mo_two_e_ints

Here, all two-electron integrals (\(1/r_{12}\)) 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_two_e_integral(i,j,k,l,ao_integrals_map) function, and to fetch an MO integral, use get_two_e_integral(i,j,k,l,mo_integrals_map) or mo_two_e_integral(i,j,k,l).

The conventions are:

• For AO integrals : (ik|jl) = (11|22)

• For MO integrals : <ij|kl> = <12|12>

EZFIO parameters

io_mo_two_e_integrals

Read/Write MO integrals from/to disk [ Write | Read | None ]

Default: None

mo_integrals_threshold

If | <ij|kl> | < mo_integrals_threshold then <ij|kl> is zero

Default: 1.e-15

Providers

banned_excitation

File : mo_two_e_ints/map_integrals.irp.f

logical, allocatable    :: banned_excitation    (mo_num,mo_num)

If true, the excitation is banned in the selection. Useful with local MOs.

Needs:

mo_integrals_map

mo_num

Needed by:

big_array_coulomb_integrals

core_fock_operator

mo_two_e_integrals_jj

big_array_coulomb_integrals

File : mo_two_e_ints/integrals_3_index.irp.f

double precision, allocatable   :: big_array_coulomb_integrals  (mo_num,mo_num,mo_num)
double precision, allocatable   :: big_array_exchange_integrals (mo_num,mo_num,mo_num)

big_array_coulomb_integrals(i,j) = <ij|ij> = (ii|jj)

big_array_exchange_integrals(i,j) = <ij|ji> = (ij|ij)

Needs:

banned_excitation mo_integrals_cache

mo_integrals_cache_min mo_integrals_map

mo_num mo_two_e_integrals_in_map

Needed by:

h_matrix_all_dets

h_matrix_cas

big_array_exchange_integrals

File : mo_two_e_ints/integrals_3_index.irp.f

double precision, allocatable   :: big_array_coulomb_integrals  (mo_num,mo_num,mo_num)
double precision, allocatable   :: big_array_exchange_integrals (mo_num,mo_num,mo_num)

big_array_coulomb_integrals(i,j) = <ij|ij> = (ii|jj)

big_array_exchange_integrals(i,j) = <ij|ji> = (ij|ij)

Needs:

banned_excitation mo_integrals_cache

mo_integrals_cache_min mo_integrals_map

mo_num mo_two_e_integrals_in_map

Needed by:

h_matrix_all_dets

h_matrix_cas

core_energy

File : mo_two_e_ints/core_quantities.irp.f

double precision        :: core_energy

energy from the core : contains all core-core contributions

Needs:

list_core mo_one_e_integrals

mo_two_e_integrals_jj n_core_orb

nuclear_repulsion

core_fock_operator

File : mo_two_e_ints/core_quantities.irp.f

double precision, allocatable   :: core_fock_operator   (mo_num,mo_num)

this is the contribution to the Fock operator from the core electrons

Needs:

banned_excitation list_act list_core mo_integrals_cache

mo_integrals_cache_min mo_integrals_map mo_num

mo_two_e_integrals_in_map n_act_orb n_core_orb

insert_into_mo_integrals_map:

File : mo_two_e_ints/map_integrals.irp.f

  subroutine insert_into_mo_integrals_map(n_integrals,                 &
buffer_i, buffer_values, thr)

Create new entry into MO map, or accumulate in an existing entry

Needs:

mo_integrals_map

Called by:

add_integrals_to_map()

add_integrals_to_map_no_exit_34()

add_integrals_to_map_three_indices()

Calls:

map_update()

mo_coef_novirt

File : mo_two_e_ints/four_idx_novvvv.irp.f

double precision, allocatable   :: mo_coef_novirt       (ao_num,n_core_inact_act_orb)

MO coefficients without virtual MOs

Needs:

ao_num list_core_inact_act

mo_coef

n_core_inact_act_orb

mo_integrals_cache

File : mo_two_e_ints/map_integrals.irp.f

double precision, allocatable   :: mo_integrals_cache   (0_8:128_8*128_8*128_8*128_8)

Cache of MO integrals for fast access

Needs:

mo_integrals_cache_min

mo_integrals_map

mo_two_e_integrals_in_map

Needed by:

big_array_coulomb_integrals

core_fock_operator

mo_two_e_integrals_jj

mo_integrals_cache_max

File : mo_two_e_ints/map_integrals.irp.f

integer*4       :: mo_integrals_cache_min
integer*4       :: mo_integrals_cache_max
integer*8       :: mo_integrals_cache_min_8
integer*8       :: mo_integrals_cache_max_8

