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591 lines
13 KiB
ReStructuredText
591 lines
13 KiB
ReStructuredText
.. _mo_two_e_ints:
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.. program:: mo_two_e_ints
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.. default-role:: option
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==================
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mo_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, and
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to fetch an |MO| integral, use
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`get_two_e_integral(i,j,k,l,mo_integrals_map)` or
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`mo_two_e_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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EZFIO parameters
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----------------
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.. option:: io_mo_two_e_integrals
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Read/Write |MO| integrals from/to disk [ Write | Read | None ]
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Default: None
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.. option:: mo_integrals_threshold
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If | <ij|kl> | < `mo_integrals_threshold` then <ij|kl> is zero
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Default: 1.e-15
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.. option:: no_vvvv_integrals
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If `True`, computes all integrals except for the integrals having 4 virtual indices
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Default: False
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.. option:: no_ivvv_integrals
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Can be switched on only if `no_vvvv_integrals` is `True`, then does not compute the integrals with 3 virtual indices and 1 belonging to the core inactive active orbitals
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Default: False
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.. option:: no_vvv_integrals
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Can be switched on only if `no_vvvv_integrals` is `True`, then does not compute the integrals with 3 virtual orbitals
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Default: False
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Providers
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---------
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.. c:var:: big_array_coulomb_integrals
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.. code:: text
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double precision, allocatable :: big_array_coulomb_integrals (mo_num,mo_num,mo_num)
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double precision, allocatable :: big_array_exchange_integrals (mo_num,mo_num,mo_num)
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File: :file:`integrals_3_index.irp.f`
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big_array_coulomb_integrals(i,j) = <ij|ij> = (ii|jj)
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big_array_exchange_integrals(i,j) = <ij|ji> = (ij|ij)
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.. c:var:: big_array_exchange_integrals
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.. code:: text
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double precision, allocatable :: big_array_coulomb_integrals (mo_num,mo_num,mo_num)
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double precision, allocatable :: big_array_exchange_integrals (mo_num,mo_num,mo_num)
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File: :file:`integrals_3_index.irp.f`
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big_array_coulomb_integrals(i,j) = <ij|ij> = (ii|jj)
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big_array_exchange_integrals(i,j) = <ij|ji> = (ij|ij)
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.. c:var:: core_energy
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.. code:: text
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double precision :: core_energy
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File: :file:`core_quantities.irp.f`
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energy from the core : contains all core-core contributions
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.. c:var:: core_fock_operator
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.. code:: text
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double precision, allocatable :: core_fock_operator (mo_num,mo_num)
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File: :file:`core_quantities.irp.f`
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this is the contribution to the Fock operator from the core electrons
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.. c:var:: insert_into_mo_integrals_map
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.. code:: text
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subroutine insert_into_mo_integrals_map(n_integrals, &
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buffer_i, buffer_values, thr)
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File: :file:`map_integrals.irp.f`
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Create new entry into MO map, or accumulate in an existing entry
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.. c:var:: mo_integrals_cache
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.. code:: text
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double precision, allocatable :: mo_integrals_cache (0_8:128_8*128_8*128_8*128_8)
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File: :file:`map_integrals.irp.f`
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Cache of MO integrals for fast access
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.. c:var:: mo_integrals_cache_max
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.. code:: text
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integer*4 :: mo_integrals_cache_min
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integer*4 :: mo_integrals_cache_max
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integer*8 :: mo_integrals_cache_min_8
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integer*8 :: mo_integrals_cache_max_8
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File: :file:`map_integrals.irp.f`
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Min and max values of the MOs for which the integrals are in the cache
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.. c:var:: mo_integrals_cache_max_8
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.. code:: text
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integer*4 :: mo_integrals_cache_min
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integer*4 :: mo_integrals_cache_max
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integer*8 :: mo_integrals_cache_min_8
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integer*8 :: mo_integrals_cache_max_8
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File: :file:`map_integrals.irp.f`
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Min and max values of the MOs for which the integrals are in the cache
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.. c:var:: mo_integrals_cache_min
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.. code:: text
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integer*4 :: mo_integrals_cache_min
