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quantum_package/src/Bielec_integrals/README.rst
Thomas Applencourt 0a8d393dbc BiInt => Bielec_integrals
2015-03-31 10:51:11 +02:00

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=============
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)``.
Needed Modules
==============
.. Do not edit this section. It was auto-generated from the
.. NEEDED_MODULES file.
* `AOs <http://github.com/LCPQ/quantum_package/tree/master/src/AOs>`_
* `Bitmask <http://github.com/LCPQ/quantum_package/tree/master/src/Bitmask>`_
* `Electrons <http://github.com/LCPQ/quantum_package/tree/master/src/Electrons>`_
* `Ezfio_files <http://github.com/LCPQ/quantum_package/tree/master/src/Ezfio_files>`_
* `MOs <http://github.com/LCPQ/quantum_package/tree/master/src/MOs>`_
* `Nuclei <http://github.com/LCPQ/quantum_package/tree/master/src/Nuclei>`_
* `Output <http://github.com/LCPQ/quantum_package/tree/master/src/Output>`_
* `Utils <http://github.com/LCPQ/quantum_package/tree/master/src/Utils>`_
* `MonoInts <http://github.com/LCPQ/quantum_package/tree/master/src/MonoInts>`_
Documentation
=============
.. Do not edit this section. It was auto-generated from the
.. NEEDED_MODULES file.
`ao_bielec_integral <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/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/BiInts/ao_bi_integrals.irp.f#L350>`_
Needed to compuet Schwartz inequalities
`ao_bielec_integrals_in_map <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/ao_bi_integrals.irp.f#L188>`_
Map of Atomic integrals
i(r1) j(r2) 1/r12 k(r1) l(r2)
`compute_ao_bielec_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/ao_bi_integrals.irp.f#L147>`_
Compute AO 1/r12 integrals for all i and fixed j,k,l
`eri <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/ao_bi_integrals.irp.f#L511>`_
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)
`general_primitive_integral <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/ao_bi_integrals.irp.f#L376>`_
Computes the integral <pq|rs> where p,q,r,s are Gaussian primitives
`give_polynom_mult_center_x <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/ao_bi_integrals.irp.f#L656>`_
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/BiInts/ao_bi_integrals.irp.f#L600>`_
recursive function involved in the bielectronic integral
`i_x1_pol_mult <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/ao_bi_integrals.irp.f#L719>`_
recursive function involved in the bielectronic integral
`i_x1_pol_mult_a1 <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/ao_bi_integrals.irp.f#L839>`_
recursive function involved in the bielectronic integral
`i_x1_pol_mult_a2 <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/ao_bi_integrals.irp.f#L893>`_
recursive function involved in the bielectronic integral
`i_x1_pol_mult_recurs <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/ao_bi_integrals.irp.f#L753>`_
recursive function involved in the bielectronic integral
`i_x2_new <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/ao_bi_integrals.irp.f#L623>`_
recursive function involved in the bielectronic integral
`i_x2_pol_mult <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/ao_bi_integrals.irp.f#L955>`_
recursive function involved in the bielectronic integral
`integrale_new <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/ao_bi_integrals.irp.f#L555>`_
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)
`n_pt_sup <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/ao_bi_integrals.irp.f#L642>`_
Returns the upper boundary of the degree of the polynom 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)
`gauleg <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/gauss_legendre.irp.f#L20>`_
Gauss-Legendre
`gauleg_t2 <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/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/BiInts/gauss_legendre.irp.f#L2>`_
t_w(i,1,k) = w(i)
t_w(i,2,k) = t(i)
`ao_integrals_map <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/map_integrals.irp.f#L6>`_
AO integrals
`bielec_integrals_index <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/map_integrals.irp.f#L17>`_
Undocumented
`clear_ao_map <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/map_integrals.irp.f#L128>`_
Frees the memory of the AO map
`clear_mo_map <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/map_integrals.irp.f#L285>`_
Frees the memory of the MO map
`get_ao_bielec_integral <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/map_integrals.irp.f#L33>`_
Gets one AO bi-electronic integral from the AO map
`get_ao_bielec_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/map_integrals.irp.f#L51>`_
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/BiInts/map_integrals.irp.f#L84>`_
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/BiInts/map_integrals.irp.f#L120>`_
Returns the number of elements in the AO map
`get_mo_bielec_integral <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/map_integrals.irp.f#L184>`_
Returns one integral <ij|kl> in the MO basis
`get_mo_bielec_integrals <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/map_integrals.irp.f#L213>`_
Returns multiple integrals <ij|kl> in the MO basis, all
i for j,k,l fixed.
`get_mo_bielec_integrals_existing_ik <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/map_integrals.irp.f#L235>`_
Returns multiple integrals <ij|kl> in the MO basis, all
i for j,k,l fixed.
`get_mo_map_size <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/map_integrals.irp.f#L277>`_
Return the number of elements in the MO map
`insert_into_ao_integrals_map <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/map_integrals.irp.f#L153>`_
Create new entry into AO map
`insert_into_mo_integrals_map <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/map_integrals.irp.f#L168>`_
Create new entry into MO map, or accumulate in an existing entry
`mo_bielec_integral <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/map_integrals.irp.f#L201>`_
Returns one integral <ij|kl> in the MO basis
`mo_integrals_map <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/map_integrals.irp.f#L142>`_
MO integrals
`add_integrals_to_map <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/mo_bi_integrals.irp.f#L40>`_
Adds integrals to tha MO map according to some bitmask
`mo_bielec_integral_jj <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/mo_bi_integrals.irp.f#L314>`_
mo_bielec_integral_jj(i,j) = J_ij
mo_bielec_integral_jj_exchange(i,j) = J_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/BiInts/mo_bi_integrals.irp.f#L316>`_
mo_bielec_integral_jj(i,j) = J_ij
mo_bielec_integral_jj_exchange(i,j) = J_ij
mo_bielec_integral_jj_anti(i,j) = J_ij - K_ij
`mo_bielec_integral_jj_exchange <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/mo_bi_integrals.irp.f#L315>`_
mo_bielec_integral_jj(i,j) = J_ij
mo_bielec_integral_jj_exchange(i,j) = J_ij
mo_bielec_integral_jj_anti(i,j) = J_ij - K_ij
`mo_bielec_integrals_in_map <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/mo_bi_integrals.irp.f#L21>`_
If True, the map of MO bielectronic integrals is provided
`mo_bielec_integrals_index <http://github.com/LCPQ/quantum_package/tree/master/src/BiInts/mo_bi_integrals.irp.f#L1>`_
Computes an unique index for i,j,k,l integrals
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