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qp2/docs/source/modules/mo_two_e_erf_ints.rst

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.. _module_mo_two_e_erf_ints:
.. program:: mo_two_e_erf_ints
.. default-role:: option
======================
mo_two_e_erf_ints
======================
Here, all two-electron integrals (:math:`erf({\mu}_{erf} * r_{12})/r_{12}`) are computed.
As they have 4 indices and many are zero, they are stored in a map, as defined
in :file:`Utils/map_module.f90`.
The range separation parameter :math:`{\mu}_{erf}` is the variable :option:`ao_two_e_erf_ints mu_erf`.
To fetch an |MO| integral, use
`get_mo_two_e_integral_erf(i,j,k,l,mo_integrals_map_erf)`
The conventions are:
* For |MO| integrals : <ij|kl> = <12|12>
Be aware that it might not be the same conventions for |MO| and |AO| integrals.
EZFIO parameters
----------------
.. option:: io_mo_two_e_integrals_erf
Read/Write MO integrals with the long range interaction from/to disk [ Write | Read | None ]
Default: None
Providers
---------
.. c:var:: core_energy_erf
File : :file:`mo_two_e_erf_ints/core_quantities_erf.irp.f`
.. code:: fortran
double precision :: core_energy_erf
energy from the core : contains all core-core contributionswith the erf interaction
Needs:
.. hlist::
:columns: 3
* :c:data:`list_inact`
* :c:data:`mo_one_e_integrals`
* :c:data:`mo_two_e_int_erf_jj`
* :c:data:`n_core_orb`
* :c:data:`nuclear_repulsion`
.. c:var:: core_fock_operator_erf
File : :file:`mo_two_e_erf_ints/core_quantities_erf.irp.f`
.. code:: fortran
double precision, allocatable :: core_fock_operator_erf (mo_num,mo_num)
this is the contribution to the Fock operator from the core electrons with the erf interaction
Needs:
.. hlist::
:columns: 3
* :c:data:`list_inact`
* :c:data:`mo_integrals_erf_cache`
* :c:data:`mo_integrals_erf_cache_min`
* :c:data:`mo_integrals_erf_map`
* :c:data:`mo_num`
* :c:data:`mo_two_e_integrals_erf_in_map`
* :c:data:`n_core_orb`
.. c:function:: insert_into_mo_integrals_erf_map:
File : :file:`mo_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
subroutine insert_into_mo_integrals_erf_map(n_integrals, &
buffer_i, buffer_values, thr)
Create new entry into |MO| map, or accumulate in an existing entry
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_integrals_erf_map`
Called by:
.. hlist::
:columns: 3
* :c:func:`add_integrals_to_map_erf`
Calls:
.. hlist::
:columns: 3
* :c:func:`map_update`
.. c:var:: int_erf_3_index
File : :file:`mo_two_e_erf_ints/ints_erf_3_index.irp.f`
.. code:: fortran
double precision, allocatable :: int_erf_3_index (mo_num,mo_num,mo_num)
double precision, allocatable :: int_erf_3_index_exc (mo_num,mo_num,mo_num)
int_erf_3_index(i,j) = <ij|ij> = (ii|jj) with the erf interaction
int_erf_3_index_exc(i,j) = <ij|ji> = (ij|ij) with the erf interaction
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_integrals_erf_cache`
* :c:data:`mo_integrals_erf_cache_min`
* :c:data:`mo_integrals_erf_map`
* :c:data:`mo_num`
* :c:data:`mo_two_e_integrals_erf_in_map`
.. c:var:: int_erf_3_index_exc
File : :file:`mo_two_e_erf_ints/ints_erf_3_index.irp.f`
.. code:: fortran
double precision, allocatable :: int_erf_3_index (mo_num,mo_num,mo_num)
double precision, allocatable :: int_erf_3_index_exc (mo_num,mo_num,mo_num)
int_erf_3_index(i,j) = <ij|ij> = (ii|jj) with the erf interaction
int_erf_3_index_exc(i,j) = <ij|ji> = (ij|ij) with the erf interaction
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_integrals_erf_cache`
* :c:data:`mo_integrals_erf_cache_min`
