In molecular physics, the molecular term symbol is a shorthand expression of the group representation and angular momenta that characterize the state of a molecule, i.e. its electronic quantum state which is an eigenstate of the electronic molecular Hamiltonian. It is the equivalent of the term symbol for the atomic case. However, the following presentation is restricted to the case of homonuclear diatomic molecules, or other symmetric molecules with an inversion centre. For heteronuclear diatomic molecules, the u/g symbol does not correspond to any exact symmetry of the electronic molecular Hamiltonian. In the case of less symmetric molecules the molecular term symbol contains the symbol of the group representation to which the molecular electronic state belongs.
It has the general form:
where
- is the total spin quantum number
- is the projection of the orbital angular momentum along the internuclear axis
- is the projection of the total angular momentum along the internuclear axis
- indicates the symmetry or parity with respect to inversion () through a centre of symmetry
- is the reflection symmetry along an arbitrary plane containing the internuclear axis
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