Non-adiabatic coupling in the ozone molecule

The question whether a Berry phase should be included in the calculation of rovibronic states of the ozone molecule in its electronic ground state has been addressed in the present work. Since several conical intersections connect the three lowest singlet states, a phase of pi generated by a symmetry-demanded conical intersection between states 2 and 3 might be present, or it might be compensated by further conical intersections. Hyperspherical coordinates were employed here as they provide a natural choice for the cyclic coordinate that is needed to investigate the presence or absence of such a topological phase. On a hyperspherical grid, we have computed the electronic energies of the three lowest singlet states using a multi-reference configuration interaction procedure. Non-adiabatic coupling terms (NACTs) along the cyclic variable were evaluated numerically. Investigation of the behaviour of the adiabatic-to-diabatic transformation angles, using the quantisation criterion of the NACTs [M. Baer and A. Alijah, Chem. Phys. Lett. 319, 489 (2000)], shows that a geometrical phase is retained. This phase has no practical effect on the well-established energy values of the rovibrational states located deeply in the three equivalent C-2v potential wells, but will come into action as highly excited states reach the dissociation region.