Min and max values of the MOs for which the integrals are in the cache

Needs:

elec_alpha_num

mo_num

Needed by:

big_array_coulomb_integrals core_fock_operator

mo_integrals_cache

mo_two_e_integrals_jj

mo_integrals_cache_max_8

File : mo_two_e_ints/map_integrals.irp.f

integer*4       :: mo_integrals_cache_min
integer*4       :: mo_integrals_cache_max
integer*8       :: mo_integrals_cache_min_8
integer*8       :: mo_integrals_cache_max_8

Min and max values of the MOs for which the integrals are in the cache

Needs:

elec_alpha_num

mo_num

Needed by:

big_array_coulomb_integrals core_fock_operator

mo_integrals_cache

mo_two_e_integrals_jj

mo_integrals_cache_min

File : mo_two_e_ints/map_integrals.irp.f

integer*4       :: mo_integrals_cache_min
integer*4       :: mo_integrals_cache_max
integer*8       :: mo_integrals_cache_min_8
integer*8       :: mo_integrals_cache_max_8

Min and max values of the MOs for which the integrals are in the cache

Needs:

elec_alpha_num

mo_num

Needed by:

big_array_coulomb_integrals core_fock_operator

mo_integrals_cache

mo_two_e_integrals_jj

mo_integrals_cache_min_8

File : mo_two_e_ints/map_integrals.irp.f

integer*4       :: mo_integrals_cache_min
integer*4       :: mo_integrals_cache_max
integer*8       :: mo_integrals_cache_min_8
integer*8       :: mo_integrals_cache_max_8

Min and max values of the MOs for which the integrals are in the cache

Needs:

elec_alpha_num

mo_num

Needed by:

big_array_coulomb_integrals core_fock_operator

mo_integrals_cache

mo_two_e_integrals_jj

mo_integrals_map

File : mo_two_e_ints/map_integrals.irp.f

type(map_type)  :: mo_integrals_map

MO integrals

Needs:

mo_num

Needed by:

banned_excitation big_array_coulomb_integrals core_fock_operator fock_operator_closed_shell_ref_bitmask

fock_wee_closed_shell h_matrix_all_dets h_matrix_cas

mo_integrals_cache mo_two_e_integrals_in_map mo_two_e_integrals_jj

mo_two_e_integral_jj_from_ao

File : mo_two_e_ints/mo_bi_integrals.irp.f

double precision, allocatable   :: mo_two_e_integral_jj_from_ao (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_jj_exchange_from_ao       (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_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:

ao_integrals_map ao_integrals_threshold ao_num

ao_two_e_integrals_in_map do_direct_integrals mo_coef

mo_coef_transp mo_num

mo_two_e_integrals_in_map

File : mo_two_e_ints/mo_bi_integrals.irp.f

logical :: mo_two_e_integrals_in_map

If True, the map of MO two-electron integrals is provided

Needs:

ao_integrals_map ao_num ao_two_e_integrals_in_map ezfio_filename full_ijkl_bitmask_4 list_core_inact_act

mo_class mo_coef mo_coef_transp mo_integrals_map mo_integrals_threshold mo_num

mpi_master n_core_inact_act_orb n_int no_vvvv_integrals read_mo_two_e_integrals

Needed by:

act_2_rdm_aa_mo act_2_rdm_ab_mo act_2_rdm_bb_mo act_2_rdm_spin_trace_mo big_array_coulomb_integrals

ci_electronic_energy core_fock_operator fock_operator_closed_shell_ref_bitmask fock_wee_closed_shell

h_matrix_all_dets h_matrix_cas mo_integrals_cache mo_two_e_integrals_jj

mo_two_e_integrals_jj

File : mo_two_e_ints/mo_bi_integrals.irp.f

double precision, allocatable   :: mo_two_e_integrals_jj        (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_jj_exchange       (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_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:

banned_excitation mo_integrals_cache

mo_integrals_cache_min mo_integrals_map

mo_num mo_two_e_integrals_in_map

Needed by:

core_energy

ref_bitmask_energy

mo_two_e_integrals_jj_anti

File : mo_two_e_ints/mo_bi_integrals.irp.f

double precision, allocatable   :: mo_two_e_integrals_jj        (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_jj_exchange       (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_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:

banned_excitation mo_integrals_cache

mo_integrals_cache_min mo_integrals_map

mo_num mo_two_e_integrals_in_map

Needed by:

core_energy

ref_bitmask_energy

mo_two_e_integrals_jj_anti_from_ao

File : mo_two_e_ints/mo_bi_integrals.irp.f

double precision, allocatable   :: mo_two_e_integral_jj_from_ao (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_jj_exchange_from_ao       (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_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:

