A NEW ISOTOPE EFFECT ON VIBRATIONAL-STATES - FROM HYPERSPHERICAL MODES OF H2O TO HYPERELLIPSOIDAL MODES OF HOT

Hyperspherical vibrational modes of H2O are distorted into hyperellips oidal modes of HOT due to symmetry breaking by isotopic substitution. Hyperellipsoidal modes are characterized by vibrational wavefunctions which extend along ellipsoidal-type arcs which cross the dissociative bond coordinates OH, OT perpendicularly. Within the simple two-dimensi onal Thiele-Wilson model of HOT, we discover a large series of hyperel lipsoidal modes which are characterized by v(3) = 9, 10, 11, ... nodes , indicating v(3), quanta in the vibrations along the ellipsoidal-type arcs. The start of this series at v(3) = 9 implies that hyperellipsoi dal modes exist only for highly excited energies, greater than or equa l to 3.4 eV above the vibrational ground-state. These quantum mechanic al results are discovered first empirically, and then explained in ter ms of illuminating semiclassical and quantum theories.