quantum numbers in documentation

docs/source/checkpoints.rst

@@ -203,7 +203,7 @@ Examples of the split option include
 
   will compute the ``fit_poten`` matrix elements for :math:`i=32\ldots 45`.
 
-  The matrix elements in fitpot*.chk are used for the refinement of the PEF, which is controlled by the section ``FITTING``, see Chapter :ref:`refine`. This section contains keywords for selection of fitpot*.chk, namely   ``J-LIST`` and ``symmetries`` specifying the values of :math:`J` and symmetries :math:`\Gamma`, respectively (both are integer) to be processed. For example:
+  The matrix elements in fitpot*.chk are used for the refinement of the PEF, which is controlled by the section ``FITTING``, see Chapter "Refine". This section contains keywords for selection of fitpot*.chk, namely   ``J-LIST`` and ``symmetries`` specifying the values of :math:`J` and symmetries :math:`\Gamma`, respectively (both are integer) to be processed. For example:
   ::
 
        FITTING

docs/source/outputs.rst

@@ -108,20 +108,7 @@ An example from a :math:`J=2` calculation on PF\ :sub:`3` is shown below.
       E 3 347.957388 (E; 2 1 0) (E ; 0 0 0 0 0 1) 1.00 (0 0 0 0 0 1 0) (2)
       E 4 348.255477 (E; 2 2 0) (E ; 0 0 0 0 0 1) 0.73 (0 0 0 0 0 1 0) (2)
 
-In this case the energies are from the doubly degenerate :math:`E` symmetry class. The first two rows are pure rotational states. The ``j k t`` section for these two states are ``2 2 0`` and ``2 1 0`` respectively. This means the total angular momentum is 2 and the projection of the angular momentum onto an axis (usually the :math:`z`-axis is chosen) is 2 and 1 respectively. The third and fourth row are ro-vibrational states with the same vibrational quantum numbers :math:`v_1, v_2,\ldots,`,  but different values of :math:`K`. The non-rigourous quantum numbers :math:`K` and :math:`v_i` are defined using the largest eigen-coefficient  approach and are approximate. They represent the measure of how the given wavefunction is similar to a single selected basis set function selected as the largest contribution the corresponding expansion.  The quality of the assignment can be judged based on the expansion eigen-coefficients
-(column with numbers :math:`\le 1` and two decimal points): coefficients smaller than 0.7 indicate that the corresponding quantum number are less reliable. Due to this approximate nature of the TROVE quantum numbers, the TROVE assignment is usually not complete and unambiguous. It is common to find states with duplicate assignments as well as some missing combinations. 
-
-In order to help resolve ensuing  ambiguity and degeneracies, the quantum numbers from the second largest contribution can be printed. This feature can be activated using the ``NASSIGNMENTS`` keyword as part of the ``PRINT`` section. The section can appear anywhere in main body of the input file, for example:
-::
-
-      DIAGONALIZER
-       SYEV
-       enermax 20000
-      end
-
-      print
-       Nassignments  2
-      end
+In this case the energies are from the doubly degenerate :math:`E` symmetry class. The first two rows are pure rotational states. The ``j k t`` section for these two states are ``2 2 0`` and ``2 1 0`` respectively. This means the total angular momentum is 2 and the projection of the angular momentum onto an axis (usually the :math:`z`-axis is chosen) is 2 and 1 respectively. The third and fourth row are ro-vibrational states with the same vibrational quantum numbers :math:`v_1, v_2,\ldots,`,  but different values of :math:`K`. 
 
 Transition Moment output
 ========================

docs/source/quantumnumbers.rst

@@ -165,14 +165,14 @@ The symmetry classification of the rotational basis functions can be also found
           7      164.73144716   1   3  B1     4   3   1   0   0   0
           8      174.65385507   1   1  A1     4   4   0   0   0   0
           9      174.65385507   1   2  A2     4   4   1   0   0   0
-     
 
-where ``class:   0`` corresponds to the rotational sub-set = 0.  
 
+where ``class:   0`` corresponds to the rotational sub-set = 0.
 
 
 
-T\ :sub:`d` symmetry 
+
+T\ :sub:`d` symmetry
 ^^^^^^^^^^^^^^^^^^^^
 
 The Wang-functions cannot be used for symmetry adaptation of the T\ :sub:`d` rotational basis. This is because the group symmetry transformations cannot be associated  with equivalent rotations about the :math:`x`, :math:`y` or :math:`z` axes only. As a result, symmetry-adapted rotational functions are obtained  as a general linear combinations of :math:`|J,k,m\rangle` with :math:`k` spanning all :math:`k=-J\ldots J`. Because of that, the rotational quantum number :math:`K` can no longer be used for classification of the symmetrised rigid-rotor combinations. Instead they are labelled  as :math:`|J,\Gamma,n\rangle`, where :math:`\Gamma` is the symmetry and :math:`n` is a counting index:
@@ -272,9 +272,20 @@ Similarity, the :math:`B_2` symmetry TROVE output is given by
         ....
 
 
+The non-rigourous quantum numbers :math:`K` and :math:`v_i` are defined using the largest eigen-coefficient  approach and are approximate. They represent the measure of how the given wavefunction is similar to a single selected basis set function selected as the largest contribution the corresponding expansion.  The quality of the assignment can be judged based on the expansion eigen-coefficients
+(column with numbers :math:`\le 1` and two decimal points): coefficients smaller than 0.7 indicate that the corresponding quantum number are less reliable. Due to this approximate nature of the TROVE quantum numbers, the TROVE assignment is usually not complete and unambiguous. It is common to find states with duplicate assignments as well as some missing combinations (see Quantum Numbers).
 
+In order to help resolve ensuing  ambiguity and degeneracies, the quantum numbers from the second largest contribution can be printed. This feature can be activated using the ``NASSIGNMENTS`` keyword as part of the ``PRINT`` section. The section can appear anywhere in main body of the input file, for example:
+::
 
+      DIAGONALIZER
+       SYEV
+       enermax 20000
+      end
 
+      print
+       Nassignments  2
+      end