ao_integrals_map ao_integrals_threshold ao_num

ao_two_e_integrals_in_map do_direct_integrals mo_coef

mo_coef_transp mo_num

mo_two_e_integrals_jj_exchange

File : mo_two_e_ints/mo_bi_integrals.irp.f

double precision, allocatable   :: mo_two_e_integrals_jj        (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_jj_exchange       (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_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:

banned_excitation mo_integrals_cache

mo_integrals_cache_min mo_integrals_map

mo_num mo_two_e_integrals_in_map

Needed by:

core_energy

ref_bitmask_energy

mo_two_e_integrals_jj_exchange_from_ao

File : mo_two_e_ints/mo_bi_integrals.irp.f

double precision, allocatable   :: mo_two_e_integral_jj_from_ao (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_jj_exchange_from_ao       (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_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:

ao_integrals_map ao_integrals_threshold ao_num

ao_two_e_integrals_in_map do_direct_integrals mo_coef

mo_coef_transp mo_num

mo_two_e_integrals_vv_anti_from_ao

File : mo_two_e_ints/mo_bi_integrals.irp.f

double precision, allocatable   :: mo_two_e_integrals_vv_from_ao        (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_vv_exchange_from_ao       (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_vv_anti_from_ao   (mo_num,mo_num)

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

Needs:

ao_integrals_map ao_integrals_threshold ao_num ao_two_e_integrals_in_map

do_direct_integrals list_virt mo_coef

mo_coef_transp mo_num n_virt_orb

mo_two_e_integrals_vv_exchange_from_ao

File : mo_two_e_ints/mo_bi_integrals.irp.f

double precision, allocatable   :: mo_two_e_integrals_vv_from_ao        (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_vv_exchange_from_ao       (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_vv_anti_from_ao   (mo_num,mo_num)

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

Needs:

ao_integrals_map ao_integrals_threshold ao_num ao_two_e_integrals_in_map

do_direct_integrals list_virt mo_coef

mo_coef_transp mo_num n_virt_orb

mo_two_e_integrals_vv_from_ao

File : mo_two_e_ints/mo_bi_integrals.irp.f

double precision, allocatable   :: mo_two_e_integrals_vv_from_ao        (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_vv_exchange_from_ao       (mo_num,mo_num)
double precision, allocatable   :: mo_two_e_integrals_vv_anti_from_ao   (mo_num,mo_num)

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

Needs:

ao_integrals_map ao_integrals_threshold ao_num ao_two_e_integrals_in_map

do_direct_integrals list_virt mo_coef

mo_coef_transp mo_num n_virt_orb

Subroutines / functions

add_integrals_to_map:

File : mo_two_e_ints/mo_bi_integrals.irp.f

subroutine add_integrals_to_map(mask_ijkl)

Adds integrals to tha MO map according to some bitmask

Needs:

ao_num ao_two_e_integrals_in_map mo_coef

mo_coef_transp mo_integrals_map mo_integrals_threshold

mo_num n_int

Called by:

four_idx_novvvv2()

mo_two_e_integrals_in_map

Calls:

bitstring_to_list() cpu_time() get_ao_two_e_integrals()

insert_into_mo_integrals_map() map_merge()

mo_two_e_integrals_index() wall_time()

add_integrals_to_map_no_exit_34:

File : mo_two_e_ints/mo_bi_integrals.irp.f

subroutine add_integrals_to_map_no_exit_34(mask_ijkl)

Adds integrals to tha MO map according to some bitmask

Needs:

ao_num ao_two_e_integrals_in_map mo_coef

mo_coef_transp mo_integrals_map mo_integrals_threshold

mo_num n_int

Calls:

bitstring_to_list() cpu_time() get_ao_two_e_integrals()

insert_into_mo_integrals_map() map_merge()

mo_two_e_integrals_index() wall_time()

add_integrals_to_map_three_indices:

File : mo_two_e_ints/mo_bi_integrals.irp.f

subroutine add_integrals_to_map_three_indices(mask_ijk)

Adds integrals to tha MO map according to some bitmask

Needs:

ao_num ao_two_e_integrals_in_map mo_coef

mo_coef_transp mo_integrals_map mo_integrals_threshold

mo_num n_int

Calls:

bitstring_to_list() cpu_time() get_ao_two_e_integrals()

insert_into_mo_integrals_map() map_merge()

mo_two_e_integrals_index() wall_time()

ao_to_mo_novirt:

File : mo_two_e_ints/four_idx_novvvv.irp.f

subroutine ao_to_mo_novirt(A_ao,LDA_ao,A_mo,LDA_mo)

Transform A from the AO basis to the MO basis excluding virtuals

$C^dagger.A_{ao}.C$

Needs:

ao_num

mo_coef_novirt

n_core_inact_act_orb

Called by:

four_idx_novvvv()

Calls:

dgemm()

clear_mo_map:

