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docs/source/modules/ao_basis.rst
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docs/source/modules/ao_basis.rst
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docs/source/modules/ao_one_e_ints.rst
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docs/source/modules/ao_one_e_ints.rst
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docs/source/modules/ao_two_e_erf_ints.rst
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docs/source/modules/ao_two_e_erf_ints.rst
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.. _module_ao_two_e_erf_ints:
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.. program:: ao_two_e_erf_ints
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.. default-role:: option
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======================
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ao_two_e_erf_ints
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======================
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Here, all two-electron integrals (:math:`erf(\mu r_{12})/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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The main parameter of this module is :option:`ao_two_e_erf_ints mu_erf` which is the range-separation parameter.
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To fetch an |AO| integral, use the
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`get_ao_two_e_integral_erf(i,j,k,l,ao_integrals_erf_map)` function.
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The conventions are:
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* For |AO| integrals : (ij|kl) = (11|22) = <ik|jl> = <12|12>
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EZFIO parameters
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----------------
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.. option:: io_ao_two_e_integrals_erf
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Read/Write |AO| integrals with the long range interaction from/to disk [ Write | Read | None ]
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Default: None
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.. option:: mu_erf
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cutting of the interaction in the range separated model
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Default: 0.5
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Providers
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---------
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.. c:var:: ao_integrals_erf_cache
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File : :file:`ao_two_e_erf_ints/map_integrals_erf.irp.f`
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.. code:: fortran
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double precision, allocatable :: ao_integrals_erf_cache (0:64*64*64*64)
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Cache of |AO| integrals for fast access
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_integrals_erf_cache_min`
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* :c:data:`ao_integrals_erf_map`
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* :c:data:`ao_two_e_integrals_erf_in_map`
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.. c:var:: ao_integrals_erf_cache_max
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File : :file:`ao_two_e_erf_ints/map_integrals_erf.irp.f`
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.. code:: fortran
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integer :: ao_integrals_erf_cache_min
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integer :: ao_integrals_erf_cache_max
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Min and max values of the AOs for which the integrals are in the cache
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`ao_integrals_erf_cache`
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.. c:var:: ao_integrals_erf_cache_min
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File : :file:`ao_two_e_erf_ints/map_integrals_erf.irp.f`
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.. code:: fortran
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integer :: ao_integrals_erf_cache_min
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integer :: ao_integrals_erf_cache_max
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Min and max values of the AOs for which the integrals are in the cache
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`ao_integrals_erf_cache`
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.. c:var:: ao_integrals_erf_map
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File : :file:`ao_two_e_erf_ints/map_integrals_erf.irp.f`
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.. code:: fortran
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type(map_type) :: ao_integrals_erf_map
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|AO| integrals
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`ao_integrals_erf_cache`
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* :c:data:`ao_two_e_integrals_erf_in_map`
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* :c:data:`mo_two_e_int_erf_jj_from_ao`
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.. c:var:: ao_two_e_integral_erf_schwartz
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File : :file:`ao_two_e_erf_ints/providers_ao_erf.irp.f`
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.. code:: fortran
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double precision, allocatable :: ao_two_e_integral_erf_schwartz (ao_num,ao_num)
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Needed to compute Schwartz inequalities
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_coef_normalized_ordered_transp`
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* :c:data:`ao_expo_ordered_transp`
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* :c:data:`ao_nucl`
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* :c:data:`ao_num`
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* :c:data:`ao_power`
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* :c:data:`ao_prim_num`
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* :c:data:`n_pt_max_integrals`
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* :c:data:`nucl_coord`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`mo_two_e_int_erf_jj_from_ao`
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.. c:var:: ao_two_e_integrals_erf_in_map
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File : :file:`ao_two_e_erf_ints/providers_ao_erf.irp.f`
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.. code:: fortran
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logical :: ao_two_e_integrals_erf_in_map
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Map of Atomic integrals
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i(r1) j(r2) 1/r12 k(r1) l(r2)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_coef_normalized_ordered_transp`
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* :c:data:`ao_expo_ordered_transp`
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* :c:data:`ao_integrals_erf_map`
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* :c:data:`ao_nucl`
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* :c:data:`ao_num`
