Rotational energy surfaces and high-J eigenvalue structure of polyatomic molecules

Abstract

A rotational analog of the vibrational potential energy surface is introduced for describing the rotational fine structure of polyatomic molecules. Classical trajectories on rotational energy (RE) surfaces are related to quantum rotational eigenvalue structure. Interpretation of RE surfaces shows how very different types of molecules may undergo dynamical symmetry breaking and a corresponding clustering of rotational energy sublevels for high angular momentum (J>10). Cluster splitting and spacing are calculated using semiclassical quantization methods. Some consequences of dynamical symmetry breaking such as mixing of nuclear spin species are discussed qualitatively.

Bifurcation in rotational spectra of nonlinear AB2 molecules

“…Energy level clustering in molecules is very interesting phenomenon, which has been studied for about twenty years [1,2,3,4]. However the main interest was concentrated on highly symmetrical molecules like tetrahydrides.…”

Phase space lattices with threefold symmetry

“…We give canonically invariant expressions, which can be derived in a non-rigorous way using the transfer matrix approach to WKB theory. These formulae may find applications in other problems involving systems with rotational symmetry in phase space, such as the rotational spectra of heavy, highly symmetric molecules (Harter and Patterson 1984). Our extensive numerical results provide evidence that these formulae are correct.…”

Studies of Rotational-Vibrational Dynamics in Highly Excited HDO Molecule

“…They introduced the classical rotational energy surface (CRES) which proved to be very helpful in understanding the qualitative features of RV spectra of such molecules [6,7]. The results presented in Table I and discussed When higher excitations are taken into account some new phenomena, generally connected with the RV coupling, perturb the clear picture presented above.…”

“…Among the states of this regime the most distinct is the state Kτ = 5 1 for which (J2x) and Βz reach their maxima, whereas Βx is minimum. This is the separatrix state, which is the quantum analog of the separatrix trajectory on the classical rotational energy surface (CRES) introduced by Harter and Patterson [6].…”

“…The large number of classical and semiclassical investigations [6][7][8][9][10][11][12] is a consequence of the fact that, in contrast to the traditional quantum methods, classical mechanics provides means for gathering information about the approximate dynamics in high-J regimes.…”