File : mo_two_e_ints/mo_bi_integrals.irp.f

subroutine clear_mo_map

Frees the memory of the MO map

Needs:

mo_integrals_map

Calls:

map_deinit()

dump_mo_integrals:

File : mo_two_e_ints/map_integrals.irp.f

subroutine dump_mo_integrals(filename)

Save to disk the MO integrals

Needs:

mo_integrals_map

mpi_master

Calls:

ezfio_set_work_empty()

four_idx_novvvv:

File : mo_two_e_ints/four_idx_novvvv.irp.f

subroutine four_idx_novvvv

Retransform MO integrals for next CAS-SCF step

Needs:

ao_integrals_map ao_num list_core_inact_act

mo_integrals_map mo_integrals_threshold

mo_num n_core_inact_act_orb

Called by:

mo_two_e_integrals_in_map

Calls:

ao_to_mo() ao_to_mo_novirt() map_append()

map_shrink() map_sort()

map_unique() two_e_integrals_index()

four_idx_novvvv2:

File : mo_two_e_ints/four_idx_novvvv.irp.f

subroutine four_idx_novvvv2

Needs:

core_inact_act_bitmask_4 full_ijkl_bitmask_4

n_int

virt_bitmask

Calls:

add_integrals_to_map()

get_mo_map_size:

File : mo_two_e_ints/map_integrals.irp.f

integer*8 function get_mo_map_size()

Return the number of elements in the MO map

Needs:

mo_integrals_map

get_mo_two_e_integrals:

File : mo_two_e_ints/map_integrals.irp.f

subroutine get_mo_two_e_integrals(j,k,l,sze,out_val,map)

Returns multiple integrals <ij|kl> in the MO basis, all i for j,k,l fixed.

Needs:

banned_excitation mo_integrals_cache

mo_integrals_cache_min

mo_two_e_integrals_in_map

Called by:

get_mo_two_e_integrals_i1j1()

get_mo_two_e_integrals_ij()

Calls:

map_get()

get_mo_two_e_integrals_coulomb_ii:

File : mo_two_e_ints/map_integrals.irp.f

subroutine get_mo_two_e_integrals_coulomb_ii(k,l,sze,out_val,map)

Returns multiple integrals <ki|li> k(1)i(2) 1/r12 l(1)i(2) :: out_val(i1) for k,l fixed.

Needs:

mo_two_e_integrals_in_map

Called by:

fock_operator_closed_shell_ref_bitmask

fock_wee_closed_shell

get_mo_two_e_integrals_exch_ii:

File : mo_two_e_ints/map_integrals.irp.f

subroutine get_mo_two_e_integrals_exch_ii(k,l,sze,out_val,map)

Returns multiple integrals <ki|il> k(1)i(2) 1/r12 i(1)l(2) :: out_val(i1) for k,l fixed.

Needs:

mo_two_e_integrals_in_map

Called by:

fock_operator_closed_shell_ref_bitmask

fock_wee_closed_shell

get_mo_two_e_integrals_i1j1:

File : mo_two_e_ints/map_integrals.irp.f

subroutine get_mo_two_e_integrals_i1j1(k,l,sze,out_array,map)

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.

Needs:

mo_two_e_integrals_in_map

Calls:

get_mo_two_e_integrals()

get_mo_two_e_integrals_ij:

File : mo_two_e_ints/map_integrals.irp.f

subroutine get_mo_two_e_integrals_ij(k,l,sze,out_array,map)

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.

Calls:

get_mo_two_e_integrals()

get_two_e_integral:

File : mo_two_e_ints/map_integrals.irp.f

double precision function get_two_e_integral(i,j,k,l,map)

Returns one integral <ij|kl> in the MO basis

Needs:

banned_excitation mo_integrals_cache

mo_integrals_cache_min

mo_two_e_integrals_in_map

Calls:

map_get()

two_e_integrals_index()

load_mo_integrals:

File : mo_two_e_ints/map_integrals.irp.f

integer function load_mo_integrals(filename)

Read from disk the MO integrals

Needs:

mo_integrals_map

Calls:

cache_map_reallocate()

map_deinit()

map_sort()

mo_two_e_integral:

File : mo_two_e_ints/map_integrals.irp.f

double precision function mo_two_e_integral(i,j,k,l)

Returns one integral <ij|kl> in the MO basis

Needs:

mo_integrals_cache

mo_integrals_map

mo_two_e_integrals_in_map

mo_two_e_integrals_index:

File : mo_two_e_ints/mo_bi_integrals.irp.f

subroutine mo_two_e_integrals_index(i,j,k,l,i1)

Computes an unique index for i,j,k,l integrals

Called by:

add_integrals_to_map()

add_integrals_to_map_no_exit_34()

add_integrals_to_map_three_indices()