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integer*4 :: mo_integrals_cache_max
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integer*8 :: mo_integrals_cache_min_8
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integer*8 :: mo_integrals_cache_max_8
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File: :file:`map_integrals.irp.f`
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Min and max values of the MOs for which the integrals are in the cache
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.. c:var:: mo_integrals_cache_min_8
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.. code:: text
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integer*4 :: mo_integrals_cache_min
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integer*4 :: mo_integrals_cache_max
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integer*8 :: mo_integrals_cache_min_8
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integer*8 :: mo_integrals_cache_max_8
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File: :file:`map_integrals.irp.f`
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Min and max values of the MOs for which the integrals are in the cache
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.. c:var:: mo_integrals_map
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.. code:: text
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type(map_type) :: mo_integrals_map
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File: :file:`map_integrals.irp.f`
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MO integrals
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.. c:var:: mo_two_e_integral_jj_from_ao
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.. code:: text
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double precision, allocatable :: mo_two_e_integral_jj_from_ao (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_jj_exchange_from_ao (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_jj_anti_from_ao (mo_num,mo_num)
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File: :file:`mo_bi_integrals.irp.f`
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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
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.. c:var:: mo_two_e_integrals_in_map
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.. code:: text
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logical :: mo_two_e_integrals_in_map
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File: :file:`mo_bi_integrals.irp.f`
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If True, the map of MO two-electron integrals is provided
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.. c:var:: mo_two_e_integrals_jj
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.. code:: text
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double precision, allocatable :: mo_two_e_integrals_jj (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_jj_exchange (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_jj_anti (mo_num,mo_num)
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File: :file:`mo_bi_integrals.irp.f`
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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
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.. c:var:: mo_two_e_integrals_jj_anti
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.. code:: text
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double precision, allocatable :: mo_two_e_integrals_jj (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_jj_exchange (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_jj_anti (mo_num,mo_num)
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File: :file:`mo_bi_integrals.irp.f`
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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
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.. c:var:: mo_two_e_integrals_jj_anti_from_ao
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.. code:: text
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double precision, allocatable :: mo_two_e_integral_jj_from_ao (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_jj_exchange_from_ao (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_jj_anti_from_ao (mo_num,mo_num)
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File: :file:`mo_bi_integrals.irp.f`
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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
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.. c:var:: mo_two_e_integrals_jj_exchange
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.. code:: text
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double precision, allocatable :: mo_two_e_integrals_jj (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_jj_exchange (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_jj_anti (mo_num,mo_num)
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File: :file:`mo_bi_integrals.irp.f`
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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
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.. c:var:: mo_two_e_integrals_jj_exchange_from_ao
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.. code:: text
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double precision, allocatable :: mo_two_e_integral_jj_from_ao (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_jj_exchange_from_ao (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_jj_anti_from_ao (mo_num,mo_num)
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File: :file:`mo_bi_integrals.irp.f`
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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
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.. c:var:: mo_two_e_integrals_vv_anti_from_ao
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.. code:: text
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double precision, allocatable :: mo_two_e_integrals_vv_from_ao (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_vv_exchange_from_ao (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_vv_anti_from_ao (mo_num,mo_num)
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File: :file:`mo_bi_integrals.irp.f`
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mo_two_e_integrals_vv_from_ao(i,j) = J_ij mo_two_e_integrals_vv_exchange_from_ao(i,j) = J_ij mo_two_e_integrals_vv_anti_from_ao(i,j) = J_ij - K_ij but only for the virtual orbitals
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.. c:var:: mo_two_e_integrals_vv_exchange_from_ao
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.. code:: text
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double precision, allocatable :: mo_two_e_integrals_vv_from_ao (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_vv_exchange_from_ao (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_vv_anti_from_ao (mo_num,mo_num)
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File: :file:`mo_bi_integrals.irp.f`
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mo_two_e_integrals_vv_from_ao(i,j) = J_ij mo_two_e_integrals_vv_exchange_from_ao(i,j) = J_ij mo_two_e_integrals_vv_anti_from_ao(i,j) = J_ij - K_ij but only for the virtual orbitals
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.. c:var:: mo_two_e_integrals_vv_from_ao
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.. code:: text
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double precision, allocatable :: mo_two_e_integrals_vv_from_ao (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_vv_exchange_from_ao (mo_num,mo_num)
