## 1.3. Nonrotating-Molecule Hamiltonian

The electronic and vibrational Hamiltonian associated with the nonrotating
molecule, as well as its energy levels and wave functions, will not be
considered in detail in this monograph.

Electronic energies and wave functions for the nonrotating molecule can be
determined from ab initio or semi-empirical treatments of the many electron
problem. The former calculations require extremely sophisticated computer
programs and many hours of computer time; the latter calculations are not
always quantitatively reliable. It will be seen below that matrix elements and
energy levels associated with the electronic part of the nonrotating-molecule
problem can usually be represented by a small number of parameters in the
calculation of the rotational energy levels.

Vibrational energies and wave functions for the nonrotating molecule can be
determined more easily than electronic energies and wave functions. Thus,
vibrational effects can be taken into account explicitly in many cases. We
shall consider only one vibrational effect in this monograph (see
sect. 4.7).

Because the nonrotating-molecule Hamiltonian is not considered in detail in
calculations of rotational energy levels, it is often represented simply by the
symbol .
Sometimes it is of interest to consider spin-orbit interaction explicitly; then
the nonrotating-molecule Hamiltonian is represented by
+ *A***L · S** or by + Σ_{i}
ξ(*r*_{i})
**l**_{i} ·
**s**_{i }, where **L** and **S** are operators
representing the total electronic orbital and total electronic spin angular
momenta respectively, and where **l**_{i} and
**s**_{i} are operators representing the same two momenta for
the individual electrons. The spin-orbit interaction operator
*A***L · S** is used to compute spin splittings
*within a given spin multiplet*. If interactions between states belonging
to different *S* or *L* values must be taken into account, then the
operator Σ_{i} ξ(*r*_{i})
**l**_{i} · **s**_{i}
must be used.