labels fixed

docs/source/frames.rst

@@ -616,8 +616,8 @@ The tetrahedral five-atomic molecule XY\ :sub:`4`  has 9 vibrational degrees of
 There should, however, be only 9 independent vibrational degrees of freedom in a 5 atomic molecule. One of the inter-bond angles :math:`\alpha_{ij}` is redundant as there should be only five independent bending vibrations, with the following redundancy condition:
 
 .. math::
-     
      :label: e-redund
+
       \left| \begin{array}{cccc}
        1               & \cos\alpha_{12} &  \cos\alpha_{13} &  \cos\alpha_{14} \\
        \cos\alpha_{12} & 1               &  \cos\alpha_{23} &  \cos\alpha_{24} \\
@@ -630,16 +630,16 @@ There should, however, be only 9 independent vibrational degrees of freedom in a
 XY\ :sub:`4`  belongs to the T\ :sub:`d`\ (M) molecular symmetry group, which consists of five irreducible representations, :math:`A_1`, :math:`A_2`, :math:`E`, :math:`F_1` and :math:`F_2`. One way to define independent bending modes is to reduce the six inter-bond angles :math:`\alpha_{ij}` to five symmetry-adapted  irreducible combinations,  which, together with four bond lengths :math:`r_i` form nine independent vibrational modes :math:`\xi_i` as follows:  four stretches
 
 .. math:: 
-    
    :label: e-vects-i
+
     \xi_i  =r_i, \;\; i = 1,2,3,4,
      
 
 two :math:`E`-symmetry bends
 
 .. math::
-     
     :label:  e-vects-5-6
+
     \begin{split}
        \xi_5^{E_a}   &= \frac{1}{\sqrt{12}} (2 \alpha_{12} - \alpha_{13} - \alpha_{14} - \alpha_{23} - \alpha_{24} + 2 \alpha_{34} ), \\
        \xi_6^{E_b}  &= \frac{1}{2} (\alpha_{13} - \alpha_{14} - \alpha_{23} + \alpha_{24} ),
@@ -649,8 +649,8 @@ two :math:`E`-symmetry bends
 and three :math:`F`-symmetry bends
 
 .. math::
-     
    :label: e-vects-7-9
+
      \begin{split}
        \xi_7^{F_{2x}}  &= \frac{1}{\sqrt{2}} ( \alpha_{24} - \alpha_{13} ),  \\
        \xi_8^{F_{2y}}  &= \frac{1}{\sqrt{2}} ( \alpha_{23} - \alpha_{14} ), \\
@@ -663,8 +663,8 @@ where the corresponding symmetries of the bending modes are indicated.
 The stretching modes :math:`r_i` can also be in principle combined into symmetry-adapted coordinates in T\ :sub:`d`\ (M):
 
 .. math:: 
-     
     :label: e-CH4-xi1=4
+
      \begin{split}
        \xi_1^{A_1}  &= \frac{1}{2} \left(  r_1 + r_2 + r_3 + r_4\right), \\
        \xi_2^{F_{2x}}  &= \frac{1}{2} \left(  r_1 - r_2 + r_3 - r_4\right), \\

docs/source/quantumnumbers.rst

@@ -102,7 +102,6 @@ In calculations of ro-vibrational energy, :math:`m` plays no direct role and can
 TROVE uses symmetry adapted rotational basis functions. For asymmetric  and symmetric tops, these are the  so-called Wang functions :math:`|J,K,\tau\rangle`\ ), which are given by
 
 .. math::
-
   :label: e-JKtay-v2
 
    \begin{split}
@@ -179,8 +178,8 @@ 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:
 
 .. math::
-
     :label: e-J,Gamma,n-CH4
+
         |J,\Gamma,n\rangle = \sum_{k} T_{n,k}^{(J,\Gamma)} | J,k,m\rangle.