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* :c:data:`ao_power`
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* :c:data:`ao_prim_num`
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* :c:data:`ezfio_filename`
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* :c:data:`io_ao_two_e_integrals_erf`
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* :c:data:`n_pt_max_integrals`
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* :c:data:`nproc`
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* :c:data:`nucl_coord`
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* :c:data:`read_ao_two_e_integrals_erf`
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* :c:data:`zmq_context`
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* :c:data:`zmq_socket_pull_tcp_address`
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* :c:data:`zmq_state`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`ao_integrals_erf_cache`
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* :c:data:`mo_two_e_int_erf_jj_from_ao`
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* :c:data:`mo_two_e_integrals_erf_in_map`
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.. c:function:: general_primitive_integral_erf:
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File : :file:`ao_two_e_erf_ints/two_e_integrals_erf.irp.f`
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.. code:: fortran
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double precision function general_primitive_integral_erf(dim, &
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P_new,P_center,fact_p,p,p_inv,iorder_p, &
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Q_new,Q_center,fact_q,q,q_inv,iorder_q)
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Computes the integral <pq|rs> where p,q,r,s are Gaussian primitives
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`mu_erf`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`add_poly_multiply`
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* :c:func:`give_polynom_mult_center_x`
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* :c:func:`multiply_poly`
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Subroutines / functions
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-----------------------
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.. c:function:: ao_two_e_integral_erf:
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File : :file:`ao_two_e_erf_ints/two_e_integrals_erf.irp.f`
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.. code:: fortran
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double precision function ao_two_e_integral_erf(i,j,k,l)
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integral of the AO basis <ik|jl> or (ij|kl)
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i(r1) j(r1) 1/r12 k(r2) l(r2)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`n_pt_max_integrals`
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* :c:data:`ao_coef_normalized_ordered_transp`
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* :c:data:`ao_power`
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* :c:data:`ao_expo_ordered_transp`
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* :c:data:`ao_prim_num`
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* :c:data:`ao_nucl`
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* :c:data:`nucl_coord`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`give_explicit_poly_and_gaussian`
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.. c:function:: ao_two_e_integral_schwartz_accel_erf:
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File : :file:`ao_two_e_erf_ints/two_e_integrals_erf.irp.f`
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.. code:: fortran
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double precision function ao_two_e_integral_schwartz_accel_erf(i,j,k,l)
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integral of the AO basis <ik|jl> or (ij|kl)
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i(r1) j(r1) 1/r12 k(r2) l(r2)
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`n_pt_max_integrals`
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* :c:data:`ao_integrals_threshold`
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* :c:data:`ao_coef_normalized_ordered_transp`
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* :c:data:`ao_power`
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* :c:data:`ao_expo_ordered_transp`
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* :c:data:`ao_prim_num`
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* :c:data:`ao_nucl`
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* :c:data:`nucl_coord`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`give_explicit_poly_and_gaussian`
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.. c:function:: ao_two_e_integrals_erf_in_map_collector:
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File : :file:`ao_two_e_erf_ints/integrals_erf_in_map_slave.irp.f`
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.. code:: fortran
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subroutine ao_two_e_integrals_erf_in_map_collector(zmq_socket_pull)
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Collects results from the AO integral calculation
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_integrals_erf_map`
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* :c:data:`ao_num`
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Called by:
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.. hlist::
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:columns: 3
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* :c:data:`ao_two_e_integrals_erf_in_map`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`end_zmq_to_qp_run_socket`
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* :c:func:`insert_into_ao_integrals_erf_map`
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.. c:function:: ao_two_e_integrals_erf_in_map_slave:
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File : :file:`ao_two_e_erf_ints/integrals_erf_in_map_slave.irp.f`
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.. code:: fortran
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subroutine ao_two_e_integrals_erf_in_map_slave(thread,iproc)
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Computes a buffer of integrals
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Needs:
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|
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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Called by:
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.. hlist::
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:columns: 3
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* :c:func:`ao_two_e_integrals_erf_in_map_slave_inproc`
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* :c:func:`ao_two_e_integrals_erf_in_map_slave_tcp`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`compute_ao_integrals_erf_jl`
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* :c:func:`end_zmq_push_socket`
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* :c:func:`end_zmq_to_qp_run_socket`
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* :c:func:`push_integrals`
