461 lines
20 KiB
ReStructuredText
461 lines
20 KiB
ReStructuredText
=============
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BiInts Module
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=============
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Here, all bi-electronic integrals (:math:`1/r_{12}`) are computed. As they have
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4 indices and many are zero, they are stored in a map, as defined in
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``Utils/map_module.f90``. To fetch an AO integral, use the
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``get_ao_bielec_integral(i,j,k,l,ao_integrals_map)`` function, and to fetch and
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MO integral, use ``get_mo_bielec_integral(i,j,k,l,mo_integrals_map)`` or
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``mo_bielec_integral(i,j,k,l)``.
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The conventions are:
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* For AO integrals : (ik|jl) = (11|22)
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* For MO integrals : <ij|kl> = <12|12>
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Needed Modules
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==============
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.. Do not edit this section It was auto-generated
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.. by the `update_README.py` script.
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.. image:: tree_dependency.png
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* `Pseudo <http://github.com/LCPQ/quantum_package/tree/master/src/Pseudo>`_
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* `Bitmask <http://github.com/LCPQ/quantum_package/tree/master/src/Bitmask>`_
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Needed Modules
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==============
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.. Do not edit this section It was auto-generated
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.. by the `update_README.py` script.
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.. image:: tree_dependency.png
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* `Pseudo <http://github.com/LCPQ/quantum_package/tree/master/src/Pseudo>`_
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* `Bitmask <http://github.com/LCPQ/quantum_package/tree/master/src/Bitmask>`_
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* `ZMQ <http://github.com/LCPQ/quantum_package/tree/master/src/ZMQ>`_
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* `FourIdx <http://github.com/LCPQ/quantum_package/tree/master/src/FourIdx>`_
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Documentation
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=============
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.. Do not edit this section It was auto-generated
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.. by the `update_README.py` script.
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`add_integrals_to_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L199>`_
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Adds integrals to tha MO map according to some bitmask
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`add_integrals_to_map_no_exit_34 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L814>`_
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Adds integrals to tha MO map according to some bitmask
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`add_integrals_to_map_three_indices <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L502>`_
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Adds integrals to tha MO map according to some bitmask
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`ao_bielec_integral <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L1>`_
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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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`ao_bielec_integral_schwartz <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L424>`_
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Needed to compute Schwartz inequalities
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`ao_bielec_integral_schwartz_accel <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L106>`_
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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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`ao_bielec_integrals_in_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L328>`_
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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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`ao_bielec_integrals_in_map_collector <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bielec_integrals_in_map_slave.irp.f#L139>`_
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Collects results from the AO integral calculation
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`ao_bielec_integrals_in_map_slave <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bielec_integrals_in_map_slave.irp.f#L74>`_
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Computes a buffer of integrals
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`ao_bielec_integrals_in_map_slave_inproc <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bielec_integrals_in_map_slave.irp.f#L11>`_
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Computes a buffer of integrals. i is the ID of the current thread.
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`ao_bielec_integrals_in_map_slave_tcp <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bielec_integrals_in_map_slave.irp.f#L1>`_
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Computes a buffer of integrals. i is the ID of the current thread.
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`ao_integrals_cache <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L123>`_
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Cache of AO integrals for fast access
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`ao_integrals_cache_max <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L113>`_
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Min and max values of the AOs for which the integrals are in the cache
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`ao_integrals_cache_min <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L112>`_
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Min and max values of the AOs for which the integrals are in the cache
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`ao_integrals_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L6>`_
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AO integrals
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`ao_integrals_threshold <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L40>`_
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If |<pq|rs>| < ao_integrals_threshold then <pq|rs> is zero
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`ao_l4 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L278>`_
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Computes the product of l values of i,j,k,and l
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`bench_maps <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/test_integrals.irp.f#L1>`_
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Performs timing benchmarks on integral access
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`bielec_integrals_index <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L19>`_
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Undocumented
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`bielec_integrals_index_reverse <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L36>`_
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Undocumented
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`big_array_coulomb_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/integrals_3_index.irp.f#L1>`_
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Undocumented
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`big_array_exchange_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/integrals_3_index.irp.f#L2>`_
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Undocumented
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`clear_ao_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L273>`_
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Frees the memory of the AO map
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`clear_mo_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1372>`_
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Frees the memory of the MO map
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`compute_ao_bielec_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L289>`_
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Compute AO 1/r12 integrals for all i and fixed j,k,l
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`compute_ao_integrals_jl <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L1156>`_
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Parallel client for AO integrals
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`disk_access_ao_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L6>`_
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Read/Write AO integrals from/to disk [ Write | Read | None ]
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`disk_access_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L74>`_
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Read/Write MO integrals from/to disk [ Write | Read | None ]
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`do_direct_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L108>`_
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Compute integrals on the fly
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`dump_ao_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f_template_729#L3>`_
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Save to disk the $ao integrals
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`dump_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f_template_729#L140>`_
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Save to disk the $ao integrals
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`eri <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L585>`_
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ATOMIC PRIMTIVE bielectronic integral between the 4 primitives ::
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primitive_1 = x1**(a_x) y1**(a_y) z1**(a_z) exp(-alpha * r1**2)
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primitive_2 = x1**(b_x) y1**(b_y) z1**(b_z) exp(- beta * r1**2)
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primitive_3 = x2**(c_x) y2**(c_y) z2**(c_z) exp(-delta * r2**2)
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primitive_4 = x2**(d_x) y2**(d_y) z2**(d_z) exp(- gama * r2**2)
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`four_idx <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/four_idx_transform.irp.f#L1>`_
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4-index transformation from AO to MO integrals
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`gauleg <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/gauss_legendre.irp.f#L20>`_
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Gauss-Legendre
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`gauleg_t2 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/gauss_legendre.irp.f#L1>`_
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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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`gauleg_w <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/gauss_legendre.irp.f#L2>`_
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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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`general_primitive_integral <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L449>`_
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Computes the integral <pq|rs> where p,q,r,s are Gaussian primitives
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`get_ao_bielec_integral <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L155>`_
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Gets one AO bi-electronic integral from the AO map
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`get_ao_bielec_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L194>`_
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Gets multiple AO bi-electronic integral from the AO map .
