Since the behavior of an interaction term under either of these two latter operations can be reversed simply by multiplying the term by a pure imaginary constant, Dorney and Watson [66,67] have suggested considering the transformation properties of operators with respect to the product of both operations. The transformation properties of terms with respect to this compound operation are invariant to multiplication by a complex constant. Since the Hamiltonian for a molecule in free space must be invariant to both Hermitian conjugation and time reversal, only terms which are invariant to the product of these two operations can occur in the Hamiltonian. Of course, a term allowed in the Hamiltonian under time-reversal × Hermitian-conjugation may still require multiplication by some complex constant to be acceptable under either time reversal or Hermitian conjugation individually.
Further discussion of the individual operations of time reversal and Hermitian conjugation or of the compound operation of time-reversal followed by Hermitian conjugation will not be given here, except to say that considerations of this kind have raised questions [45, 68] concerning two of the higher-order vibration-rotation interaction terms recently introduced by Susskind  .