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1358 lines
26 KiB
ReStructuredText
1358 lines
26 KiB
ReStructuredText
.. _module_ao_two_e_ints:
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.. program:: ao_two_e_ints
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.. default-role:: option
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==================
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ao_two_e_ints
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==================
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Here, all two-electron integrals (:math:`1/r_{12}`) are computed.
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As they have 4 indices and many are zero, they are stored in a map, as defined
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in :file:`utils/map_module.f90`.
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To fetch an |AO| integral, use the
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`get_ao_two_e_integral(i,j,k,l,ao_integrals_map)` function.
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The conventions are:
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* For |AO| integrals : (ij|kl) = (11|22) = <ik|jl> = <12|12>
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EZFIO parameters
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----------------
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.. option:: io_ao_two_e_integrals
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Read/Write |AO| integrals from/to disk [ Write | Read | None ]
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Default: None
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.. option:: ao_integrals_threshold
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If | (pq|rs) | < `ao_integrals_threshold` then (pq|rs) is zero
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Default: 1.e-15
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.. option:: do_direct_integrals
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Compute integrals on the fly (very slow, only for debugging)
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Default: False
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Providers
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---------
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.. c:var:: ao_integrals_cache
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File : :file:`ao_two_e_ints/map_integrals.irp.f`
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.. code:: fortran
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double precision, allocatable :: ao_integrals_cache (0:64*64*64*64)
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Cache of AO integrals for fast access
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_integrals_cache_min`
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* :c:data:`ao_integrals_map`
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* :c:data:`ao_two_e_integrals_in_map`
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.. c:var:: ao_integrals_cache_max
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File : :file:`ao_two_e_ints/map_integrals.irp.f`
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.. code:: fortran
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integer :: ao_integrals_cache_min
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integer :: ao_integrals_cache_max
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Min and max values of the AOs for which the integrals are in the cache
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`ao_integrals_cache`
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.. c:var:: ao_integrals_cache_min
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File : :file:`ao_two_e_ints/map_integrals.irp.f`
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.. code:: fortran
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integer :: ao_integrals_cache_min
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integer :: ao_integrals_cache_max
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Min and max values of the AOs for which the integrals are in the cache
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`ao_integrals_cache`
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.. c:var:: ao_integrals_map
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File : :file:`ao_two_e_ints/map_integrals.irp.f`
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.. code:: fortran
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type(map_type) :: ao_integrals_map
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AO integrals
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`ao_integrals_cache`
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* :c:data:`ao_two_e_integral_alpha`
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* :c:data:`ao_two_e_integrals_in_map`
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* :c:data:`mo_two_e_integral_jj_from_ao`
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* :c:data:`mo_two_e_integrals_vv_from_ao`
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.. c:var:: ao_two_e_integral_schwartz
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File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
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.. code:: fortran
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double precision, allocatable :: ao_two_e_integral_schwartz (ao_num,ao_num)
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Needed to compute Schwartz inequalities
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_coef_normalized_ordered_transp`
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* :c:data:`ao_expo_ordered_transp`
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* :c:data:`ao_nucl`
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* :c:data:`ao_num`
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* :c:data:`ao_power`
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* :c:data:`ao_prim_num`
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* :c:data:`n_pt_max_integrals`
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* :c:data:`nucl_coord`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`ao_two_e_integral_alpha`
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* :c:data:`mo_two_e_integral_jj_from_ao`
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* :c:data:`mo_two_e_integrals_vv_from_ao`
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.. c:var:: ao_two_e_integrals_in_map
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File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
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.. code:: fortran
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logical :: ao_two_e_integrals_in_map
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Map of Atomic integrals
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i(r1) j(r2) 1/r12 k(r1) l(r2)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_coef_normalized_ordered_transp`
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* :c:data:`ao_expo_ordered_transp`
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* :c:data:`ao_integrals_map`
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* :c:data:`ao_nucl`
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* :c:data:`ao_num`
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* :c:data:`ao_power`
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* :c:data:`ao_prim_num`
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* :c:data:`ezfio_filename`
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* :c:data:`io_ao_two_e_integrals`
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* :c:data:`mpi_master`
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* :c:data:`n_pt_max_integrals`
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* :c:data:`nproc`
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* :c:data:`nucl_coord`
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* :c:data:`read_ao_two_e_integrals`
