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qp2/docs/source/modules/ao_two_e_ints.rst

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Develop (#15) * fixed laplacian of aos * corrected the laplacians of aos * added dft_one_e * added new feature for new dft functionals * changed the configure to add new functionals * changed the configure * added dft_one_e/README.rst * added README.rst in new_functionals * added source/programmers_guide/new_ks.rst * Thesis Yann * Added gmp installation in configure * improved qp_e_conv_fci * Doc * Typos * Added variance_max * Fixed completion in qp_create * modif TODO * fixed DFT potential for n_states gt 1 * improved pot pbe * trying to improve sr PBE * fixed potential pbe * fixed the vxc smashed for pbe sr and normal * Comments in selection * bug fixed by peter * Fixed bug with zero beta electrons * Update README.rst * Update e_xc_new_func.irp.f * Update links.rst * Update quickstart.rst * Update quickstart.rst * updated cipsi * Fixed energies of non-expected s2 (#9) * Moved diag_algorithm in Davdison * Add print_ci_vector in tools (#11) * Fixed energies of non-expected s2 * Moved diag_algorithm in Davdison * Fixed travis * Added print_ci_vector * Documentation * Cleaned qp_set_mo_class.ml * Removed Core in taskserver * Merge develop-toto and manus (#12) * Fixed energies of non-expected s2 * Moved diag_algorithm in Davdison * Fixed travis * Added print_ci_vector * Documentation * Cleaned qp_set_mo_class.ml * Removed Core in taskserver * Frozen core for heavy atoms * Improved molden module * In sync with manus * Fixed some of the documentation errors * Develop toto (#13) * Fixed energies of non-expected s2 * Moved diag_algorithm in Davdison * Fixed travis * Added print_ci_vector * Documentation * Cleaned qp_set_mo_class.ml * Removed Core in taskserver * Frozen core for heavy atoms * Improved molden module * In sync with manus * Fixed some of the documentation errors * Develop manus (#14) * modified printing for rpt2 * Comment * Fixed plugins * Scripting for functionals * Documentation * Develop (#10) * fixed laplacian of aos * corrected the laplacians of aos * added dft_one_e * added new feature for new dft functionals * changed the configure to add new functionals * changed the configure * added dft_one_e/README.rst * added README.rst in new_functionals * added source/programmers_guide/new_ks.rst * Thesis Yann * Added gmp installation in configure * improved qp_e_conv_fci * Doc * Typos * Added variance_max * Fixed completion in qp_create * modif TODO * fixed DFT potential for n_states gt 1 * improved pot pbe * trying to improve sr PBE * fixed potential pbe * fixed the vxc smashed for pbe sr and normal * Comments in selection * bug fixed by peter * Fixed bug with zero beta electrons * Update README.rst * Update e_xc_new_func.irp.f * Update links.rst * Update quickstart.rst * Update quickstart.rst * updated cipsi * Fixed energies of non-expected s2 (#9) * Moved diag_algorithm in Davdison * some modifs * modified gfortran_debug.cfg * fixed automatization of functionals * modified e_xc_general.irp.f * minor modifs in ref_bitmask.irp.f * modifying functionals * rs_ks_scf and ks_scf compiles with the automatic handling of functionals * removed prints * fixed configure * fixed the new functionals * Merge toto * modified automatic functionals * Changed python into python2 * from_xyz suppressed * Cleaning repo * Update README.md * Update README.md * Contributors * Update GITHUB.md * bibtex
2019-03-07 16:29:06 +01:00
.. _module_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) = <ik|jl> = <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
