forte2.system.basis_utils
=========================

.. py:module:: forte2.system.basis_utils








Module Contents
---------------

.. py:data:: SPH_LABELS
   :value: [['s'], ['py', 'pz', 'px'], ['dxy', 'dyz', 'dz2', 'dxz', 'dx2-y2'], ['fy(3x2-y2)', 'fxyz',...


   
   The labels for spherical harmonics up to f orbitals.
   We follow the `Libint2 convention <https://github.com/evaleev/libint/wiki/using-modern-CPlusPlus-API#solid-harmonic-gaussians-ordering-and-normalization>`_.
















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.. py:data:: AM_LABELS
   :value: ['s', 'p', 'd', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n']


.. py:data:: MAX_L
   :value: 11


.. py:function:: ml_from_shell_index_cca(l, idx)

   
   Map Libint Standard/CCA shell index (0..2*l) to signed magnetic quantum number (m_l) value.
   CCA standard is such that Y_{lm}s are listed from Y_{l,-l}, ... Y_{l,0}, ... Y_{l,l}. Thus,
   the 0-based index position is related to the m quantum number via index - l.


   :Parameters:

       **l: int**
           Angular momentum quantum number.

       **idx: int**
           Index of the shell within the angular momentum type.



   :Returns:

       int:
           Magnetic quantum number m_l.











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.. py:function:: get_shell_label(l, idx)

   
   Get the label for a shell based on its angular momentum quantum number (l) and index (idx).


   :Parameters:

       **l** : int
           Angular momentum quantum number.

       **idx** : int
           Index of the shell within the angular momentum type.



   :Returns:

       str
           The label for the shell.











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.. py:function:: get_spinor_label(l, jdouble, mjdouble)

   
   Get the label for a shell based on its angular momentum quantum number (l),
   total angular momentum (jdouble/2), and magnetic quantum number (mjdouble/2).


   :Parameters:

       **l** : int
           Angular momentum quantum number.

       **jdouble** : int
           Total angular momentum quantum number (2*j).

       **mjdouble** : int
           Magnetic quantum number (2*mj).



   :Returns:

       str
           The label for the shell.











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.. py:function:: shell_label_to_lm(shell_label)

   
   Convert a shell label to its angular momentum quantum number (l) and index (m).


   :Parameters:

       **shell_label** : str
           The label of the shell, e.g., "s", "p", "dx2-y2", "h(9)"



   :Returns:

       list[tuple]
           A list of a single tuple containing the angular momentum quantum number (l) and the index (m), if both l and m can be determined.
           If only l can be determined, returns a list of tuples of all possible (l, m) pairs.











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.. py:class:: BasisInfo

   
   A class to hold information about the basis set of a system.


   :Parameters:

       **system** : System
           The system for which the basis set information is to be generated.

       **basis** : Basis
           The basis set.

   :Attributes:

       **basis_labels** : list[_AOLabel]
           `_AOLabel` is a data structure with the following attributes:
           - iatom: int, the index of the atom in the system.
           - Z: int, the atomic number of the atom.
           - Zidx: int, the index of the atom in the system (1-based).
           - n: int, the principal quantum number for the shell.
           - l: int, the angular momentum quantum number.
           - ml: int, the magnetic quantum number m_l.
           - m: int, the index of the basis function within the shell.

       **basis_labels_spinor** : list[_SpinorAOLabel]
           `_SpinorAOLabel` is a data structure with the following attributes:
           - iatom: int, the index of the atom in the system.
           - Z: int, the atomic number of the atom.
           - Zidx: int, the index of the atom in the system (1-based).
           - n: int, the principal quantum number for the shell.
           - l: int, the angular momentum quantum number.
           - jdouble: int, the total angular momentum quantum number (2*j).
           - mjdouble: int, the magnetic quantum number (2*m_j).

       **atom_to_aos** : dict[int : dict[int : list[int]]]
           A dict of dict where e.g., ``atom_to_aos[6][2]`` gives a list of absolute indices of all AOs on C2.













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   .. py:attribute:: system
      :type:  forte2.system.System


   .. py:attribute:: basis
      :type:  forte2.Basis


   .. py:method:: print_basis_labels(spinor=False)

      
      Pretty print the basis labels.
















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   .. py:method:: print_ao_composition(coeff, idx, nprint=5, thres=0.001, spinorbital=False)


   .. py:method:: print_spinor_composition(spinor_coeff, idx, nprint=5, thres=0.001)