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Anthony Scemama 2019-01-29 15:40:00 +01:00
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commit f4bff28cd1
123 changed files with 350 additions and 42610 deletions
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14
docs/source/_static/links.rst
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@ -12,7 +12,6 @@
.. _Irene: http://www-hpc.cea.fr/en/complexe/tgcc-Irene.htm
.. _IRPF90: http://irpf90.ups-tlse.fr
.. _LAPACK: http://www.netlib.org/lapack/
.. _Molden: http://cheminf.cmbi.ru.nl/molden/
.. _NECI: https://github.com/ghb24/NECI_STABLE
.. _Ninja: https://ninja-build.org/
.. _NWChem: http://www.nwchem-sw.org/
@ -53,12 +52,15 @@
.. |CIPSI| replace:: :abbr:`CIPSI (Configuration Interaction using a Perturbative Selection)`
.. |CI| replace:: :abbr:`CI (Configuration Interaction)`
.. |CISD| replace:: :abbr:`CISD (Configuration Interaction with Single and Double Excitations)`
.. |CASSCF| replace:: |CAS| - |SCF|
.. |CIS| replace:: :abbr:`CIS (Configuration Interaction with Single Excitations)`
.. |DFT| replace:: :abbr:`DFT (Density Functional Theory)`
.. |DDCI| replace:: :abbr:`DDCI (Difference Dedicated Configuration Interaction)`
.. |DFT| replace:: :abbr:`DFT (Density Functional Theory)`
.. |DIIS| replace:: :abbr:`DIIS (Direct Inversion of the Iterative Subspace)`
.. |FCIQMC| replace:: |FCI| - |QMC|
.. |FCI| replace:: :abbr:`FCI (Full Configuration Interaction)`
.. |HF| replace:: :abbr:`HF (Hartree-Fock)`
.. |KS-DFT| replace:: :abbr:`KS-DFT (Kohn-Sham Density Functional Theory)`
.. |MO| replace:: :abbr:`MO (Molecular Orbital)`
.. |MOs| replace:: :abbr:`MOs (Molecular Orbitals)`
.. |MP2| replace:: :abbr:`MP2 (Moller-Plesset second order perturbative correction)`
@ -67,15 +69,13 @@
.. |MRPT| replace:: :abbr:`MRPT (Multi-Reference Perturbation Theory)`
.. |PT2| replace:: :abbr:`PT2 (Second order perturbative correction)`
.. |QMC| replace:: :abbr:`QMC (Quantum Monte Carlo)`
.. |ROHF| replace:: :abbr:`ROHF (Restricted Open-Shell Hartree-Fock)`
.. |RSDFT| replace:: :abbr:`RSDFT (Range Separated Density Functional Theory)`
.. |RSH| replace:: :abbr:`RSH (Range Separated Hybrids)`
.. |rst| replace:: :abbr:`RST (ReStructured Text)`
.. |SCF| replace:: :abbr:`SCF (Self Consistent Field)`
.. |RSH| replace:: :abbr:`RSH (Range Separated Hybrids)`
.. |RSDFT| replace:: :abbr:`RSDFT (Range Separated Density Functional Theory)`
.. |KS-DFT| replace:: :abbr:`KS-DFT (Kohn-Sham Density Functional Theory)`
.. |sCI| replace:: :abbr:`sCI (Selected-CI)`
.. |WFT| replace:: :abbr:`WFT (Wave Function Theory)`
.. |CASSCF| replace:: |CAS| - |SCF|
.. |FCIQMC| replace:: |FCI| - |QMC|
.. |kalpha| replace:: :math:`|\alpha \rangle`
.. |H| replace:: :math:`\hat H`

2
docs/source/conf.py
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@ -171,7 +171,7 @@ for f in os.listdir("users_guide"):
for f in os.listdir("programs"):
name = f.split('.')[0]
if name not in []:
if name not in [""]:
filename = os.path.join("programs",name)
man_pages.append( (filename, name, qpdoc, [author], 1) )

2
docs/source/intro/selected_ci.rst
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@ -55,8 +55,6 @@ Simple Algorithm
.. |SetDI| replace:: `\{|D_I\rangle\}^{(n)}`
.. |Psi_n| replace:: `|\Psi^{(n)}\rangle`
.. |H| replace:: `\hat H`
.. |kalpha| replace:: `|\alpha\rangle`
.. |kalpha_star| replace:: `\{ |\alpha \rangle \}_\star ^{(n)}`
.. |ealpha| replace:: `e_\alpha`
.. |EPT| replace:: `E_\text{PT2}`