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.. c:function:: ao_two_e_integrals_erf_in_map_slave_inproc:
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File : :file:`ao_two_e_erf_ints/integrals_erf_in_map_slave.irp.f`
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.. code:: fortran
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subroutine ao_two_e_integrals_erf_in_map_slave_inproc(i)
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Computes a buffer of integrals. i is the ID of the current thread.
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||||
Called by:
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||||
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.. hlist::
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:columns: 3
|
||||
|
||||
* :c:data:`ao_two_e_integrals_erf_in_map`
|
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|
||||
Calls:
|
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|
||||
.. hlist::
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:columns: 3
|
||||
|
||||
* :c:func:`ao_two_e_integrals_erf_in_map_slave`
|
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|
||||
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||||
.. c:function:: ao_two_e_integrals_erf_in_map_slave_tcp:
|
||||
|
||||
|
||||
File : :file:`ao_two_e_erf_ints/integrals_erf_in_map_slave.irp.f`
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||||
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||||
.. code:: fortran
|
||||
|
||||
subroutine ao_two_e_integrals_erf_in_map_slave_tcp(i)
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Computes a buffer of integrals. i is the ID of the current thread.
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||||
|
||||
Calls:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:func:`ao_two_e_integrals_erf_in_map_slave`
|
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|
||||
|
||||
.. c:function:: clear_ao_erf_map:
|
||||
|
||||
|
||||
File : :file:`ao_two_e_erf_ints/map_integrals_erf.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
subroutine clear_ao_erf_map
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|
||||
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||||
Frees the memory of the |AO| map
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`ao_integrals_erf_map`
|
||||
|
||||
Calls:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:func:`map_deinit`
|
||||
|
||||
|
||||
.. c:function:: compute_ao_integrals_erf_jl:
|
||||
|
||||
|
||||
File : :file:`ao_two_e_erf_ints/two_e_integrals_erf.irp.f`
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||||
|
||||
.. code:: fortran
|
||||
|
||||
subroutine compute_ao_integrals_erf_jl(j,l,n_integrals,buffer_i,buffer_value)
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||||
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||||
|
||||
Parallel client for AO integrals
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`ao_overlap_abs`
|
||||
* :c:data:`ao_num`
|
||||
* :c:data:`ao_integrals_threshold`
|
||||
* :c:data:`ao_two_e_integral_erf_schwartz`
|
||||
|
||||
Called by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:func:`ao_two_e_integrals_erf_in_map_slave`
|
||||
|
||||
Calls:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:func:`two_e_integrals_index`
|
||||
|
||||
|
||||
.. c:function:: compute_ao_two_e_integrals_erf:
|
||||
|
||||
|
||||
File : :file:`ao_two_e_erf_ints/two_e_integrals_erf.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
subroutine compute_ao_two_e_integrals_erf(j,k,l,sze,buffer_value)
|
||||
|
||||
|
||||
Compute AO 1/r12 integrals for all i and fixed j,k,l
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`ao_overlap_abs`
|
||||
* :c:data:`ao_num`
|
||||
* :c:data:`ao_two_e_integral_erf_schwartz`
|
||||
|
||||
Called by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`mo_two_e_int_erf_jj_from_ao`
|
||||
|
||||
|
||||
.. c:function:: dump_ao_integrals_erf:
|
||||
|
||||
|
||||
File : :file:`ao_two_e_erf_ints/map_integrals_erf.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
subroutine dump_ao_integrals_erf(filename)
|
||||
|
||||
|
||||
Save to disk the |AO| erf integrals
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`ao_integrals_erf_map`
|
||||
|
||||
Calls:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:func:`ezfio_set_work_empty`
|
||||
|
||||
|
||||
.. c:function:: eri_erf:
|
||||
|
||||
|
||||
File : :file:`ao_two_e_erf_ints/two_e_integrals_erf.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision function ERI_erf(alpha,beta,delta,gama,a_x,b_x,c_x,d_x,a_y,b_y,c_y,d_y,a_z,b_z,c_z,d_z)
|
||||
|
||||
|
||||
Atomic primtive two-electron integral between the 4 primitives :
|
||||
|
||||
* primitive 1 : $x_1^{a_x} y_1^{a_y} z_1^{a_z} \exp(-\alpha * r1^2)$
|
||||
* primitive 2 : $x_1^{b_x} y_1^{b_y} z_1^{b_z} \exp(- \beta * r1^2)$
|
||||
* primitive 3 : $x_2^{c_x} y_2^{c_y} z_2^{c_z} \exp(-\delta * r2^2)$
|
||||
* primitive 4 : $x_2^{d_x} y_2^{d_y} z_2^{d_z} \exp(-\gamma * r2^2)$
|
||||
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`mu_erf`
|
||||
|
||||
Calls:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:func:`integrale_new_erf`
|
||||
|
||||
|
||||
.. c:function:: get_ao_erf_map_size:
|
||||
|
||||
|
||||
File : :file:`ao_two_e_erf_ints/map_integrals_erf.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
function get_ao_erf_map_size()
|
||||
|
||||
|
||||
Returns the number of elements in the |AO| map
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`ao_integrals_erf_map`
|
||||
|
||||
|
||||
.. c:function:: get_ao_two_e_integral_erf:
|
||||
|
||||
|
||||
File : :file:`ao_two_e_erf_ints/map_integrals_erf.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision function get_ao_two_e_integral_erf(i,j,k,l,map) result(result)
|
||||
|
||||
|
||||
Gets one |AO| two-electron integral from the |AO| map
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`ao_integrals_erf_cache_min`
|
||||
* :c:data:`ao_overlap_abs`
|
||||
* :c:data:`ao_integrals_threshold`
|
||||
* :c:data:`ao_integrals_erf_cache`
|
||||
* :c:data:`ao_two_e_integral_erf_schwartz`
|
||||
* :c:data:`ao_two_e_integrals_erf_in_map`
|
||||
|
||||
Calls:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:func:`map_get`
|
||||
* :c:func:`two_e_integrals_index`
|
||||
|
||||
|
||||
.. c:function:: get_ao_two_e_integrals_erf:
|
||||
|
||||
|
||||
File : :file:`ao_two_e_erf_ints/map_integrals_erf.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
subroutine get_ao_two_e_integrals_erf(j,k,l,sze,out_val)
|
||||
|
||||
|
||||
Gets multiple |AO| two-electron integral from the |AO| map .
|
||||
All i are retrieved for j,k,l fixed.
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`ao_integrals_erf_map`
|
||||
* :c:data:`ao_overlap_abs`
|
||||
* :c:data:`ao_integrals_threshold`
|
||||
* :c:data:`ao_two_e_integrals_erf_in_map`
|
||||
|
||||
Called by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:func:`add_integrals_to_map_erf`
|
||||
|
||||
|
||||
.. c:function:: get_ao_two_e_integrals_erf_non_zero:
|
||||
|
||||
|
||||
File : :file:`ao_two_e_erf_ints/map_integrals_erf.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
subroutine get_ao_two_e_integrals_erf_non_zero(j,k,l,sze,out_val,out_val_index,non_zero_int)
|
||||
|
||||
|
||||
Gets multiple |AO| two-electron integrals from the |AO| map .
|
||||
All non-zero i are retrieved for j,k,l fixed.
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`ao_integrals_erf_map`