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All i are retrieved for j,k,l fixed.
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`get_ao_bielec_integrals_non_zero <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L222>`_
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Gets multiple AO bi-electronic integral from the AO map .
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All non-zero i are retrieved for j,k,l fixed.
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`get_ao_map_size <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L264>`_
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Returns the number of elements in the AO map
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`get_mo_bielec_integral <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L383>`_
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Returns one integral <ij|kl> in the MO basis
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`get_mo_bielec_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L430>`_
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Returns multiple integrals <ij|kl> in the MO basis, all
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i for j,k,l fixed.
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`get_mo_bielec_integrals_coulomb_ii <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L515>`_
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Returns multiple integrals <ki|li>
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k(1)i(2) 1/r12 l(1)i(2) :: out_val(i1)
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for k,l fixed.
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`get_mo_bielec_integrals_exch_ii <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L548>`_
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Returns multiple integrals <ki|il>
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k(1)i(2) 1/r12 i(1)l(2) :: out_val(i1)
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for k,l fixed.
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`get_mo_bielec_integrals_ij <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L461>`_
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Returns multiple integrals <ij|kl> in the MO basis, all
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i(1)j(2) 1/r12 k(1)l(2)
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i, j for k,l fixed.
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`get_mo_map_size <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L582>`_
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Return the number of elements in the MO map
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`give_polynom_mult_center_x <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L788>`_
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subroutine that returns the explicit polynom in term of the "t"
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variable of the following polynomw :
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I_x1(a_x, d_x,p,q) * I_x1(a_y, d_y,p,q) * I_x1(a_z, d_z,p,q)
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`i_x1_new <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L713>`_
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recursive function involved in the bielectronic integral
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`i_x1_pol_mult <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L851>`_
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recursive function involved in the bielectronic integral
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`i_x1_pol_mult_a1 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L966>`_
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recursive function involved in the bielectronic integral
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`i_x1_pol_mult_a2 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L1017>`_
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recursive function involved in the bielectronic integral
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`i_x1_pol_mult_recurs <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L885>`_
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recursive function involved in the bielectronic integral
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`i_x2_new <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L746>`_
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recursive function involved in the bielectronic integral
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`i_x2_pol_mult <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L1075>`_
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recursive function involved in the bielectronic integral
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`insert_into_ao_integrals_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L299>`_
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Create new entry into AO map
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`insert_into_mo_integrals_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L313>`_
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Create new entry into MO map, or accumulate in an existing entry
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`integrale_new <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L642>`_
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calculate the integral of the polynom ::
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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)
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between ( 0 ; 1)
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`load_ao_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f_template_729#L92>`_
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Read from disk the $ao integrals
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`load_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f_template_729#L229>`_
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Read from disk the $ao integrals
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`mo_bielec_integral <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L416>`_
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Returns one integral <ij|kl> in the MO basis
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`mo_bielec_integral_jj <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1344>`_
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mo_bielec_integral_jj(i,j) = J_ij
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mo_bielec_integral_jj_exchange(i,j) = K_ij
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mo_bielec_integral_jj_anti(i,j) = J_ij - K_ij
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`mo_bielec_integral_jj_anti <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1346>`_
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mo_bielec_integral_jj(i,j) = J_ij
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mo_bielec_integral_jj_exchange(i,j) = K_ij
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mo_bielec_integral_jj_anti(i,j) = J_ij - K_ij
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`mo_bielec_integral_jj_anti_from_ao <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1077>`_
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mo_bielec_integral_jj_from_ao(i,j) = J_ij
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mo_bielec_integral_jj_exchange_from_ao(i,j) = J_ij
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mo_bielec_integral_jj_anti_from_ao(i,j) = J_ij - K_ij
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`mo_bielec_integral_jj_exchange <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1345>`_
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mo_bielec_integral_jj(i,j) = J_ij
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mo_bielec_integral_jj_exchange(i,j) = K_ij
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mo_bielec_integral_jj_anti(i,j) = J_ij - K_ij
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`mo_bielec_integral_jj_exchange_from_ao <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1076>`_