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double precision, allocatable :: mo_two_e_integrals_vv_anti_from_ao (mo_num,mo_num)
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File: :file:`mo_bi_integrals.irp.f`
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mo_two_e_integrals_vv_from_ao(i,j) = J_ij mo_two_e_integrals_vv_exchange_from_ao(i,j) = J_ij mo_two_e_integrals_vv_anti_from_ao(i,j) = J_ij - K_ij but only for the virtual orbitals
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Subroutines / functions
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-----------------------
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.. c:function:: add_integrals_to_map
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.. code:: text
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subroutine add_integrals_to_map(mask_ijkl)
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File: :file:`mo_bi_integrals.irp.f`
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Adds integrals to tha MO map according to some bitmask
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.. c:function:: add_integrals_to_map_no_exit_34
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.. code:: text
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subroutine add_integrals_to_map_no_exit_34(mask_ijkl)
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File: :file:`mo_bi_integrals.irp.f`
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Adds integrals to tha MO map according to some bitmask
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.. c:function:: add_integrals_to_map_three_indices
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.. code:: text
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subroutine add_integrals_to_map_three_indices(mask_ijk)
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File: :file:`mo_bi_integrals.irp.f`
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Adds integrals to tha MO map according to some bitmask
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.. c:function:: clear_mo_map
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.. code:: text
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subroutine clear_mo_map
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File: :file:`mo_bi_integrals.irp.f`
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Frees the memory of the MO map
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.. c:function:: dump_mo_integrals
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.. code:: text
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subroutine dump_mo_integrals(filename)
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File: :file:`map_integrals.irp.f`
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Save to disk the |MO| integrals
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.. c:function:: get_mo_map_size
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.. code:: text
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integer*8 function get_mo_map_size()
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File: :file:`map_integrals.irp.f`
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Return the number of elements in the MO map
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.. c:function:: get_mo_two_e_integrals
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.. code:: text
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subroutine get_mo_two_e_integrals(j,k,l,sze,out_val,map)
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File: :file:`map_integrals.irp.f`
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Returns multiple integrals <ij|kl> in the MO basis, all i for j,k,l fixed.
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.. c:function:: get_mo_two_e_integrals_coulomb_ii
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.. code:: text
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subroutine get_mo_two_e_integrals_coulomb_ii(k,l,sze,out_val,map)
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File: :file:`map_integrals.irp.f`
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Returns multiple integrals <ki|li> k(1)i(2) 1/r12 l(1)i(2) :: out_val(i1) for k,l fixed.
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.. c:function:: get_mo_two_e_integrals_exch_ii
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.. code:: text
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subroutine get_mo_two_e_integrals_exch_ii(k,l,sze,out_val,map)
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File: :file:`map_integrals.irp.f`
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Returns multiple integrals <ki|il> k(1)i(2) 1/r12 i(1)l(2) :: out_val(i1) for k,l fixed.
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.. c:function:: get_mo_two_e_integrals_i1j1
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.. code:: text
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subroutine get_mo_two_e_integrals_i1j1(k,l,sze,out_array,map)
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File: :file:`map_integrals.irp.f`
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Returns multiple integrals <ik|jl> in the MO basis, all i(1)j(1) 1/r12 k(2)l(2) i, j for k,l fixed.
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.. c:function:: get_mo_two_e_integrals_ij
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.. code:: text
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subroutine get_mo_two_e_integrals_ij(k,l,sze,out_array,map)
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File: :file:`map_integrals.irp.f`
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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.
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.. c:function:: get_two_e_integral
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.. code:: text
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double precision function get_two_e_integral(i,j,k,l,map)
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File: :file:`map_integrals.irp.f`
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Returns one integral <ij|kl> in the MO basis
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.. c:function:: load_mo_integrals
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.. code:: text
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integer function load_mo_integrals(filename)
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File: :file:`map_integrals.irp.f`
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Read from disk the |MO| integrals
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.. c:function:: mo_two_e_integral
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.. code:: text
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double precision function mo_two_e_integral(i,j,k,l)
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File: :file:`map_integrals.irp.f`
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Returns one integral <ij|kl> in the MO basis
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.. c:function:: mo_two_e_integrals_index
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.. code:: text
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subroutine mo_two_e_integrals_index(i,j,k,l,i1)
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File: :file:`mo_bi_integrals.irp.f`
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Computes an unique index for i,j,k,l integrals
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