|
||||
* :c:data:`ao_overlap_abs`
|
||||
* :c:data:`ao_integrals_threshold`
|
||||
* :c:data:`ao_two_e_integral_erf_schwartz`
|
||||
* :c:data:`ao_two_e_integrals_erf_in_map`
|
||||
|
||||
Called by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`mo_two_e_int_erf_jj_from_ao`
|
||||
|
||||
Calls:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:func:`map_get`
|
||||
* :c:func:`two_e_integrals_index`
|
||||
|
||||
|
||||
.. c:function:: insert_into_ao_integrals_erf_map:
|
||||
|
||||
|
||||
File : :file:`ao_two_e_erf_ints/map_integrals_erf.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
subroutine insert_into_ao_integrals_erf_map(n_integrals,buffer_i, buffer_values)
|
||||
|
||||
|
||||
Create new entry into |AO| map
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`ao_integrals_erf_map`
|
||||
|
||||
Called by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:func:`ao_two_e_integrals_erf_in_map_collector`
|
||||
|
||||
Calls:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:func:`map_append`
|
||||
|
||||
|
||||
.. c:function:: integrale_new_erf:
|
||||
|
||||
|
||||
File : :file:`ao_two_e_erf_ints/two_e_integrals_erf.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
subroutine integrale_new_erf(I_f,a_x,b_x,c_x,d_x,a_y,b_y,c_y,d_y,a_z,b_z,c_z,d_z,p,q,n_pt)
|
||||
|
||||
|
||||
Calculate the integral of the polynomial :
|
||||
|
||||
$I_x1(a_x+b_x, c_x+d_x,p,q) \, I_x1(a_y+b_y, c_y+d_y,p,q) \, I_x1(a_z+b_z, c_z+d_z,p,q)$
|
||||
|
||||
between $( 0 ; 1)$
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`mu_erf`
|
||||
* :c:data:`n_pt_max_integrals`
|
||||
* :c:data:`gauleg_t2`
|
||||
|
||||
Called by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:func:`eri_erf`
|
||||
|
||||
Calls:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:func:`i_x1_new`
|
||||
|
||||
|
||||
.. c:function:: load_ao_integrals_erf:
|
||||
|
||||
|
||||
File : :file:`ao_two_e_erf_ints/map_integrals_erf.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
integer function load_ao_integrals_erf(filename)
|
||||
|
||||
|
||||
Read from disk the |AO| erf integrals
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`ao_integrals_erf_map`
|
||||
|
||||
Calls:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:func:`cache_map_reallocate`
|
||||
* :c:func:`map_deinit`
|
||||
* :c:func:`map_sort`
|
||||
|
||||
|
||||
.. c:function:: save_erf_two_e_integrals_ao:
|
||||
|
||||
|
||||
File : :file:`ao_two_e_erf_ints/routines_save_integrals_erf.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
subroutine save_erf_two_e_integrals_ao
|
||||
|
||||
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`ao_integrals_erf_map`
|
||||
* :c:data:`ezfio_filename`
|
||||
* :c:data:`ao_two_e_integrals_erf_in_map`
|
||||
|
||||
Called by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:func:`routine`
|
||||
|
||||
Calls:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:func:`ezfio_set_ao_two_e_erf_ints_io_ao_two_e_integrals_erf`
|
||||
* :c:func:`ezfio_set_work_empty`
|
||||
* :c:func:`map_save_to_disk`
|
||||
|
||||
|
||||
.. c:function:: save_erf_two_e_ints_ao_into_ints_ao:
|
||||
|
||||
|
||||
File : :file:`ao_two_e_erf_ints/routines_save_integrals_erf.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
subroutine save_erf_two_e_ints_ao_into_ints_ao
|
||||
|
||||
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`ao_integrals_erf_map`
|
||||
* :c:data:`ezfio_filename`
|
||||
* :c:data:`ao_two_e_integrals_erf_in_map`
|
||||
|
||||
Calls:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:func:`ezfio_set_ao_two_e_ints_io_ao_two_e_integrals`
|
||||
* :c:func:`ezfio_set_work_empty`
|
||||
* :c:func:`map_save_to_disk`
|
||||
|
1285
docs/source/modules/ao_two_e_ints.rst
Normal file
1285
docs/source/modules/ao_two_e_ints.rst
Normal file
File diff suppressed because it is too large
Load Diff
52
docs/source/modules/aux_quantities.rst
Normal file
52
docs/source/modules/aux_quantities.rst
Normal file
@ -0,0 +1,52 @@
|
||||
.. _module_aux_quantities:
|
||||
|
||||
.. program:: aux_quantities
|
||||
|
||||
.. default-role:: option
|
||||
|
||||
==============
|
||||
aux_quantities
|
||||
==============
|
||||
|
||||
|
||||
This module contains some global variables (such as densities and energies)
|
||||
which are stored in the EZFIO folder in a different place than determinants.
|
||||
This is used in practice to store density matrices which can be obtained from
|
||||
any methods, as long as they are stored in the same MO basis which is used for
|
||||
the calculations. In |RSDFT| calculations, this can be done to perform damping
|
||||
on the density in order to speed up convergence.
|
||||
|
||||
The main providers of that module are:
|
||||
|
||||
* `data_one_e_dm_alpha_mo` and `data_one_e_dm_beta_mo` which are the
|
||||
one-body alpha and beta densities which are necessary read from the EZFIO
|
||||
folder.
|
||||
|
||||
|
||||
Thanks to these providers you can use any density matrix that does not
|
||||
necessary corresponds to that of the current wave function.
|
||||
|
||||
|
||||
|
||||
EZFIO parameters
|
||||
----------------
|
||||
|
||||
.. option:: data_energy_var
|
||||
|
||||
Variational energy computed with the wave function
|
||||
|
||||
|
||||
.. option:: data_energy_proj
|
||||
|
||||
Projected energy computed with the wave function
|
||||
|
||||
|
||||
.. option:: data_one_e_dm_alpha_mo
|
||||
|
||||
Alpha one body density matrix on the |MO| basis computed with the wave function
|
||||
|
||||
|
||||
.. option:: data_one_e_dm_beta_mo
|
||||
|
||||
Beta one body density matrix on the |MO| basis computed with the wave function
|
||||
|
833
docs/source/modules/becke_numerical_grid.rst
Normal file
833
docs/source/modules/becke_numerical_grid.rst
Normal file
@ -0,0 +1,833 @@
|
||||
.. _module_becke_numerical_grid:
|
||||
|
||||
.. program:: becke_numerical_grid
|
||||
|
||||
.. default-role:: option
|
||||
|
||||
====================
|
||||
becke_numerical_grid
|
||||
====================
|
||||
|
||||
This module contains all quantities needed to build Becke's grid used in general for DFT integration. Note that it can be used for whatever integration in R^3 as long as the functions to be integrated are mostly concentrated near the atomic regions.
|
||||
|
||||
This grid is built as the reunion of a spherical grid around each atom. Each spherical grid contains
|
||||
a certain number of radial and angular points. No pruning is done on the angular part of the grid.
|
||||
|
||||
The main keyword for that module is:
|
||||
|
||||
* :option:`becke_numerical_grid grid_type_sgn` which controls the precision of the grid according the standard **SG-n** grids. This keyword controls the two providers `n_points_integration_angular` `n_points_radial_grid`.
|
||||
|
||||
The main providers of that module are:
|
||||
|
||||
* `n_points_integration_angular` which is the number of angular integration points. WARNING: it obeys to specific rules so it cannot be any integer number. Some of the possible values are [ 50 | 74 | 170 | 194 | 266 | 302 | 590 | 1202 | 2030 | 5810 ] for instance. See :file:`angular.f` for more details.
|
||||
* `n_points_radial_grid` which is the number of radial angular points. This can be any strictly positive integer. Nevertheless, a minimum of 50 is in general necessary.
|
||||
* `final_grid_points` which are the (x,y,z) coordinates of the grid points.
