forte2.symmetry.sym_utils
=========================

.. py:module:: forte2.symmetry.sym_utils






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

.. py:data:: SYMMETRY_OPS

.. py:data:: CHARACTER_TABLE

.. py:data:: COTTON_LABELS

.. py:function:: equivalent_under_operation(coords, charges, op, tol)

   
   Check if a set of coordinates and charges is equivalent to itself under a
   given symmetry operation.


   :Parameters:

       **coords** : ndarray of shape (N, 3)
           The coordinates of the atoms.

       **charges** : list of length N
           The nuclear charges of the atoms.

       **op** : callable
           A function representing the symmetry operation that takes a 3-vector and returns the transformed 3-vector.

       **tol** : float
           The tolerance for comparing distances.



   :Returns:

       **has_op** : bool
           True if the system is invariant under the operation, False otherwise.











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.. py:function:: rotation_mat(axis, theta)

   
   Euler-Rodrigues formula for rotation matrix


   :Parameters:

       **axis** : ndarray of shape (3,)
           The axis to rotate around. Will be normalized internally.

       **theta** : float
           Rotation angle



   :Returns:

       **R** : ndarray of shape (3, 3)
           The rotation matrix.











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.. py:function:: reflection_mat(plane)

   
   Return the 3x3 reflection matrix for the mirror plane σ(x_i, x_j).


   :Parameters:

       **plane: tuple (i, j) with i != j and i,j ∈ {0,1,2} mapping to x,y,z.**
           Example: (0,1) -> σ_xy (flip z).



   :Returns:

       **R** : ndarray of shape (3, 3)
           ..

       The reflection matrix.
           ..











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