Shell
=====

Represents a contracted Gaussian basis shell.

Constructor
-----------

.. code-block:: python

   Shell(nprim, l, pure, alpha, coeff, origin, normalize=True)

Parameters
----------
* **nprim** *(int)* — number of primitive Gaussians.
* **l** *(int)* — angular momentum quantum number (0=s, 1=p, 2=d, ...).
* **pure** *(bool)* — ``True`` for spherical harmonics, ``False`` for Cartesian.
* **alpha** *(list[float])* — Gaussian exponents.
* **coeff** *(list[float])* — contraction coefficients.
* **origin** *(list[float])* — center coordinates `[x, y, z]` (Bohr).
* **normalize** *(bool, optional)* — normalize primitives (default ``True``).

Properties
----------
* ``pure`` (bool) — spherical/cartesian type (read/write).
* ``l`` (int) — angular momentum.
* ``nprim`` (int) — number of primitives.
* ``alpha`` / ``coeff`` — exponent and coefficient arrays.
* ``origin`` — center coordinates.
* ``ncart``, ``nspher``, ``nao`` — counts for cartesian/spherical functions and AOs.
* ``cutoff`` — cutoff radius.

Methods
-------
* ``set_tol(tol)`` — set shell tolerance for cutoff computation.
* ``scale_coeff(scale)`` — scale contraction coefficients.

Special behavior
----------------
* ``len(shell)`` returns the number of primitives.
* ``shell[i]`` returns the ``(alpha[i], coeff[i])`` pair.

Example
-------

.. code-block:: python

   s_shell = gxc.Shell(
       nprim=6, l=0, pure=True,
       alpha=[3047.5, 457.4, 103.9, 29.21, 9.286, 3.163],
       coeff=[0.00183, 0.01403, 0.06884, 0.2321, 0.4679, 0.3623],
       origin=[0.0, 0.0, 0.0]
   )
   print(s_shell.nao)  # 1 (s-shell has 1 AO)