Footnotes
- Figures in brackets indicate the literature
references.
- 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.
- 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.
- 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).
- 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.
- 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.
- Note that some early printings of [18]
contain sign errors in this table. All entries in the second and fourth rows
should be positive.
