Vibronic reduction factors in E ⊗ (β1 + β2) and their Berry’s phase manifestations

In a linearly coupled dihedral E ⊗ (β1 + β2) Jahn–Teller system one finds two different q-factors (say, q1 and q2) and a p-factor. For stronger β1- than β2-coupling, one obtains q1 > q2 and in the strong linear vibronic coupling limit, q1 → 0.5, q2 → 0. At all strengths, the historical relation “p = 2q − 1” turns into p = q1 + q2 − 1. A slowly rotating external field induces in the electronic wave-functions, upon a full turn, a Berry’s phase equal to the solid angle subtended by the field’s vector at the origin. We have calculated (by employing a quasi-classical approximation to solve the dynamic problem for the ground vibronic state) the corresponding phase change, now diminished by the vibronic reduction factors.