It is shown that standard computations of electronic structures of polyatomic systems that yield the global minimum configuration and vibrational frequencies may be faulty if the symmetry of this configuration is lower than the highest possible one and the origin of this distortion, which is always due to the Jahn-Teller effect, is neglected; this may lead, in particular, to the loss of the Berry phase factor that changes the vibronic energy level spectrum and which we show to be present even when there are no apparent conical intersections. The general case and the ozone molecule are analyzed.