1245
docs/source/modules/ao_basis.rst
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2015
docs/source/modules/ao_one_e_ints.rst
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901
docs/source/modules/ao_two_e_erf_ints.rst
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@ -1,901 +0,0 @@
.. _module_ao_two_e_erf_ints:
.. program:: ao_two_e_erf_ints
.. default-role:: option
======================
ao_two_e_erf_ints
======================
Here, all two-electron integrals (:math:`erf(\mu 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 main parameter of this module is :option:`ao_two_e_erf_ints mu_erf` which is the range-separation parameter.
To fetch an |AO| integral, use the
`get_ao_two_e_integral_erf(i,j,k,l,ao_integrals_erf_map)` function.
The conventions are:
* For |AO| integrals : (ij|kl) = (11|22) = <ik|jl> = <12|12>
EZFIO parameters
----------------
.. option:: io_ao_two_e_integrals_erf
Read/Write |AO| integrals with the long range interaction from/to disk [ Write | Read | None ]
Default: None
.. option:: mu_erf
cutting of the interaction in the range separated model
Default: 0.5
Providers
---------
.. c:var:: ao_integrals_erf_cache
File : :file:`ao_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
double precision, allocatable :: ao_integrals_erf_cache (0:64*64*64*64)
Cache of |AO| integrals for fast access
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_erf_cache_min`
* :c:data:`ao_integrals_erf_map`
* :c:data:`ao_two_e_integrals_erf_in_map`
.. c:var:: ao_integrals_erf_cache_max
File : :file:`ao_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
integer :: ao_integrals_erf_cache_min
integer :: ao_integrals_erf_cache_max
Min and max values of the AOs for which the integrals are in the cache
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_erf_cache`
.. c:var:: ao_integrals_erf_cache_min
File : :file:`ao_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
integer :: ao_integrals_erf_cache_min
integer :: ao_integrals_erf_cache_max
Min and max values of the AOs for which the integrals are in the cache
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_erf_cache`
.. c:var:: ao_integrals_erf_map
File : :file:`ao_two_e_erf_ints/map_integrals_erf.irp.f`
.. code:: fortran
type(map_type) :: ao_integrals_erf_map
|AO| integrals
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_erf_cache`
* :c:data:`ao_two_e_integrals_erf_in_map`
* :c:data:`mo_two_e_int_erf_jj_from_ao`
.. c:var:: ao_two_e_integral_erf_schwartz
File : :file:`ao_two_e_erf_ints/providers_ao_erf.irp.f`
.. code:: fortran
double precision, allocatable :: ao_two_e_integral_erf_schwartz (ao_num,ao_num)
Needed to compute Schwartz inequalities
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_normalized_ordered_transp`
* :c:data:`ao_expo_ordered_transp`
* :c:data:`ao_nucl`
* :c:data:`ao_num`
* :c:data:`ao_power`
* :c:data:`ao_prim_num`
* :c:data:`n_pt_max_integrals`
* :c:data:`nucl_coord`
Needed by:
.. hlist::
:columns: 3
* :c:data:`mo_two_e_int_erf_jj_from_ao`
.. c:var:: ao_two_e_integrals_erf_in_map
File : :file:`ao_two_e_erf_ints/providers_ao_erf.irp.f`
.. code:: fortran
logical :: ao_two_e_integrals_erf_in_map
Map of Atomic integrals
i(r1) j(r2) 1/r12 k(r1) l(r2)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_normalized_ordered_transp`
* :c:data:`ao_expo_ordered_transp`
* :c:data:`ao_integrals_erf_map`
* :c:data:`ao_nucl`
* :c:data:`ao_num`
* :c:data:`ao_power`
* :c:data:`ao_prim_num`
* :c:data:`ezfio_filename`
* :c:data:`io_ao_two_e_integrals_erf`
* :c:data:`n_pt_max_integrals`
* :c:data:`nproc`
* :c:data:`nucl_coord`
* :c:data:`read_ao_two_e_integrals_erf`
* :c:data:`zmq_context`
* :c:data:`zmq_socket_pull_tcp_address`
* :c:data:`zmq_state`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_erf_cache`
* :c:data:`mo_two_e_int_erf_jj_from_ao`
* :c:data:`mo_two_e_integrals_erf_in_map`
.. c:function:: general_primitive_integral_erf:
File : :file:`ao_two_e_erf_ints/two_e_integrals_erf.irp.f`
.. code:: fortran
double precision function general_primitive_integral_erf(dim, &
P_new,P_center,fact_p,p,p_inv,iorder_p, &
Q_new,Q_center,fact_q,q,q_inv,iorder_q)