File : :file:`ao_two_e_ints/map_integrals.irp.f`
.. code:: fortran
double precision, allocatable :: ao_integrals_cache (0:64*64*64*64)
Cache of AO integrals for fast access
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_cache_min`
* :c:data:`ao_integrals_map`
* :c:data:`ao_two_e_integrals_in_map`
.. c:var:: ao_integrals_cache_max
File : :file:`ao_two_e_ints/map_integrals.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_cache`
.. c:var:: ao_integrals_cache_min
File : :file:`ao_two_e_ints/map_integrals.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_cache`
.. c:var:: ao_integrals_map
File : :file:`ao_two_e_ints/map_integrals.irp.f`
.. code:: fortran
type(map_type) :: ao_integrals_map
AO integrals
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_cache`
* :c:data:`ao_two_e_integral_alpha`
* :c:data:`ao_two_e_integrals_in_map`
* :c:data:`mo_two_e_integral_jj_from_ao`
* :c:data:`mo_two_e_integrals_vv_from_ao`
.. c:var:: ao_two_e_integral_schwartz
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
double precision, allocatable :: ao_two_e_integral_schwartz (ao_num,ao_num)
Needed to compute Schwartz inequalities
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_normalized_ordered_transp`
* :c:data:`ao_expo_ordered_transp`
* :c:data:`ao_nucl`
* :c:data:`ao_num`
* :c:data:`ao_power`
* :c:data:`ao_prim_num`
* :c:data:`n_pt_max_integrals`
* :c:data:`nucl_coord`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_two_e_integral_alpha`
* :c:data:`mo_two_e_integral_jj_from_ao`
* :c:data:`mo_two_e_integrals_vv_from_ao`
.. c:var:: ao_two_e_integrals_in_map
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
logical :: ao_two_e_integrals_in_map
Map of Atomic integrals
i(r1) j(r2) 1/r12 k(r1) l(r2)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_normalized_ordered_transp`
* :c:data:`ao_expo_ordered_transp`
* :c:data:`ao_integrals_map`
* :c:data:`ao_nucl`
* :c:data:`ao_num`
* :c:data:`ao_power`
* :c:data:`ao_prim_num`
* :c:data:`ezfio_filename`
* :c:data:`io_ao_two_e_integrals`
* :c:data:`mpi_master`
* :c:data:`n_pt_max_integrals`
* :c:data:`nproc`
* :c:data:`nucl_coord`
* :c:data:`read_ao_two_e_integrals`
* :c:data:`zmq_context`
* :c:data:`zmq_socket_pull_tcp_address`
* :c:data:`zmq_state`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_cache`
* :c:data:`ao_two_e_integral_alpha`
* :c:data:`mo_two_e_integral_jj_from_ao`
* :c:data:`mo_two_e_integrals_erf_in_map`
* :c:data:`mo_two_e_integrals_in_map`
* :c:data:`mo_two_e_integrals_vv_from_ao`
.. c:var:: gauleg_t2
File : :file:`ao_two_e_ints/gauss_legendre.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`n_pt_max_integrals`
.. c:var:: gauleg_w
File : :file:`ao_two_e_ints/gauss_legendre.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`n_pt_max_integrals`
.. c:function:: general_primitive_integral:
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:func:`add_poly_multiply`
* :c:func:`give_polynom_mult_center_x`
* :c:func:`multiply_poly`
.. c:function:: i_x1_new:
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`n_pt_max_integrals`
Called by:
.. hlist::
:columns: 3
* :c:func:`i_x1_new`
* :c:func:`i_x2_new`
* :c:func:`integrale_new`
* :c:func:`integrale_new_erf`
Calls:
.. hlist::
:columns: 3
* :c:func:`i_x1_new`
* :c:func:`i_x2_new`
.. c:function:: i_x1_pol_mult_a1:
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:func:`i_x1_pol_mult`
* :c:func:`i_x1_pol_mult_a2`
* :c:func:`i_x1_pol_mult_recurs`
Calls:
.. hlist::
:columns: 3
* :c:func:`i_x2_pol_mult`
* :c:func:`multiply_poly`
.. c:function:: i_x1_pol_mult_a2:
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:func:`i_x1_pol_mult`