* :c:data:`mo_integrals_erf_map`
* :c:data:`mo_num`
* :c:data:`mo_two_e_integrals_erf_in_map`
.. c:var:: mo_integrals_erf_cache
File : :file:`mo_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
double precision, allocatable :: mo_integrals_erf_cache (0:64*64*64*64)
Cache of |MO| integrals for fast access
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_integrals_erf_cache_min`
* :c:data:`mo_integrals_erf_map`
* :c:data:`mo_two_e_integrals_erf_in_map`
Needed by:
.. hlist::
:columns: 3
* :c:data:`core_fock_operator_erf`
* :c:data:`int_erf_3_index`
* :c:data:`mo_two_e_int_erf_jj`
.. c:var:: mo_integrals_erf_cache_max
File : :file:`mo_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
integer :: mo_integrals_erf_cache_min
integer :: mo_integrals_erf_cache_max
Min and max values of the MOs for which the integrals are in the cache
Needs:
.. hlist::
:columns: 3
* :c:data:`elec_alpha_num`
* :c:data:`mo_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`core_fock_operator_erf`
* :c:data:`int_erf_3_index`
* :c:data:`mo_integrals_erf_cache`
* :c:data:`mo_two_e_int_erf_jj`
.. c:var:: mo_integrals_erf_cache_min
File : :file:`mo_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
integer :: mo_integrals_erf_cache_min
integer :: mo_integrals_erf_cache_max
Min and max values of the MOs for which the integrals are in the cache
Needs:
.. hlist::
:columns: 3
* :c:data:`elec_alpha_num`
* :c:data:`mo_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`core_fock_operator_erf`
* :c:data:`int_erf_3_index`
* :c:data:`mo_integrals_erf_cache`
* :c:data:`mo_two_e_int_erf_jj`
.. c:var:: mo_integrals_erf_map
File : :file:`mo_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
type(map_type) :: mo_integrals_erf_map
|MO| integrals
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`core_fock_operator_erf`
* :c:data:`int_erf_3_index`
* :c:data:`mo_integrals_erf_cache`
* :c:data:`mo_two_e_int_erf_jj`
* :c:data:`mo_two_e_integrals_erf_in_map`
.. c:var:: mo_two_e_int_erf_jj
File : :file:`mo_two_e_erf_ints/mo_bi_integrals_erf.irp.f`
.. code:: fortran
double precision, allocatable :: mo_two_e_int_erf_jj (mo_num,mo_num)
double precision, allocatable :: mo_two_e_int_erf_jj_exchange (mo_num,mo_num)
double precision, allocatable :: mo_two_e_int_erf_jj_anti (mo_num,mo_num)
mo_two_e_integrals_jj(i,j) = J_ij
mo_two_e_integrals_jj_exchange(i,j) = K_ij
mo_two_e_integrals_jj_anti(i,j) = J_ij - K_ij
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_integrals_erf_cache`
* :c:data:`mo_integrals_erf_cache_min`
* :c:data:`mo_integrals_erf_map`
* :c:data:`mo_num`
* :c:data:`mo_two_e_integrals_erf_in_map`
Needed by:
.. hlist::
:columns: 3
* :c:data:`core_energy_erf`
.. c:var:: mo_two_e_int_erf_jj_anti
File : :file:`mo_two_e_erf_ints/mo_bi_integrals_erf.irp.f`
.. code:: fortran
double precision, allocatable :: mo_two_e_int_erf_jj (mo_num,mo_num)
double precision, allocatable :: mo_two_e_int_erf_jj_exchange (mo_num,mo_num)
double precision, allocatable :: mo_two_e_int_erf_jj_anti (mo_num,mo_num)
mo_two_e_integrals_jj(i,j) = J_ij
mo_two_e_integrals_jj_exchange(i,j) = K_ij
mo_two_e_integrals_jj_anti(i,j) = J_ij - K_ij
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_integrals_erf_cache`
* :c:data:`mo_integrals_erf_cache_min`
* :c:data:`mo_integrals_erf_map`
* :c:data:`mo_num`
* :c:data:`mo_two_e_integrals_erf_in_map`
Needed by:
.. hlist::
:columns: 3
* :c:data:`core_energy_erf`
.. c:var:: mo_two_e_int_erf_jj_anti_from_ao
File : :file:`mo_two_e_erf_ints/mo_bi_integrals_erf.irp.f`
