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 + AL · 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 AL · 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.