Vibronic potentials in chemical physics: adiabatic approximation vs. supersymmetry

We analyze the supersymmetric features of isolated double-well potentials, both symmetric ones and ones under an asymmetric perturbation. Our studies are in concert with results obtained elsewhere. Further on, a particular interest is paid to double- and single-valley potentials occurring in pairs on applying the adiabatic approximation to coupled electron-vibrational mode systems. Among the latter are Holstein's small polarons and the vibronic (off-center) band-species performing a finite-orbital-momentum helical motion. Our results seem to revive an earlier assertion for the existence of artifacts in the adiabatic approximation.