Computes the integral <pq|rs> where p,q,r,s are Gaussian primitives
Needs:
.. hlist::
:columns: 3
* :c:data:`mu_erf`
Calls:
.. hlist::
:columns: 3
* :c:func:`add_poly_multiply`
* :c:func:`give_polynom_mult_center_x`
* :c:func:`multiply_poly`
Subroutines / functions
-----------------------
.. c:function:: ao_two_e_integral_erf:
File : :file:`ao_two_e_erf_ints/two_e_integrals_erf.irp.f`
.. code:: fortran
double precision function ao_two_e_integral_erf(i,j,k,l)
integral of the AO basis <ik|jl> or (ij|kl)
i(r1) j(r1) 1/r12 k(r2) l(r2)
Needs:
.. hlist::
:columns: 3
* :c:data:`n_pt_max_integrals`
* :c:data:`ao_coef_normalized_ordered_transp`
* :c:data:`ao_power`
* :c:data:`ao_expo_ordered_transp`
* :c:data:`ao_prim_num`
* :c:data:`ao_nucl`
* :c:data:`nucl_coord`
Calls:
.. hlist::
:columns: 3
* :c:func:`give_explicit_poly_and_gaussian`
.. c:function:: ao_two_e_integral_schwartz_accel_erf:
File : :file:`ao_two_e_erf_ints/two_e_integrals_erf.irp.f`
.. code:: fortran
double precision function ao_two_e_integral_schwartz_accel_erf(i,j,k,l)
integral of the AO basis <ik|jl> or (ij|kl)
i(r1) j(r1) 1/r12 k(r2) l(r2)
Needs:
.. hlist::
:columns: 3
* :c:data:`n_pt_max_integrals`
* :c:data:`ao_integrals_threshold`
* :c:data:`ao_coef_normalized_ordered_transp`
* :c:data:`ao_power`
* :c:data:`ao_expo_ordered_transp`
* :c:data:`ao_prim_num`
* :c:data:`ao_nucl`
* :c:data:`nucl_coord`
Calls:
.. hlist::
:columns: 3
* :c:func:`give_explicit_poly_and_gaussian`
.. c:function:: ao_two_e_integrals_erf_in_map_collector:
File : :file:`ao_two_e_erf_ints/integrals_erf_in_map_slave.irp.f`
.. code:: fortran
subroutine ao_two_e_integrals_erf_in_map_collector(zmq_socket_pull)
Collects results from the AO integral calculation
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_erf_map`
* :c:data:`ao_num`
Called by:
.. hlist::
:columns: 3
* :c:data:`ao_two_e_integrals_erf_in_map`
Calls:
.. hlist::
:columns: 3
* :c:func:`end_zmq_to_qp_run_socket`
* :c:func:`insert_into_ao_integrals_erf_map`
.. c:function:: ao_two_e_integrals_erf_in_map_slave:
File : :file:`ao_two_e_erf_ints/integrals_erf_in_map_slave.irp.f`
.. code:: fortran
subroutine ao_two_e_integrals_erf_in_map_slave(thread,iproc)
Computes a buffer of integrals
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
Called by:
.. hlist::
:columns: 3
* :c:func:`ao_two_e_integrals_erf_in_map_slave_inproc`
* :c:func:`ao_two_e_integrals_erf_in_map_slave_tcp`
Calls:
.. hlist::
:columns: 3
* :c:func:`compute_ao_integrals_erf_jl`
* :c:func:`end_zmq_push_socket`
* :c:func:`end_zmq_to_qp_run_socket`
* :c:func:`push_integrals`
.. c:function:: ao_two_e_integrals_erf_in_map_slave_inproc:
File : :file:`ao_two_e_erf_ints/integrals_erf_in_map_slave.irp.f`
.. code:: fortran
subroutine ao_two_e_integrals_erf_in_map_slave_inproc(i)
Computes a buffer of integrals. i is the ID of the current thread.
Called by:
.. hlist::
:columns: 3
* :c:data:`ao_two_e_integrals_erf_in_map`
Calls:
.. hlist::
:columns: 3
* :c:func:`ao_two_e_integrals_erf_in_map_slave`
.. 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`
.. code:: fortran
subroutine ao_two_e_integrals_erf_in_map_slave_tcp(i)
Computes a buffer of integrals. i is the ID of the current thread.
Calls:
.. hlist::
:columns: 3
* :c:func:`ao_two_e_integrals_erf_in_map_slave`
.. 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
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`
.. code:: fortran
subroutine compute_ao_integrals_erf_jl(j,l,n_integrals,buffer_i,buffer_value)
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 = x1**(a_x) y1**(a_y) z1**(a_z) exp(-alpha * r1**2)
primitive_2 = x1**(b_x) y1**(b_y) z1**(b_z) exp(- beta * r1**2)
primitive_3 = x2**(c_x) y2**(c_y) z2**(c_z) exp(-delta * r2**2)
primitive_4 = x2**(d_x) y2**(d_y) z2**(d_z) exp(- gama * 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 polynom ::
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`

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.. _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

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.. _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`
* :