=============
BiInts Module
=============
Here, all bi-electronic 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
``Utils/map_module.f90``. To fetch an AO integral, use the
``get_ao_bielec_integral(i,j,k,l,ao_integrals_map)`` function, and to fetch and
MO integral, use ``get_mo_bielec_integral(i,j,k,l,mo_integrals_map)`` or
``mo_bielec_integral(i,j,k,l)``.
The conventions are:
* For AO integrals : (ik|jl) = (11|22)
* For MO integrals : <ij|kl> = <12|12>
Needed Modules
==============
.. Do not edit this section It was auto-generated
.. by the `update_README.py` script.
.. image:: tree_dependency.png
* `Pseudo <http://github.com/LCPQ/quantum_package/tree/master/src/Pseudo>`_
* `Bitmask <http://github.com/LCPQ/quantum_package/tree/master/src/Bitmask>`_
Needed Modules
==============
.. Do not edit this section It was auto-generated
.. by the `update_README.py` script.
.. image:: tree_dependency.png
* `Pseudo <http://github.com/LCPQ/quantum_package/tree/master/src/Pseudo>`_
* `Bitmask <http://github.com/LCPQ/quantum_package/tree/master/src/Bitmask>`_
* `ZMQ <http://github.com/LCPQ/quantum_package/tree/master/src/ZMQ>`_
* `FourIdx <http://github.com/LCPQ/quantum_package/tree/master/src/FourIdx>`_
Documentation
=============
.. Do not edit this section It was auto-generated
.. by the `update_README.py` script.
`add_integrals_to_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L199>`_
Adds integrals to tha MO map according to some bitmask
`add_integrals_to_map_no_exit_34 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L814>`_
Adds integrals to tha MO map according to some bitmask
`add_integrals_to_map_three_indices <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L502>`_
Adds integrals to tha MO map according to some bitmask
`ao_bielec_integral <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L1>`_
integral of the AO basis <ik|jl> or (ij|kl)
i(r1) j(r1) 1/r12 k(r2) l(r2)
`ao_bielec_integral_schwartz <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L424>`_
Needed to compute Schwartz inequalities
`ao_bielec_integral_schwartz_accel <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L106>`_
integral of the AO basis <ik|jl> or (ij|kl)
i(r1) j(r1) 1/r12 k(r2) l(r2)
`ao_bielec_integrals_in_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L328>`_
Map of Atomic integrals
i(r1) j(r2) 1/r12 k(r1) l(r2)
`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>`_
Collects results from the AO integral calculation
`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>`_
Computes a buffer of integrals
`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>`_
Computes a buffer of integrals. i is the ID of the current thread.
`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>`_
Computes a buffer of integrals. i is the ID of the current thread.
`ao_integrals_cache <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L123>`_
Cache of AO integrals for fast access
`ao_integrals_cache_max <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L113>`_
Min and max values of the AOs for which the integrals are in the cache
`ao_integrals_cache_min <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L112>`_
Min and max values of the AOs for which the integrals are in the cache
`ao_integrals_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L6>`_
AO integrals
`ao_integrals_threshold <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L40>`_
If |<pq|rs>| < ao_integrals_threshold then <pq|rs> is zero
`ao_l4 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L278>`_
Computes the product of l values of i,j,k,and l
`bench_maps <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/test_integrals.irp.f#L1>`_
Performs timing benchmarks on integral access
`bielec_integrals_index <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L19>`_
Undocumented
`bielec_integrals_index_reverse <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L36>`_
Undocumented
`big_array_coulomb_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/integrals_3_index.irp.f#L1>`_
Undocumented
`big_array_exchange_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/integrals_3_index.irp.f#L2>`_
Undocumented
`clear_ao_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L273>`_
Frees the memory of the AO map
`clear_mo_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1372>`_
Frees the memory of the MO map
`compute_ao_bielec_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L289>`_
Compute AO 1/r12 integrals for all i and fixed j,k,l
`compute_ao_integrals_jl <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L1156>`_
Parallel client for AO integrals
`disk_access_ao_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L6>`_
Read/Write AO integrals from/to disk [ Write | Read | None ]
`disk_access_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L74>`_
Read/Write MO integrals from/to disk [ Write | Read | None ]
`do_direct_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L108>`_
Compute integrals on the fly
`dump_ao_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f_template_729#L3>`_
Save to disk the $ao integrals
`dump_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f_template_729#L140>`_
Save to disk the $ao integrals
`eri <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L585>`_
ATOMIC PRIMTIVE bielectronic 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)
`four_idx <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/four_idx_transform.irp.f#L1>`_
4-index transformation from AO to MO integrals
`gauleg <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/gauss_legendre.irp.f#L20>`_
Gauss-Legendre
`gauleg_t2 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/gauss_legendre.irp.f#L1>`_
t_w(i,1,k) = w(i)
t_w(i,2,k) = t(i)
`gauleg_w <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/gauss_legendre.irp.f#L2>`_
t_w(i,1,k) = w(i)
t_w(i,2,k) = t(i)
`general_primitive_integral <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L449>`_
Computes the integral <pq|rs> where p,q,r,s are Gaussian primitives
`get_ao_bielec_integral <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L155>`_
Gets one AO bi-electronic integral from the AO map
`get_ao_bielec_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L194>`_
Gets multiple AO bi-electronic integral from the AO map .