|
||||
* `final_weight_at_r_vector` which are the weights at each grid point
|
||||
|
||||
|
||||
For a simple example of how to use the grid, see :file:`example.irp.f`.
|
||||
|
||||
The spherical integration uses Lebedev-Laikov grids, which was used from the code distributed through CCL (http://www.ccl.net/).
|
||||
See next section for explanations and citation policies.
|
||||
|
||||
.. code-block:: text
|
||||
|
||||
This subroutine is part of a set of subroutines that generate
|
||||
Lebedev grids [1-6] for integration on a sphere. The original
|
||||
C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
||||
translated into fortran by Dr. Christoph van Wuellen.
|
||||
This subroutine was translated using a C to fortran77 conversion
|
||||
tool written by Dr. Christoph van Wuellen.
|
||||
|
||||
Users of this code are asked to include reference [1] in their
|
||||
publications, and in the user- and programmers-manuals
|
||||
describing their codes.
|
||||
|
||||
This code was distributed through CCL (http://www.ccl.net/).
|
||||
|
||||
[1] V.I. Lebedev, and D.N. Laikov
|
||||
"A quadrature formula for the sphere of the 131st
|
||||
algebraic order of accuracy"
|
||||
Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
||||
|
||||
[2] V.I. Lebedev
|
||||
"A quadrature formula for the sphere of 59th algebraic
|
||||
order of accuracy"
|
||||
Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
||||
|
||||
[3] V.I. Lebedev, and A.L. Skorokhodov
|
||||
"Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
||||
Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
||||
|
||||
[4] V.I. Lebedev
|
||||
"Spherical quadrature formulas exact to orders 25-29"
|
||||
Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
||||
|
||||
[5] V.I. Lebedev
|
||||
"Quadratures on a sphere"
|
||||
Computational Mathematics and Mathematical Physics, Vol. 16,
|
||||
1976, pp. 10-24.
|
||||
|
||||
[6] V.I. Lebedev
|
||||
"Values of the nodes and weights of ninth to seventeenth
|
||||
order Gauss-Markov quadrature formulae invariant under the
|
||||
octahedron group with inversion"
|
||||
Computational Mathematics and Mathematical Physics, Vol. 15,
|
||||
1975, pp. 44-51.
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
EZFIO parameters
|
||||
----------------
|
||||
|
||||
.. option:: grid_type_sgn
|
||||
|
||||
Type of grid used for the Becke's numerical grid. Can be, by increasing accuracy: [ 0 | 1 | 2 | 3 ]
|
||||
|
||||
Default: 2
|
||||
|
||||
|
||||
Providers
|
||||
---------
|
||||
|
||||
.. c:var:: alpha_knowles
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/integration_radial.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision, allocatable :: alpha_knowles (100)
|
||||
|
||||
|
||||
Recommended values for the alpha parameters according to the paper of Knowles (JCP, 104, 1996)
|
||||
as a function of the nuclear charge
|
||||
|
||||
Needed by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`final_weight_at_r`
|
||||
* :c:data:`grid_points_per_atom`
|
||||
|
||||
|
||||
.. c:var:: angular_quadrature_points
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/grid_becke.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision, allocatable :: angular_quadrature_points (n_points_integration_angular,3)
|
||||
double precision, allocatable :: weights_angular_points (n_points_integration_angular)
|
||||
|
||||
|
||||
weights and grid points for the integration on the angular variables on
|
||||
the unit sphere centered on (0,0,0)
|
||||
According to the LEBEDEV scheme
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`n_points_radial_grid`
|
||||
|
||||
Needed by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`final_weight_at_r`
|
||||
* :c:data:`grid_points_per_atom`
|
||||
|
||||
|
||||
.. c:var:: dr_radial_integral
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/grid_becke.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision, allocatable :: grid_points_radial (n_points_radial_grid)
|
||||
double precision :: dr_radial_integral
|
||||
|
||||
|
||||
points in [0,1] to map the radial integral [0,\infty]
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`n_points_radial_grid`
|
||||
|
||||
Needed by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`final_weight_at_r`
|
||||
* :c:data:`grid_points_per_atom`
|
||||
|
||||
|
||||
.. c:var:: final_grid_points
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/grid_becke_vector.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision, allocatable :: final_grid_points (3,n_points_final_grid)
|
||||
double precision, allocatable :: final_weight_at_r_vector (n_points_final_grid)
|
||||
integer, allocatable :: index_final_points (3,n_points_final_grid)
|
||||
integer, allocatable :: index_final_points_reverse (n_points_integration_angular,n_points_radial_grid,nucl_num)
|
||||
|
||||
|
||||
final_grid_points(1:3,j) = (/ x, y, z /) of the jth grid point
|
||||
|
||||
final_weight_at_r_vector(i) = Total weight function of the ith grid point which contains the Lebedev, Voronoi and radial weights contributions
|
||||
|
||||
index_final_points(1:3,i) = gives the angular, radial and atomic indices associated to the ith grid point
|
||||
|
||||
index_final_points_reverse(i,j,k) = index of the grid point having i as angular, j as radial and l as atomic indices
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`final_weight_at_r`
|
||||
* :c:data:`grid_points_per_atom`
|
||||
* :c:data:`n_points_final_grid`
|
||||
* :c:data:`n_points_radial_grid`
|
||||
* :c:data:`nucl_num`
|
||||
|
||||
Needed by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`aos_grad_in_r_array`
|
||||
* :c:data:`aos_in_r_array`
|
||||
* :c:data:`aos_lapl_in_r_array`
|
||||
* :c:data:`aos_sr_vc_alpha_lda_w`
|
||||
* :c:data:`aos_sr_vc_alpha_pbe_w`
|
||||
* :c:data:`aos_vc_alpha_lda_w`
|
||||
* :c:data:`aos_vc_alpha_pbe_w`
|
||||
* :c:data:`energy_sr_x_lda`
|
||||
* :c:data:`energy_sr_x_pbe`
|
||||
* :c:data:`energy_x_lda`
|
||||
* :c:data:`energy_x_pbe`
|
||||
* :c:data:`mos_in_r_array`
|
||||
* :c:data:`one_e_dm_alpha_at_r`
|
||||
* :c:data:`one_e_dm_and_grad_alpha_in_r`
|
||||
|
||||
|
||||
.. c:var:: final_weight_at_r
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/grid_becke.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision, allocatable :: final_weight_at_r (n_points_integration_angular,n_points_radial_grid,nucl_num)
|
||||
|
||||
|
||||
Total weight on each grid point which takes into account all Lebedev, Voronoi and radial weights.