* :c:func:`i_x1_pol_mult_recurs`
Calls:
.. hlist::
:columns: 3
* :c:func:`i_x1_pol_mult_a1`
* :c:func:`i_x2_pol_mult`
* :c:func:`multiply_poly`
.. c:function:: i_x1_pol_mult_recurs:
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:func:`i_x1_pol_mult`
* :c:func:`i_x1_pol_mult_recurs`
Calls:
.. hlist::
:columns: 3
* :c:func:`i_x1_pol_mult_a1`
* :c:func:`i_x1_pol_mult_a2`
* :c:func:`i_x1_pol_mult_recurs`
* :c:func:`multiply_poly`
.. c:function:: i_x2_new:
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
recursive subroutine I_x2_new(c,B_10,B_01,B_00,res,n_pt)
recursive function involved in the two-electron integral
Needs:
.. hlist::
:columns: 3
* :c:data:`n_pt_max_integrals`
Called by:
.. hlist::
:columns: 3
* :c:func:`i_x1_new`
Calls:
.. hlist::
:columns: 3
* :c:func:`i_x1_new`
.. c:function:: i_x2_pol_mult:
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:func:`i_x1_pol_mult`
* :c:func:`i_x1_pol_mult_a1`
* :c:func:`i_x1_pol_mult_a2`
* :c:func:`i_x2_pol_mult`
Calls:
.. hlist::
:columns: 3
* :c:func:`i_x2_pol_mult`
* :c:func:`multiply_poly`
Subroutines / functions
-----------------------
.. c:function:: ao_l4:
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
integer function ao_l4(i,j,k,l)
Computes the product of l values of i,j,k,and l
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_l`
.. c:function:: ao_two_e_integral:
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`n_pt_max_integrals`
* :c:data:`ao_coef_normalized_ordered_transp`
* :c:data:`ao_power`
* :c:data:`ao_expo_ordered_transp`
* :c:data:`ao_prim_num`
* :c:data:`ao_nucl`
* :c:data:`nucl_coord`
Calls:
.. hlist::
:columns: 3
* :c:func:`give_explicit_poly_and_gaussian`
.. c:function:: ao_two_e_integral_schwartz_accel:
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`n_pt_max_integrals`
* :c:data:`ao_integrals_threshold`
* :c:data:`ao_coef_normalized_ordered_transp`
* :c:data:`ao_power`
* :c:data:`ao_expo_ordered_transp`
* :c:data:`ao_prim_num`
* :c:data:`ao_nucl`
* :c:data:`nucl_coord`
Calls:
.. hlist::
:columns: 3
* :c:func:`give_explicit_poly_and_gaussian`
.. c:function:: ao_two_e_integrals_in_map_collector:
File : :file:`ao_two_e_ints/integrals_in_map_slave.irp.f`
.. code:: fortran
subroutine ao_two_e_integrals_in_map_collector(zmq_socket_pull)
Collects results from the AO integral calculation
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_map`
* :c:data:`ao_num`
Called by:
.. hlist::
:columns: 3
* :c:data:`ao_two_e_integrals_in_map`
Calls:
.. hlist::
:columns: 3
* :c:func:`end_zmq_to_qp_run_socket`
* :c:func:`insert_into_ao_integrals_map`
.. c:function:: ao_two_e_integrals_in_map_slave:
File : :file:`ao_two_e_ints/integrals_in_map_slave.irp.f`
.. code:: fortran
subroutine ao_two_e_integrals_in_map_slave(thread,iproc)
Computes a buffer of integrals
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
Called by:
.. hlist::
:columns: 3
* :c:func:`ao_two_e_integrals_in_map_slave_inproc`
* :c:func:`ao_two_e_integrals_in_map_slave_tcp`
Calls:
.. hlist::
:columns: 3
* :c:func:`compute_ao_integrals_jl`
* :c:func:`end_zmq_push_socket`
* :c:func:`end_zmq_to_qp_run_socket`
* :c:func:`push_integrals`
.. c:function:: ao_two_e_integrals_in_map_slave_inproc:
File : :file:`ao_two_e_ints/integrals_in_map_slave.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_two_e_integrals_in_map`
Calls:
.. hlist::
:columns: 3
* :c:func:`ao_two_e_integrals_in_map_slave`
.. c:function:: ao_two_e_integrals_in_map_slave_tcp:
File : :file:`ao_two_e_ints/integrals_in_map_slave.irp.f`
.. code:: fortran
subroutine ao_two_e_integrals_in_map_slave_tcp(i)
Computes a buffer of integrals. i is the ID of the current thread.
