered_transp

ao_power ao_expo_ordered_transp ao_prim_num

ao_nucl nucl_coord

Calls:

give_explicit_poly_and_gaussian()

ao_two_e_integrals_in_map_collector:()

File : ao_two_e_ints/integrals_in_map_slave.irp.f

subroutine ao_two_e_integrals_in_map_collector(zmq_socket_pull)

Collects results from the AO integral calculation

Needs:

ao_integrals_map

ao_num

Called by:

ao_two_e_integrals_in_map

Calls:

end_zmq_to_qp_run_socket()

insert_into_ao_integrals_map()

ao_two_e_integrals_in_map_slave:()

File : ao_two_e_ints/integrals_in_map_slave.irp.f

subroutine ao_two_e_integrals_in_map_slave(thread,iproc)

Computes a buffer of integrals

Needs:

ao_num

Called by:

ao_two_e_integrals_in_map_slave_inproc()

ao_two_e_integrals_in_map_slave_tcp()

Calls:

compute_ao_integrals_jl() end_zmq_push_socket()

end_zmq_to_qp_run_socket()

push_integrals()

ao_two_e_integrals_in_map_slave_inproc:()

File : ao_two_e_ints/integrals_in_map_slave.irp.f

subroutine ao_two_e_integrals_in_map_slave_inproc(i)

Computes a buffer of integrals. i is the ID of the current thread.

Called by:

ao_two_e_integrals_in_map

Calls:

ao_two_e_integrals_in_map_slave()

ao_two_e_integrals_in_map_slave_tcp:()

File : ao_two_e_ints/integrals_in_map_slave.irp.f

subroutine ao_two_e_integrals_in_map_slave_tcp(i)

Computes a buffer of integrals. i is the ID of the current thread.

Calls:

ao_two_e_integrals_in_map_slave()

clear_ao_map:()

File : ao_two_e_ints/map_integrals.irp.f

subroutine clear_ao_map

Frees the memory of the AO map

Needs:

ao_integrals_map

Calls:

map_deinit()

compute_ao_integrals_jl:()

File : ao_two_e_ints/two_e_integrals.irp.f

subroutine compute_ao_integrals_jl(j,l,n_integrals,buffer_i,buffer_value)

Parallel client for AO integrals

Needs:

ao_overlap_abs ao_num

ao_integrals_threshold

ao_two_e_integral_schwartz

Called by:

ao_two_e_integrals_in_map_slave()

Calls:

two_e_integrals_index()

compute_ao_two_e_integrals:()

File : ao_two_e_ints/two_e_integrals.irp.f

subroutine compute_ao_two_e_integrals(j,k,l,sze,buffer_value)

Compute AO 1/r12 integrals for all i and fixed j,k,l

Needs:

ao_overlap_abs

ao_num

ao_two_e_integral_schwartz

Called by:

mo_two_e_integral_jj_from_ao

mo_two_e_integrals_vv_from_ao

dump_ao_integrals:()

File : ao_two_e_ints/map_integrals.irp.f

subroutine dump_ao_integrals(filename)

Save to disk the AO integrals

Needs:

ao_integrals_map

mpi_master

Calls:

ezfio_set_work_empty()

eri:()

File : ao_two_e_ints/two_e_integrals.irp.f

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)

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)

Calls:

integrale_new()

gauleg:()

File : ao_two_e_ints/gauss_legendre.irp.f

subroutine gauleg(x1,x2,x,w,n)

Gauss-Legendre

Called by:

gauleg_t2

get_ao_map_size:()

File : ao_two_e_ints/map_integrals.irp.f

function get_ao_map_size()

Returns the number of elements in the AO map

Needs:

ao_integrals_map

get_ao_two_e_integral:()

File : ao_two_e_ints/map_integrals.irp.f

double precision function get_ao_two_e_integral(i,j,k,l,map) result(result)

Gets one AO bi-electronic integral from the AO map

Needs:

ao_overlap_abs ao_integrals_threshold

ao_two_e_integral_schwartz ao_integrals_cache

ao_integrals_cache_min ao_two_e_integrals_in_map

Calls:

map_get()

two_e_integrals_index()

get_ao_two_e_integrals:()

File : ao_two_e_ints/map_integrals.irp.f

subroutine get_ao_two_e_integrals(j,k,l,sze,out_val)

Gets multiple AO bi-electronic integral from the AO map . All i are retrieved for j,k,l fixed.