.. code:: fortran
double precision, allocatable :: mo_two_e_int_erf_jj_from_ao (mo_num,mo_num)
double precision, allocatable :: mo_two_e_int_erf_jj_exchange_from_ao (mo_num,mo_num)
double precision, allocatable :: mo_two_e_int_erf_jj_anti_from_ao (mo_num,mo_num)
mo_two_e_integral_jj_from_ao(i,j) = J_ij
mo_two_e_integrals_jj_exchange_from_ao(i,j) = J_ij
mo_two_e_integrals_jj_anti_from_ao(i,j) = J_ij - K_ij
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_erf_map`
* :c:data:`ao_integrals_threshold`
* :c:data:`ao_num`
* :c:data:`ao_overlap_abs`
* :c:data:`ao_two_e_integral_erf_schwartz`
* :c:data:`ao_two_e_integrals_erf_in_map`
* :c:data:`do_direct_integrals`
* :c:data:`mo_coef`
* :c:data:`mo_coef_transp`
* :c:data:`mo_num`
.. c:var:: mo_two_e_int_erf_jj_exchange
File : :file:`mo_two_e_erf_ints/mo_bi_integrals_erf.irp.f`
.. code:: fortran
double precision, allocatable :: mo_two_e_int_erf_jj (mo_num,mo_num)
double precision, allocatable :: mo_two_e_int_erf_jj_exchange (mo_num,mo_num)
double precision, allocatable :: mo_two_e_int_erf_jj_anti (mo_num,mo_num)
mo_two_e_integrals_jj(i,j) = J_ij
mo_two_e_integrals_jj_exchange(i,j) = K_ij
mo_two_e_integrals_jj_anti(i,j) = J_ij - K_ij
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_integrals_erf_cache`
* :c:data:`mo_integrals_erf_cache_min`
* :c:data:`mo_integrals_erf_map`
* :c:data:`mo_num`
* :c:data:`mo_two_e_integrals_erf_in_map`
Needed by:
.. hlist::
:columns: 3
* :c:data:`core_energy_erf`
.. c:var:: mo_two_e_int_erf_jj_exchange_from_ao
File : :file:`mo_two_e_erf_ints/mo_bi_integrals_erf.irp.f`
.. code:: fortran
double precision, allocatable :: mo_two_e_int_erf_jj_from_ao (mo_num,mo_num)
double precision, allocatable :: mo_two_e_int_erf_jj_exchange_from_ao (mo_num,mo_num)
double precision, allocatable :: mo_two_e_int_erf_jj_anti_from_ao (mo_num,mo_num)
mo_two_e_integral_jj_from_ao(i,j) = J_ij
mo_two_e_integrals_jj_exchange_from_ao(i,j) = J_ij
mo_two_e_integrals_jj_anti_from_ao(i,j) = J_ij - K_ij
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_erf_map`
* :c:data:`ao_integrals_threshold`
* :c:data:`ao_num`
* :c:data:`ao_overlap_abs`
* :c:data:`ao_two_e_integral_erf_schwartz`
* :c:data:`ao_two_e_integrals_erf_in_map`
* :c:data:`do_direct_integrals`
* :c:data:`mo_coef`
* :c:data:`mo_coef_transp`
* :c:data:`mo_num`
.. c:var:: mo_two_e_int_erf_jj_from_ao
File : :file:`mo_two_e_erf_ints/mo_bi_integrals_erf.irp.f`
.. code:: fortran
double precision, allocatable :: mo_two_e_int_erf_jj_from_ao (mo_num,mo_num)
double precision, allocatable :: mo_two_e_int_erf_jj_exchange_from_ao (mo_num,mo_num)
double precision, allocatable :: mo_two_e_int_erf_jj_anti_from_ao (mo_num,mo_num)
mo_two_e_integral_jj_from_ao(i,j) = J_ij
mo_two_e_integrals_jj_exchange_from_ao(i,j) = J_ij
mo_two_e_integrals_jj_anti_from_ao(i,j) = J_ij - K_ij
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_erf_map`
* :c:data:`ao_integrals_threshold`
* :c:data:`ao_num`
* :c:data:`ao_overlap_abs`
* :c:data:`ao_two_e_integral_erf_schwartz`
* :c:data:`ao_two_e_integrals_erf_in_map`
* :c:data:`do_direct_integrals`
* :c:data:`mo_coef`
* :c:data:`mo_coef_transp`
* :c:data:`mo_num`
.. c:var:: mo_two_e_integrals_erf_in_map
File : :file:`mo_two_e_erf_ints/mo_bi_integrals_erf.irp.f`
.. code:: fortran
logical :: mo_two_e_integrals_erf_in_map
If True, the map of MO two-electron integrals is provided
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`ao_two_e_integrals_erf_in_map`
* :c:data:`ao_two_e_integrals_in_map`
* :c:data:`ezfio_filename`