Calls:
.. hlist::
:columns: 3
* :c:func:`ao_two_e_integrals_in_map_slave`
.. c:function:: clear_ao_map:
File : :file:`ao_two_e_ints/map_integrals.irp.f`
.. code:: fortran
subroutine clear_ao_map
Frees the memory of the AO map
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_map`
Calls:
.. hlist::
:columns: 3
* :c:func:`map_deinit`
.. c:function:: compute_ao_integrals_jl:
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
subroutine compute_ao_integrals_jl(j,l,n_integrals,buffer_i,buffer_value)
Parallel client for AO integrals
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_overlap_abs`
* :c:data:`ao_num`
* :c:data:`ao_integrals_threshold`
* :c:data:`ao_two_e_integral_schwartz`
Called by:
.. hlist::
:columns: 3
* :c:func:`ao_two_e_integrals_in_map_slave`
Calls:
.. hlist::
:columns: 3
* :c:func:`two_e_integrals_index`
.. c:function:: compute_ao_two_e_integrals:
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_overlap_abs`
* :c:data:`ao_num`
* :c:data:`ao_two_e_integral_schwartz`
Called by:
.. hlist::
:columns: 3
* :c:data:`mo_two_e_integral_jj_from_ao`
* :c:data:`mo_two_e_integrals_vv_from_ao`
.. c:function:: dump_ao_integrals:
File : :file:`ao_two_e_ints/map_integrals.irp.f`
.. code:: fortran
subroutine dump_ao_integrals(filename)
Save to disk the |AO| integrals
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_map`
* :c:data:`mpi_master`
Calls:
.. hlist::
:columns: 3
* :c:func:`ezfio_set_work_empty`
.. c:function:: eri:
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:func:`integrale_new`
.. c:function:: gauleg:
File : :file:`ao_two_e_ints/gauss_legendre.irp.f`
.. code:: fortran
subroutine gauleg(x1,x2,x,w,n)
Gauss-Legendre
Called by:
.. hlist::
:columns: 3
* :c:data:`gauleg_t2`
.. c:function:: get_ao_map_size:
File : :file:`ao_two_e_ints/map_integrals.irp.f`
.. code:: fortran
function get_ao_map_size()
Returns the number of elements in the AO map
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_map`
.. c:function:: get_ao_two_e_integral:
File : :file:`ao_two_e_ints/map_integrals.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_overlap_abs`
* :c:data:`ao_integrals_threshold`
* :c:data:`ao_two_e_integral_schwartz`
* :c:data:`ao_integrals_cache`
* :c:data:`ao_integrals_cache_min`
* :c:data:`ao_two_e_integrals_in_map`
Calls:
.. hlist::
:columns: 3
* :c:func:`map_get`
* :c:func:`two_e_integrals_index`
.. c:function:: get_ao_two_e_integrals:
File : :file:`ao_two_e_ints/map_integrals.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_map`
* :c:data:`ao_overlap_abs`
* :c:data:`ao_integrals_threshold`
* :c:data:`ao_two_e_integrals_in_map`
Called by:
.. hlist::
:columns: 3
* :c:func:`add_integrals_to_map`
* :c:func:`add_integrals_to_map_no_exit_34`
* :c:func:`add_integrals_to_map_three_indices`
.. c:function:: get_ao_two_e_integrals_non_zero:
File : :file:`ao_two_e_ints/map_integrals.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_map`
* :c:data:`ao_overlap_abs`
* :c:data:`ao_integrals_threshold`
* :c:data:`ao_two_e_integral_schwartz`
* :c:data:`ao_two_e_integrals_in_map`
Called by:
.. hlist::
:columns: 3
* :c:data:`mo_two_e_integral_jj_from_ao`
* :c:data:`mo_two_e_integrals_vv_from_ao`
Calls:
.. hlist::
:columns: 3
* :c:func:`map_get`
* :c:func:`two_e_integrals_index`
.. c:function:: give_polynom_mult_center_x:
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
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 :
$I_{x_1}(a_x,d_x,p,q) \, I_{x_1}(a_y,d_y,p,q) \ I_{x_1}(a_z,d_z,p,q)$
Called by:
.. hlist::
:columns: 3
* :c:func:`general_primitive_integral`
* :c:func:`general_primitive_integral_erf`
Calls:
.. hlist::
:columns: 3
* :c:func:`i_x1_pol_mult`
