symmerty

docs/source/frames.rst

@@ -84,7 +84,7 @@ This ``Transform`` type is very similar to ``R-RHO-Z``, but with the molecular f
 
 
 ``R-ALPHA-Z``
-^^^^^^^^^^^
+^^^^^^^^^^^^^
 
 - ``R-ALPHA-Z`` is very similar to ``R-RHO-Z`` with the difference in the bending coordinate, which in the interbond angle :math:`\alpha` in this case. In the ```Rigid` reference configuration, it is a displacement from the equilibrium value :math:`\alpha_{\rm e}`:
 .. math::

docs/source/symmetry.rst

@@ -60,7 +60,7 @@ TROVE uses the symmetry properties of the vibrational coordinates, i.e. how they
 
 
 +--------------+---------------+--------------+---------------+---------------+
-|              | :math:`E`     |     (12)\    |  :math:`E^*`  |(12)\ :sup:`*` |
+| Coordinates  | :math:`E`     |     (12)\    |  :math:`E^*`  |(12)\ :sup:`*` |
 +==============+===============+==============+===============+===============+
 |:math:`r_1`   | :math:`r_1`   |  :math:`r_2` |:math:`r_1`    |  :math:`r_2`  |
 +--------------+---------------+--------------+---------------+---------------+
@@ -98,6 +98,35 @@ C3v(M)
 It can be used for the molecules PH\ :sub:`3` [15SoAlTe]_, SbH\ :sub:`3` [10YuCaYa]_, AsH\ :sub:`3` [19CoYuKo]_, PF\ :sub:`3` [19MaChYa]_, CH\ :sub:`3`\ Cl [18OwYaTe]_, CH\ :sub:`3`\ F, isotopologue CDH\ :sub:`3` etc.
 
 
+Coordinate transformation properties 
+------------------------------------
+
+
+``R-ALPHA``
+^^^^^^^^^^^
+
+This is a rigid frame with 6 valence coordinates :math:`r_1`, :math:`r_2`, :math:`r_3`, :math:`\alpha_1`, :math:`\alpha_2` and :math:`\alpha_3`. 
+
+
++----------------+----------------+------------------+------------------+------------------+-------------------+------------------+
+| Coordinates    |     :math:`E`  |    (123)\        |       (132)\     |    (23)\ :sup:`*`|    (13)\ :sup:`*` |    (12)\ :sup:`*`|
++================+================+==================+==================+==================+===================+==================+
+|    :math:`r_1` |    :math:`r_1` |     :math:`r_2`  |     :math:`r_3`  |     :math:`r_1`  |      :math:`r_3`  |     :math:`r_2`  |
++----------------+----------------+------------------+------------------+------------------+-------------------+------------------+
+|    :math:`r_2` |    :math:`r_2` |     :math:`r_3`  |     :math:`r_1`  |     :math:`r_3`  |      :math:`r_2`  |     :math:`r_1`  |
++----------------+----------------+------------------+------------------+------------------+-------------------+------------------+
+|    :math:`r_3` |    :math:`r_3` |     :math:`r_2`  |     :math:`r_2`  |     :math:`r_2`  |      :math:`r_1`  |     :math:`r_3`  |
++----------------+----------------+------------------+------------------+------------------+-------------------+------------------+
+|:math:`\alpha1` |:math:`\alpha1` | :math:`\alpha2`  | :math:`\alpha3`  | :math:`\alpha1`  |  :math:`\alpha3`  | :math:`\alpha2`  |
++----------------+----------------+------------------+------------------+------------------+-------------------+------------------+
+|:math:`\alpha2` |:math:`\alpha2` | :math:`\alpha3`  | :math:`\alpha1`  | :math:`\alpha3`  |  :math:`\alpha2`  | :math:`\alpha1`  |
++----------------+----------------+------------------+------------------+------------------+-------------------+------------------+
+|:math:`\alpha3` |:math:`\alpha3` | :math:`\alpha2`  | :math:`\alpha2`  | :math:`\alpha2`  |  :math:`\alpha1`  | :math:`\alpha3`  |
++----------------+----------------+------------------+------------------+------------------+-------------------+------------------+
+
+
+
+
 D\ :sub:`3h`\ (M)
 =================