page_title: Symmetry of diatomic molecules
section_title: Point groups for diatomic molecules
hierarchical_section_title: Symmetry of diatomic molecules / Point groups for diatomic molecules
caption_attribution_description: Pictorial representation of action by creation and annihilation operators on Bosonic Fock state.
context_page_description: Molecular symmetry in physics and chemistry describes the symmetry present in molecules and the classification of molecules according to their symmetry. Molecular symmetry is a fundamental concept in the application of Quantum Mechanics in physics and chemistry, for example it can be used to predict or explain many of a molecule's properties, such as its dipole moment and its allowed spectroscopic transitions, without doing the exact rigorous calculations. To do this it is necessary to classify the states of the molecule using the irreducible representations from the character table of the symmetry group of the molecule. Among all the molecular symmetries, diatomic molecules show some distinct features and they are relatively easier to analyze.
context_section_description: There are two point groups for diatomic molecules:  for heteronuclear diatomics, and  for homonuclear diatomics.
  :
  The group , contains rotations  through any angle  about the axis of symmetry and an infinite number of reflections  through the planes containing the inter-nuclear axis (or the vertical axis, that is reason of the subscript 'v').In the group  all planes of symmetry are equivalent, so that all reflections  form a single class with a continuous series of elements; the axis of symmetry is bilateral, so that there is a continuous series of classes, each containing two elements . Note that this group is Non-abelian and there exists an infinite number of irreducible representations in the group. The character table of the group is as follows:
  :
  
  In addition to axial reflection symmetry, homonuclear diatomic molecules are symmetric with respect to inversion or reflection through any axis in the plane passing through the point of symmetry and perpendicular to the inter-nuclear axis.
    The classes of the group  can be obtained from those of the group  using the relation between the two groups: . Like ,  is  non-Abelian and there are an infinite number of irreducible representations in the group. The character table of this group is as follows:
caption: Inversion symmetry in homonuclear diatomic molecules, giving rise to symmetry group 
    
      
        
          
            
              
                D
              
              
                ∞
                h
              
            
          
        
      
      {\displaystyle {{D}_{\infty h}}}
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