All i are retrieved for j,k,l fixed.
`get_ao_bielec_integrals_non_zero <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L222>`_
Gets multiple AO bi-electronic integral from the AO map .
All non-zero i are retrieved for j,k,l fixed.
`get_ao_map_size <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L264>`_
Returns the number of elements in the AO map
`get_mo_bielec_integral <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L383>`_
Returns one integral <ij|kl> in the MO basis
`get_mo_bielec_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L430>`_
Returns multiple integrals <ij|kl> in the MO basis, all
i for j,k,l fixed.
`get_mo_bielec_integrals_coulomb_ii <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L515>`_
Returns multiple integrals <ki|li>
k(1)i(2) 1/r12 l(1)i(2) :: out_val(i1)
for k,l fixed.
`get_mo_bielec_integrals_exch_ii <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L548>`_
Returns multiple integrals <ki|il>
k(1)i(2) 1/r12 i(1)l(2) :: out_val(i1)
for k,l fixed.
`get_mo_bielec_integrals_ij <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L461>`_
Returns multiple integrals <ij|kl> in the MO basis, all
i(1)j(2) 1/r12 k(1)l(2)
i, j for k,l fixed.
`get_mo_map_size <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L582>`_
Return the number of elements in the MO map
`give_polynom_mult_center_x <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L788>`_
subroutine that returns the explicit polynom in term of the "t"
variable of the following polynomw :
I_x1(a_x, d_x,p,q) * I_x1(a_y, d_y,p,q) * I_x1(a_z, d_z,p,q)
`i_x1_new <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L713>`_
recursive function involved in the bielectronic integral
`i_x1_pol_mult <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L851>`_
recursive function involved in the bielectronic integral
`i_x1_pol_mult_a1 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L966>`_
recursive function involved in the bielectronic integral
`i_x1_pol_mult_a2 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L1017>`_
recursive function involved in the bielectronic integral
`i_x1_pol_mult_recurs <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L885>`_
recursive function involved in the bielectronic integral
`i_x2_new <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L746>`_
recursive function involved in the bielectronic integral
`i_x2_pol_mult <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L1075>`_
recursive function involved in the bielectronic integral
`insert_into_ao_integrals_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L299>`_
Create new entry into AO map
`insert_into_mo_integrals_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L313>`_
Create new entry into MO map, or accumulate in an existing entry
`integrale_new <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L642>`_
calculate the integral of the polynom ::
I_x1(a_x+b_x, c_x+d_x,p,q) * I_x1(a_y+b_y, c_y+d_y,p,q) * I_x1(a_z+b_z, c_z+d_z,p,q)
between ( 0 ; 1)
`load_ao_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f_template_729#L92>`_
Read from disk the $ao integrals
`load_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f_template_729#L229>`_
Read from disk the $ao integrals
`mo_bielec_integral <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L416>`_
Returns one integral <ij|kl> in the MO basis
`mo_bielec_integral_jj <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1344>`_
mo_bielec_integral_jj(i,j) = J_ij
mo_bielec_integral_jj_exchange(i,j) = K_ij
mo_bielec_integral_jj_anti(i,j) = J_ij - K_ij
`mo_bielec_integral_jj_anti <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1346>`_
mo_bielec_integral_jj(i,j) = J_ij
mo_bielec_integral_jj_exchange(i,j) = K_ij
mo_bielec_integral_jj_anti(i,j) = J_ij - K_ij
`mo_bielec_integral_jj_anti_from_ao <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1077>`_
mo_bielec_integral_jj_from_ao(i,j) = J_ij
mo_bielec_integral_jj_exchange_from_ao(i,j) = J_ij
mo_bielec_integral_jj_anti_from_ao(i,j) = J_ij - K_ij
`mo_bielec_integral_jj_exchange <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1345>`_
mo_bielec_integral_jj(i,j) = J_ij
mo_bielec_integral_jj_exchange(i,j) = K_ij
mo_bielec_integral_jj_anti(i,j) = J_ij - K_ij
`mo_bielec_integral_jj_exchange_from_ao <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1076>`_
mo_bielec_integral_jj_from_ao(i,j) = J_ij
mo_bielec_integral_jj_exchange_from_ao(i,j) = J_ij