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mo_bielec_integral_jj_from_ao(i,j) = J_ij
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mo_bielec_integral_jj_exchange_from_ao(i,j) = J_ij
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mo_bielec_integral_jj_anti_from_ao(i,j) = J_ij - K_ij
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`mo_bielec_integral_jj_from_ao <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1075>`_
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mo_bielec_integral_jj_from_ao(i,j) = J_ij
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mo_bielec_integral_jj_exchange_from_ao(i,j) = J_ij
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mo_bielec_integral_jj_anti_from_ao(i,j) = J_ij - K_ij
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`mo_bielec_integral_vv_anti_from_ao <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1203>`_
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mo_bielec_integral_vv_from_ao(i,j) = J_ij
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mo_bielec_integral_vv_exchange_from_ao(i,j) = J_ij
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mo_bielec_integral_vv_anti_from_ao(i,j) = J_ij - K_ij
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but only for the virtual orbitals
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`mo_bielec_integral_vv_exchange_from_ao <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1202>`_
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mo_bielec_integral_vv_from_ao(i,j) = J_ij
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mo_bielec_integral_vv_exchange_from_ao(i,j) = J_ij
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mo_bielec_integral_vv_anti_from_ao(i,j) = J_ij - K_ij
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but only for the virtual orbitals
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`mo_bielec_integral_vv_from_ao <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1201>`_
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mo_bielec_integral_vv_from_ao(i,j) = J_ij
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mo_bielec_integral_vv_exchange_from_ao(i,j) = J_ij
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mo_bielec_integral_vv_anti_from_ao(i,j) = J_ij - K_ij
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but only for the virtual orbitals
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`mo_bielec_integrals_in_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L22>`_
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If True, the map of MO bielectronic integrals is provided
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`mo_bielec_integrals_index <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1>`_
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Computes an unique index for i,j,k,l integrals
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`mo_integrals_cache <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L344>`_
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Cache of MO integrals for fast access
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`mo_integrals_cache_max <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L330>`_
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Min and max values of the MOs for which the integrals are in the cache
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`mo_integrals_cache_max_8 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L332>`_
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Min and max values of the MOs for which the integrals are in the cache
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`mo_integrals_cache_min <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L329>`_
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Min and max values of the MOs for which the integrals are in the cache
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`mo_integrals_cache_min_8 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L331>`_
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Min and max values of the MOs for which the integrals are in the cache
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`mo_integrals_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L286>`_
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MO integrals
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`mo_integrals_threshold <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L210>`_
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If |<ij|kl>| < ao_integrals_threshold then <pq|rs> is zero
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`n_pt_sup <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L774>`_
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Returns the upper boundary of the degree of the polynomial involved in the
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bielctronic integral :
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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)
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`no_ivvv_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L176>`_
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Can be switched on only if no_vvvv_integrals is True, then do not computes the integrals having 3 virtual index and 1 belonging to the core inactive active orbitals
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`no_vvv_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L142>`_
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Can be switched on only if no_vvvv_integrals is True, then do not computes the integrals having 3 virtual orbitals
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`no_vvvv_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L244>`_
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If True, computes all integrals except for the integrals having 4 virtual index
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`provide_all_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1384>`_
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Undocumented
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`push_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bielec_integrals_in_map_slave.irp.f#L21>`_
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Push integrals in the push socket
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`qp_ao_ints <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/qp_ao_ints.irp.f#L1>`_
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Increments a running calculation to compute AO integrals
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`read_ao_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/read_write.irp.f#L1>`_
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One level of abstraction for disk_access_ao_integrals and disk_access_mo_integrals
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`read_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/read_write.irp.f#L2>`_
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One level of abstraction for disk_access_ao_integrals and disk_access_mo_integrals
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`set_integrals_exchange_jj_into_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L177>`_
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Undocumented
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`set_integrals_jj_into_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L155>`_
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Undocumented
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`write_ao_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/read_write.irp.f#L3>`_
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One level of abstraction for disk_access_ao_integrals and disk_access_mo_integrals
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`write_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/read_write.irp.f#L4>`_
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One level of abstraction for disk_access_ao_integrals and disk_access_mo_integrals
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