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`alpha_knowles`
|
||||
* :c:data:`angular_quadrature_points`
|
||||
* :c:data:`grid_points_radial`
|
||||
* :c:data:`m_knowles`
|
||||
* :c:data:`n_points_radial_grid`
|
||||
* :c:data:`nucl_charge`
|
||||
* :c:data:`nucl_num`
|
||||
* :c:data:`weight_at_r`
|
||||
|
||||
Needed by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`final_grid_points`
|
||||
* :c:data:`n_points_final_grid`
|
||||
|
||||
|
||||
.. c:var:: final_weight_at_r_vector
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/grid_becke_vector.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision, allocatable :: final_grid_points (3,n_points_final_grid)
|
||||
double precision, allocatable :: final_weight_at_r_vector (n_points_final_grid)
|
||||
integer, allocatable :: index_final_points (3,n_points_final_grid)
|
||||
integer, allocatable :: index_final_points_reverse (n_points_integration_angular,n_points_radial_grid,nucl_num)
|
||||
|
||||
|
||||
final_grid_points(1:3,j) = (/ x, y, z /) of the jth grid point
|
||||
|
||||
final_weight_at_r_vector(i) = Total weight function of the ith grid point which contains the Lebedev, Voronoi and radial weights contributions
|
||||
|
||||
index_final_points(1:3,i) = gives the angular, radial and atomic indices associated to the ith grid point
|
||||
|
||||
index_final_points_reverse(i,j,k) = index of the grid point having i as angular, j as radial and l as atomic indices
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`final_weight_at_r`
|
||||
* :c:data:`grid_points_per_atom`
|
||||
* :c:data:`n_points_final_grid`
|
||||
* :c:data:`n_points_radial_grid`
|
||||
* :c:data:`nucl_num`
|
||||
|
||||
Needed by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`aos_grad_in_r_array`
|
||||
* :c:data:`aos_in_r_array`
|
||||
* :c:data:`aos_lapl_in_r_array`
|
||||
* :c:data:`aos_sr_vc_alpha_lda_w`
|
||||
* :c:data:`aos_sr_vc_alpha_pbe_w`
|
||||
* :c:data:`aos_vc_alpha_lda_w`
|
||||
* :c:data:`aos_vc_alpha_pbe_w`
|
||||
* :c:data:`energy_sr_x_lda`
|
||||
* :c:data:`energy_sr_x_pbe`
|
||||
* :c:data:`energy_x_lda`
|
||||
* :c:data:`energy_x_pbe`
|
||||
* :c:data:`mos_in_r_array`
|
||||
* :c:data:`one_e_dm_alpha_at_r`
|
||||
* :c:data:`one_e_dm_and_grad_alpha_in_r`
|
||||
|
||||
|
||||
.. c:var:: grid_points_per_atom
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/grid_becke.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision, allocatable :: grid_points_per_atom (3,n_points_integration_angular,n_points_radial_grid,nucl_num)
|
||||
|
||||
|
||||
x,y,z coordinates of grid points used for integration in 3d space
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`alpha_knowles`
|
||||
* :c:data:`angular_quadrature_points`
|
||||
* :c:data:`grid_points_radial`
|
||||
* :c:data:`m_knowles`
|
||||
* :c:data:`n_points_radial_grid`
|
||||
* :c:data:`nucl_charge`
|
||||
* :c:data:`nucl_coord`
|
||||
* :c:data:`nucl_num`
|
||||
|
||||
Needed by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`final_grid_points`
|
||||
* :c:data:`one_e_dm_alpha_in_r`
|
||||
* :c:data:`weight_at_r`
|
||||
|
||||
|
||||
.. c:var:: grid_points_radial
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/grid_becke.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision, allocatable :: grid_points_radial (n_points_radial_grid)
|
||||
double precision :: dr_radial_integral
|
||||
|
||||
|
||||
points in [0,1] to map the radial integral [0,\infty]
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`n_points_radial_grid`
|
||||
|
||||
Needed by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`final_weight_at_r`
|
||||
* :c:data:`grid_points_per_atom`
|
||||
|
||||
|
||||
.. c:var:: index_final_points
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/grid_becke_vector.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision, allocatable :: final_grid_points (3,n_points_final_grid)
|
||||
double precision, allocatable :: final_weight_at_r_vector (n_points_final_grid)
|
||||
integer, allocatable :: index_final_points (3,n_points_final_grid)
|
||||
integer, allocatable :: index_final_points_reverse (n_points_integration_angular,n_points_radial_grid,nucl_num)
|
||||
|
||||
|
||||
final_grid_points(1:3,j) = (/ x, y, z /) of the jth grid point
|
||||
|
||||
final_weight_at_r_vector(i) = Total weight function of the ith grid point which contains the Lebedev, Voronoi and radial weights contributions
|
||||
|
||||
index_final_points(1:3,i) = gives the angular, radial and atomic indices associated to the ith grid point
|
||||
|
||||
index_final_points_reverse(i,j,k) = index of the grid point having i as angular, j as radial and l as atomic indices
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`final_weight_at_r`
|
||||
* :c:data:`grid_points_per_atom`
|
||||
* :c:data:`n_points_final_grid`
|
||||
* :c:data:`n_points_radial_grid`
|
||||
* :c:data:`nucl_num`
|
||||
|
||||
Needed by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`aos_grad_in_r_array`
|
||||
* :c:data:`aos_in_r_array`
|
||||
* :c:data:`aos_lapl_in_r_array`
|
||||
* :c:data:`aos_sr_vc_alpha_lda_w`
|
||||
* :c:data:`aos_sr_vc_alpha_pbe_w`
|
||||
* :c:data:`aos_vc_alpha_lda_w`
|
||||
* :c:data:`aos_vc_alpha_pbe_w`
|
||||
* :c:data:`energy_sr_x_lda`
|
||||
* :c:data:`energy_sr_x_pbe`
|