* :c:data:`full_ijkl_bitmask_4`
* :c:data:`mo_coef`
* :c:data:`mo_coef_transp`
* :c:data:`mo_integrals_erf_map`
* :c:data:`mo_integrals_threshold`
* :c:data:`mo_num`
* :c:data:`n_int`
* :c:data:`read_mo_two_e_integrals_erf`
Needed by:
.. hlist::
:columns: 3
* :c:data:`core_fock_operator_erf`
* :c:data:`int_erf_3_index`
* :c:data:`mo_integrals_erf_cache`
* :c:data:`mo_two_e_int_erf_jj`
Subroutines / functions
-----------------------
.. c:function:: add_integrals_to_map_erf:
File : :file:`mo_two_e_erf_ints/mo_bi_integrals_erf.irp.f`
.. code:: fortran
subroutine add_integrals_to_map_erf(mask_ijkl)
Adds integrals to tha MO map according to some bitmask
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_coef`
* :c:data:`mo_integrals_threshold`
* :c:data:`mo_coef_transp`
* :c:data:`ao_num`
* :c:data:`n_int`
* :c:data:`mo_num`
* :c:data:`ao_two_e_integrals_in_map`
* :c:data:`mo_integrals_erf_map`
Called by:
.. hlist::
:columns: 3
* :c:data:`mo_two_e_integrals_erf_in_map`
Calls:
.. hlist::
:columns: 3
* :c:func:`bitstring_to_list`
* :c:func:`bitstring_to_str`
* :c:func:`cpu_time`
* :c:func:`get_ao_two_e_integrals_erf`
* :c:func:`insert_into_mo_integrals_erf_map`
* :c:func:`map_merge`
* :c:func:`mo_two_e_integrals_index`
* :c:func:`wall_time`
.. c:function:: clear_mo_erf_map:
File : :file:`mo_two_e_erf_ints/mo_bi_integrals_erf.irp.f`
.. code:: fortran
subroutine clear_mo_erf_map
Frees the memory of the MO map
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_integrals_erf_map`
Calls:
.. hlist::
:columns: 3
* :c:func:`map_deinit`
.. c:function:: get_mo_erf_map_size:
File : :file:`mo_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
integer*8 function get_mo_erf_map_size()
Returns the number of elements in the |MO| map
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_integrals_erf_map`
.. c:function:: get_mo_two_e_integral_erf:
File : :file:`mo_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
double precision function get_mo_two_e_integral_erf(i,j,k,l,map)
Returns one integral $\langle ij|kl \rangle$ in the |MO| basis
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_integrals_erf_cache`
* :c:data:`mo_integrals_erf_cache_min`
* :c:data:`mo_two_e_integrals_erf_in_map`
Calls:
.. hlist::
:columns: 3
* :c:func:`map_get`
* :c:func:`two_e_integrals_index`
.. c:function:: get_mo_two_e_integrals_erf:
File : :file:`mo_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
subroutine get_mo_two_e_integrals_erf(j,k,l,sze,out_val,map)
Returns multiple integrals $\langle ij|kl \rangle$ in the |MO| basis, all
i for j,k,l fixed.
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_two_e_integrals_erf_in_map`
Calls:
.. hlist::
:columns: 3
* :c:func:`map_get_many`
* :c:func:`two_e_integrals_index`
.. c:function:: get_mo_two_e_integrals_erf_coulomb_ii:
File : :file:`mo_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
subroutine get_mo_two_e_integrals_erf_coulomb_ii(k,l,sze,out_val,map)
Returns multiple integrals $\langle ki|li \rangle$
k(1)i(2) 1/r12 l(1)i(2) :: out_val(i1)
for k,l fixed.
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_two_e_integrals_erf_in_map`
Calls:
.. hlist::
:columns: 3
* :c:func:`map_get_many`
* :c:func:`two_e_integrals_index`
.. c:function:: get_mo_two_e_integrals_erf_exch_ii:
File : :file:`mo_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
subroutine get_mo_two_e_integrals_erf_exch_ii(k,l,sze,out_val,map)
Returns multiple integrals $\langle ki|il \rangle$
$\int k(1)i(2) \frac{1}{r_{12}} i(1)l(2)$ :: out_val(i1)
for k,l fixed.