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* :c:data:`zmq_context`
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* :c:data:`zmq_socket_pull_tcp_address`
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* :c:data:`zmq_state`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`ao_integrals_cache`
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* :c:data:`ao_two_e_integral_alpha`
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* :c:data:`mo_two_e_integral_jj_from_ao`
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* :c:data:`mo_two_e_integrals_erf_in_map`
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* :c:data:`mo_two_e_integrals_in_map`
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* :c:data:`mo_two_e_integrals_vv_from_ao`
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.. c:var:: gauleg_t2
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File : :file:`ao_two_e_ints/gauss_legendre.irp.f`
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.. code:: fortran
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double precision, allocatable :: gauleg_t2 (n_pt_max_integrals,n_pt_max_integrals/2)
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double precision, allocatable :: gauleg_w (n_pt_max_integrals,n_pt_max_integrals/2)
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t_w(i,1,k) = w(i)
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t_w(i,2,k) = t(i)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`n_pt_max_integrals`
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.. c:var:: gauleg_w
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File : :file:`ao_two_e_ints/gauss_legendre.irp.f`
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.. code:: fortran
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double precision, allocatable :: gauleg_t2 (n_pt_max_integrals,n_pt_max_integrals/2)
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double precision, allocatable :: gauleg_w (n_pt_max_integrals,n_pt_max_integrals/2)
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t_w(i,1,k) = w(i)
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t_w(i,2,k) = t(i)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`n_pt_max_integrals`
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.. c:function:: general_primitive_integral:
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File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
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.. code:: fortran
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double precision function general_primitive_integral(dim, &
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P_new,P_center,fact_p,p,p_inv,iorder_p, &
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Q_new,Q_center,fact_q,q,q_inv,iorder_q)
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Computes the integral <pq|rs> where p,q,r,s are Gaussian primitives
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`add_poly_multiply`
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* :c:func:`give_polynom_mult_center_x`
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* :c:func:`multiply_poly`
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.. c:function:: i_x1_new:
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File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
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.. code:: fortran
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recursive subroutine I_x1_new(a,c,B_10,B_01,B_00,res,n_pt)
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recursive function involved in the two-electron integral
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`n_pt_max_integrals`
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Called by:
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.. hlist::
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:columns: 3
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* :c:func:`i_x1_new`
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* :c:func:`i_x2_new`
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* :c:func:`integrale_new`
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* :c:func:`integrale_new_erf`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`i_x1_new`
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* :c:func:`i_x2_new`
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.. c:function:: i_x1_pol_mult_a1:
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File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
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.. code:: fortran
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recursive subroutine I_x1_pol_mult_a1(c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in)
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Recursive function involved in the two-electron integral
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Called by:
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.. hlist::
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:columns: 3
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* :c:func:`i_x1_pol_mult`
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* :c:func:`i_x1_pol_mult_a2`
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* :c:func:`i_x1_pol_mult_recurs`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`i_x2_pol_mult`
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* :c:func:`multiply_poly`
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.. c:function:: i_x1_pol_mult_a2:
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File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
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.. code:: fortran
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recursive subroutine I_x1_pol_mult_a2(c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in)
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Recursive function involved in the two-electron integral
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Called by:
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.. hlist::
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:columns: 3
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* :c:func:`i_x1_pol_mult`
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* :c:func:`i_x1_pol_mult_recurs`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`i_x1_pol_mult_a1`
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* :c:func:`i_x2_pol_mult`
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* :c:func:`multiply_poly`
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.. c:function:: i_x1_pol_mult_recurs:
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File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
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.. code:: fortran
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recursive subroutine I_x1_pol_mult_recurs(a,c,B_10,B_01,B_00,C_00,D_00,d,nd,n_pt_in)
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Recursive function involved in the two-electron integral
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Called by:
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.. hlist::
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:columns: 3
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* :c:func:`i_x1_pol_mult`
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* :c:func:`i_x1_pol_mult_recurs`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`i_x1_pol_mult_a1`
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* :c:func:`i_x1_pol_mult_a2`
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* :c:func:`i_x1_pol_mult_recurs`
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* :c:func:`multiply_poly`
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.. c:function:: i_x2_new:
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File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
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.. code:: fortran
