Table of Contents of Rotational Energy Levels and Line Intensities in Diatomic Molecules


  1. Figures in brackets indicate the literature references.

  2. The material cited here deals with a rotating diatomic molecule in which electron spin is ignored. It can be seen from the discussion in [3] that a closely analogous treatment can be carried out in which spin is included.

  3. Note that Van Vleck's paper deals with nonlinear molecules. Because of the absence of the third Eulerian angle in linear molecules, his arguments must be altered somewhat for diatomic molecules. No elegant discussion of this problem exists [9]. Note also, that we have ignored in eq (1.14) the quantum number M occurring in the wave functions |Ω J M⟩, since the operators J+, J-, and Jz are all diagonal in M and independent of M.

  4. Actually, both S and Σ are slightly bad quantum numbers, but the results originally given by Hill and Van Vleck did not allow for this. The fact that S and Σ are not perfectly good quantum numbers can be taken into account by the introduction of small parameters γ analogous to the γ in eq (1.15).

  5. Hund's case (a) energy levels are obtained if all terms other than the first in (1.11) are ignored. Since we are interested here in studying a transition between Hund's case (a) and Hund's case (b), only the fourth and fifth terms in (1.11) were ignored in deriving (1.19). It is the third term in (1.11), i.e., B(S2 - Sz2), which contributes the + ½B present in (1.21) but normally absent in Hund's case (a) energy level expressions.

  6. Standard spectroscopic notation leads to a little confusion here, since the symbol Σ represents both an electronic state characterized by Λ = 0, e.g., a 3Σ state, and also the projection of S along the internuclear axis, e.g., Σ =  1, 0.

  7. Note that some early printings of [18] contain sign errors in this table. All entries in the second and fourth rows should be positive.

Table of Contents