.. _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 : = <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) = = (ii|jj) with the erf interaction int_erf_3_index_exc(i,j) = = (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) = = (ii|jj) with the erf interaction int_erf_3_index_exc(i,j) = = (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`