.. c:function:: i_x1_pol_mult:
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:func:`give_polynom_mult_center_x`
Calls:
.. hlist::
:columns: 3
* :c:func:`i_x1_pol_mult_a1`
* :c:func:`i_x1_pol_mult_a2`
* :c:func:`i_x1_pol_mult_recurs`
* :c:func:`i_x2_pol_mult`
.. c:function:: insert_into_ao_integrals_map:
File : :file:`ao_two_e_ints/map_integrals.irp.f`
.. code:: fortran
subroutine insert_into_ao_integrals_map(n_integrals,buffer_i, buffer_values)
Create new entry into AO map
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_map`
Called by:
.. hlist::
:columns: 3
* :c:func:`ao_two_e_integrals_in_map_collector`
Calls:
.. hlist::
:columns: 3
* :c:func:`map_append`
.. c:function:: integrale_new:
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
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)
Calculates the integral of the polynomial :
$I_{x_1}(a_x+b_x,c_x+d_x,p,q) \, I_{x_1}(a_y+b_y,c_y+d_y,p,q) \, I_{x_1}(a_z+b_z,c_z+d_z,p,q)$
in $( 0 ; 1)$
Needs:
.. hlist::
:columns: 3
* :c:data:`n_pt_max_integrals`
* :c:data:`gauleg_t2`
Called by:
.. hlist::
:columns: 3
* :c:func:`eri`
Calls:
.. hlist::
:columns: 3
* :c:func:`i_x1_new`
.. c:function:: load_ao_integrals:
File : :file:`ao_two_e_ints/map_integrals.irp.f`
.. code:: fortran
integer function load_ao_integrals(filename)
Read from disk the |AO| integrals
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_map`
Calls:
.. hlist::
:columns: 3
* :c:func:`cache_map_reallocate`
* :c:func:`map_deinit`
* :c:func:`map_sort`
.. c:function:: n_pt_sup:
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
.. code:: fortran
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
two-electron integral :
$I_x(a_x,b_x,c_x,d_x) \, I_y(a_y,b_y,c_y,d_y) \, I_z(a_z,b_z,c_z,d_z)$
.. c:function:: push_integrals:
File : :file:`ao_two_e_ints/integrals_in_map_slave.irp.f`
.. code:: fortran
subroutine push_integrals(zmq_socket_push, n_integrals, buffer_i, buffer_value, task_id)
Push integrals in the push socket
Called by:
.. hlist::
:columns: 3
* :c:func:`ao_two_e_integrals_erf_in_map_slave`
* :c:func:`ao_two_e_integrals_in_map_slave`
.. c:function:: two_e_integrals_index:
File : :file:`ao_two_e_ints/map_integrals.irp.f`
.. code:: fortran
subroutine two_e_integrals_index(i,j,k,l,i1)
Called by:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_cache`
* :c:data:`ao_integrals_erf_cache`
* :c:data:`ao_integrals_erf_map`
* :c:data:`ao_integrals_map`
* :c:func:`compute_ao_integrals_erf_jl`
* :c:func:`compute_ao_integrals_jl`
* :c:func:`get_ao_two_e_integral`
* :c:func:`get_ao_two_e_integral_erf`
* :c:func:`get_ao_two_e_integrals_erf_non_zero`
* :c:func:`get_ao_two_e_integrals_non_zero`
* :c:func:`get_mo_two_e_integral_erf`
* :c:func:`get_mo_two_e_integrals_coulomb_ii`
* :c:func:`get_mo_two_e_integrals_erf`
* :c:func:`get_mo_two_e_integrals_erf_coulomb_ii`
* :c:func:`get_mo_two_e_integrals_erf_exch_ii`
* :c:func:`get_mo_two_e_integrals_erf_i1j1`
* :c:func:`get_mo_two_e_integrals_erf_ij`
* :c:func:`get_mo_two_e_integrals_exch_ii`
* :c:func:`get_mo_two_e_integrals_i1j1`
* :c:func:`get_mo_two_e_integrals_ij`
* :c:func:`get_two_e_integral`
* :c:data:`mo_integrals_cache`
* :c:data:`mo_integrals_erf_cache`
* :c:data:`mo_integrals_erf_map`
* :c:data:`mo_integrals_map`
* :c:func:`two_e_integrals_index_reverse`
.. c:function:: two_e_integrals_index_reverse:
File : :file:`ao_two_e_ints/map_integrals.irp.f`
.. code:: fortran
subroutine two_e_integrals_index_reverse(i,j,k,l,i1)
Called by:
.. hlist::
:columns: 3
* :c:data:`ao_two_e_integral_alpha`
Calls:
.. hlist::
:columns: 3
* :c:func:`two_e_integrals_index`
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