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recursive subroutine I_x2_new(c,B_10,B_01,B_00,res,n_pt)
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recursive function involved in the two-electron integral
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`n_pt_max_integrals`
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Called by:
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.. hlist::
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:columns: 3
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* :c:func:`i_x1_new`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`i_x1_new`
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.. c:function:: i_x2_pol_mult:
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File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
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.. code:: fortran
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recursive subroutine I_x2_pol_mult(c,B_10,B_01,B_00,C_00,D_00,d,nd,dim)
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Recursive function involved in the two-electron integral
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Called by:
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.. hlist::
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:columns: 3
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* :c:func:`i_x1_pol_mult`
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* :c:func:`i_x1_pol_mult_a1`
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* :c:func:`i_x1_pol_mult_a2`
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* :c:func:`i_x2_pol_mult`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`i_x2_pol_mult`
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* :c:func:`multiply_poly`
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Subroutines / functions
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-----------------------
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.. c:function:: ao_l4:
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File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
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.. code:: fortran
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integer function ao_l4(i,j,k,l)
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Computes the product of l values of i,j,k,and l
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_l`
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.. c:function:: ao_two_e_integral:
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File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
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.. code:: fortran
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double precision function ao_two_e_integral(i,j,k,l)
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integral of the AO basis <ik|jl> or (ij|kl)
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i(r1) j(r1) 1/r12 k(r2) l(r2)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`n_pt_max_integrals`
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* :c:data:`ao_coef_normalized_ordered_transp`
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* :c:data:`ao_power`
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* :c:data:`ao_expo_ordered_transp`
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* :c:data:`ao_prim_num`
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* :c:data:`ao_nucl`
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* :c:data:`nucl_coord`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`give_explicit_poly_and_gaussian`
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.. c:function:: ao_two_e_integral_schwartz_accel:
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File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
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.. code:: fortran
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double precision function ao_two_e_integral_schwartz_accel(i,j,k,l)
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integral of the AO basis <ik|jl> or (ij|kl)
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i(r1) j(r1) 1/r12 k(r2) l(r2)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`n_pt_max_integrals`
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* :c:data:`ao_integrals_threshold`
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* :c:data:`ao_coef_normalized_ordered_transp`
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* :c:data:`ao_power`
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* :c:data:`ao_expo_ordered_transp`
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* :c:data:`ao_prim_num`
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* :c:data:`ao_nucl`
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* :c:data:`nucl_coord`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`give_explicit_poly_and_gaussian`
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.. c:function:: ao_two_e_integrals_in_map_collector:
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File : :file:`ao_two_e_ints/integrals_in_map_slave.irp.f`
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.. code:: fortran
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subroutine ao_two_e_integrals_in_map_collector(zmq_socket_pull)
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Collects results from the AO integral calculation
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Needs:
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|
.. hlist::
|
|
:columns: 3
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|
* :c:data:`ao_integrals_map`
|
|
* :c:data:`ao_num`
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|
Called by:
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.. hlist::
|
|
:columns: 3
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* :c:data:`ao_two_e_integrals_in_map`
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Calls:
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|
.. hlist::
|
|
:columns: 3
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|
* :c:func:`end_zmq_to_qp_run_socket`
|
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* :c:func:`insert_into_ao_integrals_map`
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.. c:function:: ao_two_e_integrals_in_map_slave:
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File : :file:`ao_two_e_ints/integrals_in_map_slave.irp.f`
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.. code:: fortran
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subroutine ao_two_e_integrals_in_map_slave(thread,iproc)
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Computes a buffer of integrals
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Needs:
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|
.. hlist::
|
|
:columns: 3
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|
* :c:data:`ao_num`
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|
Called by:
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|
.. hlist::
|
|
:columns: 3
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|
|
* :c:func:`ao_two_e_integrals_in_map_slave_inproc`
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* :c:func:`ao_two_e_integrals_in_map_slave_tcp`
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Calls:
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|
.. hlist::
|
|
:columns: 3
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|
|
* :c:func:`compute_ao_integrals_jl`
|
|
* :c:func:`end_zmq_push_socket`
|
|
* :c:func:`end_zmq_to_qp_run_socket`
|
|
* :c:func:`push_integrals`
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.. c:function:: ao_two_e_integrals_in_map_slave_inproc:
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File : :file:`ao_two_e_ints/integrals_in_map_slave.irp.f`
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.. code:: fortran
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subroutine ao_two_e_integrals_in_map_slave_inproc(i)
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Computes a buffer of integrals. i is the ID of the current thread.