||||
* :c:data:`energy_x_lda`
|
||||
* :c:data:`energy_x_pbe`
|
||||
* :c:data:`mos_in_r_array`
|
||||
* :c:data:`one_e_dm_alpha_at_r`
|
||||
* :c:data:`one_e_dm_and_grad_alpha_in_r`
|
||||
|
||||
|
||||
.. c:var:: index_final_points_reverse
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/grid_becke_vector.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision, allocatable :: final_grid_points (3,n_points_final_grid)
|
||||
double precision, allocatable :: final_weight_at_r_vector (n_points_final_grid)
|
||||
integer, allocatable :: index_final_points (3,n_points_final_grid)
|
||||
integer, allocatable :: index_final_points_reverse (n_points_integration_angular,n_points_radial_grid,nucl_num)
|
||||
|
||||
|
||||
final_grid_points(1:3,j) = (/ x, y, z /) of the jth grid point
|
||||
|
||||
final_weight_at_r_vector(i) = Total weight function of the ith grid point which contains the Lebedev, Voronoi and radial weights contributions
|
||||
|
||||
index_final_points(1:3,i) = gives the angular, radial and atomic indices associated to the ith grid point
|
||||
|
||||
index_final_points_reverse(i,j,k) = index of the grid point having i as angular, j as radial and l as atomic indices
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`final_weight_at_r`
|
||||
* :c:data:`grid_points_per_atom`
|
||||
* :c:data:`n_points_final_grid`
|
||||
* :c:data:`n_points_radial_grid`
|
||||
* :c:data:`nucl_num`
|
||||
|
||||
Needed by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`aos_grad_in_r_array`
|
||||
* :c:data:`aos_in_r_array`
|
||||
* :c:data:`aos_lapl_in_r_array`
|
||||
* :c:data:`aos_sr_vc_alpha_lda_w`
|
||||
* :c:data:`aos_sr_vc_alpha_pbe_w`
|
||||
* :c:data:`aos_vc_alpha_lda_w`
|
||||
* :c:data:`aos_vc_alpha_pbe_w`
|
||||
* :c:data:`energy_sr_x_lda`
|
||||
* :c:data:`energy_sr_x_pbe`
|
||||
* :c:data:`energy_x_lda`
|
||||
* :c:data:`energy_x_pbe`
|
||||
* :c:data:`mos_in_r_array`
|
||||
* :c:data:`one_e_dm_alpha_at_r`
|
||||
* :c:data:`one_e_dm_and_grad_alpha_in_r`
|
||||
|
||||
|
||||
.. c:var:: m_knowles
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/grid_becke.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
integer :: m_knowles
|
||||
|
||||
|
||||
value of the "m" parameter in the equation (7) of the paper of Knowles (JCP, 104, 1996)
|
||||
|
||||
Needed by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`final_weight_at_r`
|
||||
* :c:data:`grid_points_per_atom`
|
||||
|
||||
|
||||
.. c:var:: n_points_final_grid
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/grid_becke_vector.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
integer :: n_points_final_grid
|
||||
|
||||
|
||||
Number of points which are non zero
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`final_weight_at_r`
|
||||
* :c:data:`n_points_radial_grid`
|
||||
* :c:data:`nucl_num`
|
||||
|
||||
Needed by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`aos_grad_in_r_array`
|
||||
* :c:data:`aos_in_r_array`
|
||||
* :c:data:`aos_lapl_in_r_array`
|
||||
* :c:data:`aos_sr_vc_alpha_lda_w`
|
||||
* :c:data:`aos_sr_vc_alpha_pbe_w`
|
||||
* :c:data:`aos_vc_alpha_lda_w`
|
||||
* :c:data:`aos_vc_alpha_pbe_w`
|
||||
* :c:data:`energy_sr_x_lda`
|
||||
* :c:data:`energy_sr_x_pbe`
|
||||
* :c:data:`energy_x_lda`
|
||||
* :c:data:`energy_x_pbe`
|
||||
* :c:data:`final_grid_points`
|
||||
* :c:data:`mos_grad_in_r_array`
|
||||
* :c:data:`mos_in_r_array`
|
||||
* :c:data:`mos_lapl_in_r_array`
|
||||
* :c:data:`one_e_dm_alpha_at_r`
|
||||
* :c:data:`one_e_dm_and_grad_alpha_in_r`
|
||||
* :c:data:`potential_sr_c_alpha_ao_lda`
|
||||
* :c:data:`potential_sr_x_alpha_ao_lda`
|
||||
* :c:data:`potential_sr_x_alpha_ao_pbe`
|
||||
* :c:data:`potential_x_alpha_ao_lda`
|
||||
* :c:data:`potential_x_alpha_ao_pbe`
|
||||
|
||||
|
||||
.. c:var:: n_points_grid_per_atom
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/grid_becke.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
integer :: n_points_grid_per_atom
|
||||
|
||||
|
||||
Number of grid points per atom
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`n_points_radial_grid`
|
||||
|
||||
|
||||
|
||||
.. c:var:: n_points_integration_angular
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/grid_becke.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
integer :: n_points_radial_grid
|
||||
integer :: n_points_integration_angular
|
||||
|
||||
|
||||
n_points_radial_grid = number of radial grid points per atom
|
||||
|
||||
n_points_integration_angular = number of angular grid points per atom
|
||||
|
||||
These numbers are automatically set by setting the grid_type_sgn parameter
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`grid_type_sgn`
|
||||
|
||||
Needed by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`angular_quadrature_points`
|
||||
* :c:data:`final_grid_points`
|
||||
* :c:data:`final_weight_at_r`
|
||||
* :c:data:`grid_points_per_atom`
|
||||
* :c:data:`grid_points_radial`
|
||||
* :c:data:`n_points_final_grid`
|
||||
* :c:data:`n_points_grid_per_atom`
|
||||
* :c:data:`one_e_dm_alpha_in_r`
|
||||
* :c:data:`weight_at_r`
|
||||
|
||||
|
||||
.. c:var:: n_points_radial_grid
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/grid_becke.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
integer :: n_points_radial_grid