mo_bielec_integral_jj_anti_from_ao(i,j) = J_ij - K_ij
`mo_bielec_integral_jj_from_ao <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1075>`_
mo_bielec_integral_jj_from_ao(i,j) = J_ij
mo_bielec_integral_jj_exchange_from_ao(i,j) = J_ij
mo_bielec_integral_jj_anti_from_ao(i,j) = J_ij - K_ij
`mo_bielec_integral_vv_anti_from_ao <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1203>`_
mo_bielec_integral_vv_from_ao(i,j) = J_ij
mo_bielec_integral_vv_exchange_from_ao(i,j) = J_ij
mo_bielec_integral_vv_anti_from_ao(i,j) = J_ij - K_ij
but only for the virtual orbitals
`mo_bielec_integral_vv_exchange_from_ao <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1202>`_
mo_bielec_integral_vv_from_ao(i,j) = J_ij
mo_bielec_integral_vv_exchange_from_ao(i,j) = J_ij
mo_bielec_integral_vv_anti_from_ao(i,j) = J_ij - K_ij
but only for the virtual orbitals
`mo_bielec_integral_vv_from_ao <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1201>`_
mo_bielec_integral_vv_from_ao(i,j) = J_ij
mo_bielec_integral_vv_exchange_from_ao(i,j) = J_ij
mo_bielec_integral_vv_anti_from_ao(i,j) = J_ij - K_ij
but only for the virtual orbitals
`mo_bielec_integrals_in_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L22>`_
If True, the map of MO bielectronic integrals is provided
`mo_bielec_integrals_index <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1>`_
Computes an unique index for i,j,k,l integrals
`mo_integrals_cache <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L344>`_
Cache of MO integrals for fast access
`mo_integrals_cache_max <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L330>`_
Min and max values of the MOs for which the integrals are in the cache
`mo_integrals_cache_max_8 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L332>`_
Min and max values of the MOs for which the integrals are in the cache
`mo_integrals_cache_min <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L329>`_
Min and max values of the MOs for which the integrals are in the cache
`mo_integrals_cache_min_8 <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L331>`_
Min and max values of the MOs for which the integrals are in the cache
`mo_integrals_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/map_integrals.irp.f#L286>`_
MO integrals
`mo_integrals_threshold <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L210>`_
If |<ij|kl>| < ao_integrals_threshold then <pq|rs> is zero
`n_pt_sup <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bi_integrals.irp.f#L774>`_
Returns the upper boundary of the degree of the polynomial involved in the
bielctronic integral :
Ix(a_x,b_x,c_x,d_x) * Iy(a_y,b_y,c_y,d_y) * Iz(a_z,b_z,c_z,d_z)
`no_ivvv_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L176>`_
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
`no_vvv_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L142>`_
Can be switched on only if no_vvvv_integrals is True, then do not computes the integrals having 3 virtual orbitals
`no_vvvv_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ezfio_interface.irp.f#L244>`_
If True, computes all integrals except for the integrals having 4 virtual index
`provide_all_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L1384>`_
Undocumented
`push_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/ao_bielec_integrals_in_map_slave.irp.f#L21>`_
Push integrals in the push socket
`qp_ao_ints <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/qp_ao_ints.irp.f#L1>`_
Increments a running calculation to compute AO integrals
`read_ao_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/read_write.irp.f#L1>`_
One level of abstraction for disk_access_ao_integrals and disk_access_mo_integrals
`read_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/read_write.irp.f#L2>`_
One level of abstraction for disk_access_ao_integrals and disk_access_mo_integrals
`set_integrals_exchange_jj_into_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L177>`_
Undocumented
`set_integrals_jj_into_map <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/mo_bi_integrals.irp.f#L155>`_
Undocumented
`write_ao_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/read_write.irp.f#L3>`_
One level of abstraction for disk_access_ao_integrals and disk_access_mo_integrals
`write_mo_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/Integrals_Bielec/read_write.irp.f#L4>`_
One level of abstraction for disk_access_ao_integrals and disk_access_mo_integrals
Anthony Scemama
87109fb96b
