  We treat a system (a molecule or a solid) in which electrons are coupled
linearly to any number and type of harmonic oscillators and which is further
subject to external forces of arbitrary symmetry. With the treatment restricted
to the lowest pair of electronic states, approximate "vibronic"
(vibration-electronic) ground state wave functions are constructed having the
form of simple, closed expressions. The basis of the method is to regard
electronic density operators as classical variables. It extends an earlier
"guessed solution", devised for the dynamical Jahn-Teller effect in cubic
symmetry, to situations having lower (e.g., dihedral) symmetry or without any
symmetry at all. While the proposed solution is expected to be quite close to
the exact one, its formal simplicity allows straightforward calculations of
several interesting quantities, like energies and vibronic reduction (or Ham)
factors. We calculate for dihedral symmetry two different $q$-factors ("$q_z$"
and "$q_x$") and a $p$-factor. In simplified situations we obtain $p=q_z +q_x
-1$. The formalism enables quantitative estimates to be made for the dynamical
narrowing of hyperfine lines in the observed ESR spectrum of the dihedral
cyclobutane radical cation.