|
||||
integer :: n_points_integration_angular
|
||||
|
||||
|
||||
n_points_radial_grid = number of radial grid points per atom
|
||||
|
||||
n_points_integration_angular = number of angular grid points per atom
|
||||
|
||||
These numbers are automatically set by setting the grid_type_sgn parameter
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`grid_type_sgn`
|
||||
|
||||
Needed by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`angular_quadrature_points`
|
||||
* :c:data:`final_grid_points`
|
||||
* :c:data:`final_weight_at_r`
|
||||
* :c:data:`grid_points_per_atom`
|
||||
* :c:data:`grid_points_radial`
|
||||
* :c:data:`n_points_final_grid`
|
||||
* :c:data:`n_points_grid_per_atom`
|
||||
* :c:data:`one_e_dm_alpha_in_r`
|
||||
* :c:data:`weight_at_r`
|
||||
|
||||
|
||||
.. c:var:: weight_at_r
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/grid_becke.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision, allocatable :: weight_at_r (n_points_integration_angular,n_points_radial_grid,nucl_num)
|
||||
|
||||
|
||||
Weight function at grid points : w_n(r) according to the equation (22)
|
||||
of Becke original paper (JCP, 88, 1988)
|
||||
|
||||
The "n" discrete variable represents the nucleis which in this array is
|
||||
represented by the last dimension and the points are labelled by the
|
||||
other dimensions.
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`grid_points_per_atom`
|
||||
* :c:data:`n_points_radial_grid`
|
||||
* :c:data:`nucl_coord_transp`
|
||||
* :c:data:`nucl_dist_inv`
|
||||
* :c:data:`nucl_num`
|
||||
* :c:data:`slater_bragg_type_inter_distance_ua`
|
||||
|
||||
Needed by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`final_weight_at_r`
|
||||
|
||||
|
||||
.. c:var:: weights_angular_points
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/grid_becke.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision, allocatable :: angular_quadrature_points (n_points_integration_angular,3)
|
||||
double precision, allocatable :: weights_angular_points (n_points_integration_angular)
|
||||
|
||||
|
||||
weights and grid points for the integration on the angular variables on
|
||||
the unit sphere centered on (0,0,0)
|
||||
According to the LEBEDEV scheme
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`n_points_radial_grid`
|
||||
|
||||
Needed by:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`final_weight_at_r`
|
||||
* :c:data:`grid_points_per_atom`
|
||||
|
||||
|
||||
|
||||
Subroutines / functions
|
||||
-----------------------
|
||||
|
||||
.. c:function:: cell_function_becke:
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/step_function_becke.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision function cell_function_becke(r,atom_number)
|
||||
|
||||
|
||||
atom_number :: atom on which the cell function of Becke (1988, JCP,88(4))
|
||||
r(1:3) :: x,y,z coordinantes of the current point
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`nucl_dist_inv`
|
||||
* :c:data:`slater_bragg_type_inter_distance_ua`
|
||||
* :c:data:`nucl_coord_transp`
|
||||
* :c:data:`nucl_num`
|
||||
|
||||
|
||||
.. c:function:: derivative_knowles_function:
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/integration_radial.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision function derivative_knowles_function(alpha,m,x)
|
||||
|
||||
|
||||
Derivative of the function proposed by Knowles (JCP, 104, 1996) for distributing the radial points
|
||||
|
||||
|
||||
.. c:function:: example_becke_numerical_grid:
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/example.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
subroutine example_becke_numerical_grid
|
||||
|
||||
|
||||
subroutine that illustrates the main features available in becke_numerical_grid
|
||||
|
||||
Needs:
|
||||
|
||||
.. hlist::
|
||||
:columns: 3
|
||||
|
||||
* :c:data:`n_points_final_grid`
|
||||
* :c:data:`final_weight_at_r`
|
||||
* :c:data:`n_points_radial_grid`
|
||||
* :c:data:`grid_points_per_atom`
|
||||
* :c:data:`final_grid_points`
|
||||
* :c:data:`nucl_coord`
|
||||
* :c:data:`nucl_num`
|
||||
|
||||
|
||||
.. c:function:: f_function_becke:
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/step_function_becke.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision function f_function_becke(x)
|
||||
|
||||
|
||||
|
||||
|
||||
.. c:function:: knowles_function:
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/integration_radial.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision function knowles_function(alpha,m,x)
|
||||
|
||||
|
||||
Function proposed by Knowles (JCP, 104, 1996) for distributing the radial points :
|
||||
the Log "m" function ( equation (7) in the paper )
|
||||
|
||||
|
||||
.. c:function:: step_function_becke:
|
||||
|
||||
|
||||
File : :file:`becke_numerical_grid/step_function_becke.irp.f`
|
||||
|
||||
.. code:: fortran
|
||||
|
||||
double precision function step_function_becke(x)
|
||||
|
||||
|
||||
Step function of the Becke paper (1988, JCP,88(4))
|
||||
|
3489
docs/source/modules/bitmask.rst
Normal file
3489
docs/source/modules/bitmask.rst
Normal file
File diff suppressed because it is too large
Load Diff
2269
docs/source/modules/cipsi.rst
Normal file
2269
docs/source/modules/cipsi.rst
Normal file