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Called by:
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|
.. hlist::
|
|
:columns: 3
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|
|
* :c:data:`ao_two_e_integrals_in_map`
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Calls:
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|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`ao_two_e_integrals_in_map_slave`
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.. c:function:: ao_two_e_integrals_in_map_slave_tcp:
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|
File : :file:`ao_two_e_ints/integrals_in_map_slave.irp.f`
|
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|
.. code:: fortran
|
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|
|
subroutine ao_two_e_integrals_in_map_slave_tcp(i)
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|
Computes a buffer of integrals. i is the ID of the current thread.
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|
Calls:
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|
.. hlist::
|
|
:columns: 3
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|
* :c:func:`ao_two_e_integrals_in_map_slave`
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.. c:function:: clear_ao_map:
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|
File : :file:`ao_two_e_ints/map_integrals.irp.f`
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|
.. code:: fortran
|
|
|
|
subroutine clear_ao_map
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|
Frees the memory of the AO map
|
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|
Needs:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`ao_integrals_map`
|
|
|
|
Calls:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`map_deinit`
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|
.. c:function:: compute_ao_integrals_jl:
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|
File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
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|
.. code:: fortran
|
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|
|
subroutine compute_ao_integrals_jl(j,l,n_integrals,buffer_i,buffer_value)
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|
|
Parallel client for AO integrals
|
|
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|
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
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|
|
|
* :c:func:`two_e_integrals_index`
|
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|
.. c:function:: compute_ao_two_e_integrals:
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File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
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|
.. code:: fortran
|
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|
|
subroutine compute_ao_two_e_integrals(j,k,l,sze,buffer_value)
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|
|
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:
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|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`mo_two_e_integral_jj_from_ao`
|
|
* :c:data:`mo_two_e_integrals_vv_from_ao`
|
|
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|
|
.. c:function:: dump_ao_integrals:
|
|
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|
|
File : :file:`ao_two_e_ints/map_integrals.irp.f`
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|
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|
.. code:: fortran
|
|
|
|
subroutine dump_ao_integrals(filename)
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|
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|
|
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`
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|
|
.. c:function:: eri:
|
|
|
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|
|
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`
|
|
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|
|
.. c:function:: gauleg:
|
|
|
|
|
|
File : :file:`ao_two_e_ints/gauss_legendre.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
subroutine gauleg(x1,x2,x,w,n)
|
|
|
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|
|
Gauss-Legendre
|
|
|
|
Called by:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`gauleg_t2`
|
|
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|
|
.. 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.