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_two_e_integrals_erf_in_map`
Calls:
.. hlist::
:columns: 3
* :c:func:`map_get_many`
* :c:func:`two_e_integrals_index`
.. c:function:: get_mo_two_e_integrals_erf_i1j1:
File : :file:`mo_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
subroutine get_mo_two_e_integrals_erf_i1j1(k,l,sze,out_array,map)
Returns multiple integrals $\langle ik|jl \rangle$ in the |MO| basis, all
$\int i(1)j(1) \frac{\erf(\mu * r_{12})}{r_{12}} k(2)l(2)$
i, j for k,l fixed.
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_two_e_integrals_erf_in_map`
* :c:data:`mo_integrals_erf_map`
Calls:
.. hlist::
:columns: 3
* :c:func:`i2radix_sort`
* :c:func:`i8radix_sort`
* :c:func:`iradix_sort`
* :c:func:`map_get_many`
* :c:func:`two_e_integrals_index`
.. c:function:: get_mo_two_e_integrals_erf_ij:
File : :file:`mo_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
subroutine get_mo_two_e_integrals_erf_ij(k,l,sze,out_array,map)
Returns multiple integrals $\langle ij|kl \rangle$ in the |MO| basis, all
$\int i(1)j(2) \frac{1}{r_{12}} k(1)l(2)$
i, j for k,l fixed.
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_two_e_integrals_erf_in_map`
* :c:data:`mo_integrals_erf_map`
Calls:
.. hlist::
:columns: 3
* :c:func:`i2radix_sort`
* :c:func:`i8radix_sort`
* :c:func:`iradix_sort`
* :c:func:`map_get_many`
* :c:func:`two_e_integrals_index`
.. c:function:: load_mo_integrals_erf:
File : :file:`mo_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
integer function load_mo_integrals_erf(filename)
Read from disk the |MO| erf integrals
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_integrals_erf_map`
Calls:
.. hlist::
:columns: 3
* :c:func:`cache_map_reallocate`
* :c:func:`map_deinit`
* :c:func:`map_sort`
.. c:function:: mo_two_e_integral_erf:
File : :file:`mo_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
double precision function mo_two_e_integral_erf(i,j,k,l)
Returns one integral $\langle ij|kl \rangle$ in the |MO| basis
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_integrals_erf_cache`
* :c:data:`mo_integrals_erf_map`
* :c:data:`mo_two_e_integrals_erf_in_map`
.. c:function:: mo_two_e_integrals_erf_index:
File : :file:`mo_two_e_erf_ints/mo_bi_integrals_erf.irp.f`
.. code:: fortran
subroutine mo_two_e_integrals_erf_index(i,j,k,l,i1)
Computes an unique index for i,j,k,l integrals
.. c:function:: provide_all_mo_integrals_erf:
File : :file:`mo_two_e_erf_ints/mo_bi_integrals_erf.irp.f`
.. code:: fortran
subroutine provide_all_mo_integrals_erf
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_two_e_integrals_erf_in_map`
* :c:data:`mo_two_e_int_erf_jj`
* :c:data:`mo_two_e_int_erf_jj`
* :c:data:`mo_integrals_erf_map`
* :c:data:`mo_two_e_int_erf_jj`
.. c:function:: save_erf_two_e_integrals_mo:
File : :file:`mo_two_e_erf_ints/routines_save_integrals_erf.irp.f`
.. code:: fortran
subroutine save_erf_two_e_integrals_mo
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_two_e_integrals_erf_in_map`
* :c:data:`ezfio_filename`
* :c:data:`mo_integrals_erf_map`
Called by:
.. hlist::
:columns: 3
* :c:func:`routine`
Calls:
.. hlist::
:columns: 3
* :c:func:`ezfio_set_mo_two_e_erf_ints_io_mo_two_e_integrals_erf`
* :c:func:`ezfio_set_work_empty`
* :c:func:`map_save_to_disk`
.. c:function:: save_erf_two_e_ints_mo_into_ints_mo:
File : :file:`mo_two_e_erf_ints/routines_save_integrals_erf.irp.f`
.. code:: fortran
subroutine save_erf_two_e_ints_mo_into_ints_mo
Needs:
.. hlist::
:columns: 3
* :c:data:`mo_two_e_integrals_erf_in_map`
* :c:data:`ezfio_filename`
* :c:data:`mo_integrals_erf_map`
Calls:
.. hlist::
:columns: 3
* :c:func:`ezfio_set_mo_two_e_ints_io_mo_two_e_integrals`
* :c:func:`ezfio_set_work_empty`
* :c:func:`map_save_to_disk`
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