Needs:

ao_integrals_map ao_overlap_abs

ao_integrals_threshold

ao_two_e_integrals_in_map

Called by:

add_integrals_to_map()

add_integrals_to_map_no_exit_34()

add_integrals_to_map_three_indices()

get_ao_two_e_integrals_non_zero:()

File : ao_two_e_ints/map_integrals.irp.f

subroutine get_ao_two_e_integrals_non_zero(j,k,l,sze,out_val,out_val_index,non_zero_int)

Gets multiple AO bi-electronic integral from the AO map . All non-zero i are retrieved for j,k,l fixed.

Needs:

ao_integrals_map ao_overlap_abs

ao_integrals_threshold ao_two_e_integral_schwartz

ao_two_e_integrals_in_map

Called by:

mo_two_e_integral_jj_from_ao

mo_two_e_integrals_vv_from_ao

Calls:

map_get()

two_e_integrals_index()

give_polynom_mult_center_x:()

File : ao_two_e_ints/two_e_integrals.irp.f

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)

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)

Called by:

general_primitive_integral()

general_primitive_integral_erf()

Calls:

i_x1_pol_mult()

i_x1_pol_mult:()

File : ao_two_e_ints/two_e_integrals.irp.f

subroutine I_x1_pol_mult(a,c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in)

recursive function involved in the two-electron integral

Called by:

give_polynom_mult_center_x()

Calls:

i_x1_pol_mult_a1() i_x1_pol_mult_a2()

i_x1_pol_mult_recurs()

i_x2_pol_mult()

insert_into_ao_integrals_map:()

File : ao_two_e_ints/map_integrals.irp.f

subroutine insert_into_ao_integrals_map(n_integrals,buffer_i, buffer_values)

Create new entry into AO map

Needs:

ao_integrals_map

Called by:

ao_two_e_integrals_in_map_collector()

Calls:

map_append()

integrale_new:()

File : ao_two_e_ints/two_e_integrals.irp.f

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)

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)

Needs:

n_pt_max_integrals

gauleg_t2

Called by:

eri()

Calls:

i_x1_new()

load_ao_integrals:()

File : ao_two_e_ints/map_integrals.irp.f

integer function load_ao_integrals(filename)

Read from disk the AO integrals

Needs:

ao_integrals_map

Calls:

cache_map_reallocate()

map_deinit()

map_sort()

n_pt_sup:()

File : ao_two_e_ints/two_e_integrals.irp.f

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)

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)

push_integrals:()

File : ao_two_e_ints/integrals_in_map_slave.irp.f

subroutine push_integrals(zmq_socket_push, n_integrals, buffer_i, buffer_value, task_id)

Push integrals in the push socket

Called by:

ao_two_e_integrals_erf_in_map_slave()

ao_two_e_integrals_in_map_slave()

two_e_integrals_index:()

File : ao_two_e_ints/map_integrals.irp.f

subroutine two_e_integrals_index(i,j,k,l,i1)

Called by:

ao_integrals_cache ao_integrals_erf_cache ao_integrals_erf_map ao_integrals_map compute_ao_integrals_erf_jl() compute_ao_integrals_jl() get_ao_two_e_integral() get_ao_two_e_integral_erf() get_ao_two_e_integrals_erf_non_zero()

get_ao_two_e_integrals_non_zero() get_mo_two_e_integral_erf() get_mo_two_e_integrals_coulomb_ii() get_mo_two_e_integrals_erf() get_mo_two_e_integrals_erf_coulomb_ii() get_mo_two_e_integrals_erf_exch_ii() get_mo_two_e_integrals_erf_i1j1() get_mo_two_e_integrals_erf_ij() get_mo_two_e_integrals_exch_ii()

get_mo_two_e_integrals_i1j1() get_mo_two_e_integrals_ij() get_two_e_integral() mo_integrals_cache mo_integrals_erf_cache mo_integrals_erf_map mo_integrals_map two_e_integrals_index_reverse()

two_e_integrals_index_reverse:()

File : ao_two_e_ints/map_integrals.irp.f

subroutine two_e_integrals_index_reverse(i,j,k,l,i1)

Called by:

ao_two_e_integral_alpha

Calls:

two_e_integrals_index()