|
|
physicist convention : <ij|kl>
|
|
|
|
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:: get_ao_two_e_integrals_non_zero_jl:
|
|
|
|
|
|
File : :file:`ao_two_e_ints/map_integrals.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
subroutine get_ao_two_e_integrals_non_zero_jl(j,l,thresh,sze_max,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_two_e_integral_schwartz`
|
|
* :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_non_zero_jl_from_list:
|
|
|
|
|
|
File : :file:`ao_two_e_ints/map_integrals.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
subroutine get_ao_two_e_integrals_non_zero_jl_from_list(j,l,thresh,list,n_list,sze_max,out_val,out_val_index,non_zero_int)
|
|
|
|
|
|
Gets multiple AO two-electron integrals 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_two_e_integral_schwartz`
|
|
* :c:data:`ao_two_e_integrals_in_map`
|
|
|
|
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:
|
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.. hlist::
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:columns: 3
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* :c:func:`eri`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`i_x1_new`
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.. c:function:: load_ao_integrals:
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File : :file:`ao_two_e_ints/map_integrals.irp.f`
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.. code:: fortran
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integer function load_ao_integrals(filename)
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Read from disk the |AO| integrals
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_integrals_map`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`cache_map_reallocate`
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* :c:func:`map_deinit`
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* :c:func:`map_sort`
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.. c:function:: n_pt_sup:
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File : :file:`ao_two_e_ints/two_e_integrals.irp.f`
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.. code:: fortran
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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)
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Returns the upper boundary of the degree of the polynomial involved in the
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two-electron integral :
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$I_x(a_x,b_x,c_x,d_x) \, I_y(a_y,b_y,c_y,d_y) \, I_z(a_z,b_z,c_z,d_z)$
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.. c:function:: push_integrals:
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File : :file:`ao_two_e_ints/integrals_in_map_slave.irp.f`
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.. code:: fortran
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subroutine push_integrals(zmq_socket_push, n_integrals, buffer_i, buffer_value, task_id)
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Push integrals in the push socket
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Called by:
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.. hlist::
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:columns: 3
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* :c:func:`ao_two_e_integrals_erf_in_map_slave`
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* :c:func:`ao_two_e_integrals_in_map_slave`
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.. c:function:: two_e_integrals_index:
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File : :file:`ao_two_e_ints/map_integrals.irp.f`
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.. code:: fortran
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subroutine two_e_integrals_index(i,j,k,l,i1)
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Gives a unique index for i,j,k,l using permtuation symmetry.
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i <-> k, j <-> l, and (i,k) <-> (j,l)
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Called by:
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.. hlist::
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:columns: 3
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* :c:data:`ao_integrals_cache`
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* :c:data:`ao_integrals_erf_cache`
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* :c:data:`ao_integrals_erf_map`
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* :c:data:`ao_integrals_map`
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* :c:func:`compute_ao_integrals_erf_jl`
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* :c:func:`compute_ao_integrals_jl`
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* :c:func:`get_ao_two_e_integral`
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* :c:func:`get_ao_two_e_integral_erf`
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* :c:func:`get_ao_two_e_integrals_erf_non_zero`
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* :c:func:`get_ao_two_e_integrals_non_zero`
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* :c:func:`get_ao_two_e_integrals_non_zero_jl`
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* :c:func:`get_ao_two_e_integrals_non_zero_jl_from_list`
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* :c:func:`get_mo_two_e_integral_erf`
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* :c:func:`get_mo_two_e_integrals_coulomb_ii`
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* :c:func:`get_mo_two_e_integrals_erf`
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* :c:func:`get_mo_two_e_integrals_erf_coulomb_ii`
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* :c:func:`get_mo_two_e_integrals_erf_exch_ii`
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* :c:func:`get_mo_two_e_integrals_erf_i1j1`
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* :c:func:`get_mo_two_e_integrals_erf_ij`
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* :c:func:`get_mo_two_e_integrals_exch_ii`
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* :c:func:`get_mo_two_e_integrals_i1j1`
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* :c:func:`get_mo_two_e_integrals_ij`
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* :c:func:`get_two_e_integral`
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* :c:data:`mo_integrals_cache`
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* :c:data:`mo_integrals_erf_cache`
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* :c:data:`mo_integrals_erf_map`
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* :c:data:`mo_integrals_map`
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* :c:func:`test`
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.. c:function:: two_e_integrals_index_reverse:
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File : :file:`ao_two_e_ints/map_integrals.irp.f`
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.. code:: fortran
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subroutine two_e_integrals_index_reverse(i,j,k,l,i1)
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Computes the 4 indices $i,j,k,l$ from a unique index $i_1$.
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For 2 indices $i,j$ and $i \le j$, we have
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$p = i(i-1)/2 + j$.
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The key point is that because $j < i$,
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$i(i-1)/2 < p \le i(i+1)/2$. So $i$ can be found by solving
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$i^2 - i - 2p=0$. One obtains $i=1 + \sqrt{1+8p}/2$
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and $j = p - i(i-1)/2$.
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This rule is applied 3 times. First for the symmetry of the
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pairs (i,k) and (j,l), and then for the symmetry within each pair.
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Called by:
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.. hlist::
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:columns: 3
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* :c:data:`ao_two_e_integral_alpha`
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* :c:func:`test`
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