Rotational symmetry and degeneracy: a cotangent-perturbed rigid rotator of unperturbed level multiplicity

2005

We investigate the classical mechanics of diatomic and symmetric top molecules in tilted fields. These molecules exhibit regular, chaotic or mixed phase space depending on the tilt angle β, the energy E, and the relative intensity of the fields ω/∆ω. In the integrable collinear problem the projection of the angular momentum into the spatial z axis is a constant of motion, m, which allows us to explore the geometry of the phase space, and to use energy momentum diagrams to classify the motions of the rotor. For β = 0 the system is non-integrable showing mostly regular dynamics in the high-energy (free-rotor) and low-energy (pendular) limits; for energy near the tilted fields barrier the phase space is highly chaotic with degree of chaos increasing with β between 0 and π/2. Periodic orbits and bifurcation diagrams are obtained from symmetry lines and their iterations under the Poincaré map. These bifurcation diagrams are used to observe the changes in the basic structure of the phase space as β changes between collinear and perpendicular fields. Some quantum eigenstates are localized near stable or unstable periodic orbits showing tori quantization or scarring respectively. For asymmetric top molecules only the case of collinear fields is treated. In parallel fields m is a constant of the motion and it is possible to define an effective potential V m (θ, ψ). In an E-m diagram the equilibrium solutions of V m (θ, ψ) are curves that enclose regions of qualitatively different accessible θ-ψ configuration space. Interestingly these regions can be used to classify the quantum eigenstates. For plane rotors primitive semiclassical mechanics is used to calculate the rotational excitation caused by laser pulses. Depending on the pulse intensity and duration several methods are employed from the analytical sudden approximation to primitive semiclassical initial value representation (IVR) integrals. The calculated transition probabilities are in good agreement with the quantum probabilities considering the simplicity of the methods. In the case of plane rotors in electric fields we calculate energy spectra, orientation (cos ϕ), and alignment (cos 2 ϕ), using the Herman-Kluk propagator in terms of periodic coherent states. These results are in good agreement with the quantum analogues although the number of trajectories used is discouragingly large. For diatomic rotors in tilted fields, the HK propagator was used to calculate energy spectra with good agreement for high-energy and not very dense eigenspectra. Some steps are taken towards the development of HK-type propagator for rotational coherent states. BIOGRAPHICAL SKETCH Carlos Alberto Arango was born on September 6th, 1973, in the colonial city of Popayán Colombia. His family moved to the warmer city of Santiago de Cali in 1976 where he completed elementary and secondary education graduating from Colegio Americano in 1990. In the summer of 1991 he began college with major in Chemistry at Universidad del Valle in Cali, graduating in summer 1997 after finishing his thesis under the direction of Gustavo Sánchez. He continued studying in the same university obtaining a M.Sc. in chemistry in summer 2000, with thesis directed by professor Julio Arce. In summer 2000 he entered the Ph.D. program in

1984

The theory of the vibrational angular momentum terna ~t 2 in the effective molecular rotational Hamilton operator is briefly reviewed. Novel vibrational matrix elements of ~z, offdiagonal in the basis of the coupled linear oscillator basis functions, ate derived for asymmetric top molecules. These matrix elements contain two or three distinct vibrational quantum numbers, respectively. A group-theoretical scheme; the use of repeated Jahn's rules, is given for testing the existenoe of the proposed matrix elements. Finally suggestions are made for the application of the latter.

International Journal of Modern Physics E, 2004

We consider the generalized rotor Hamiltonians capable of describing quantum systems invariant with respect to symmetry point-groups that go beyond the usual D2-symmetry of a tri-axial rotor. We discuss the canonical de-quantisation procedure to obtain the classical analogs of the original quantum Hamiltonians. Classical and quantum solutions to the Hamiltonians relevant in the nuclear physics applications are illustrated and compared using the 'usual' (D2) and an…

1991

A recently proposed model for linear polyatomic molecules is investigated. New dynamical quantum variables (e's), associated to internal rotations and generic ofthese models, are exhibited. The e's and the angular momentum operators generate a rank-two semisimple Lie algebra. The associated Lie group is non-compact. The self-adjointness ofthe Hamiltonian is established. SI Notice that i-!~in eq. (23) of ref. [1] should be replaced by all "bond" distances, masses and (large) frequencies HC-(2M)'fl~M,C

Physical Chemistry Chemical Physics, 2011

We extend the A k q polarization-parameter model, which describes product angular momentum polarization from one photon photodissociation of polyatomic molecules in the molecular frame [J. Chem. Phys., 2010, 132, 224310], to the case of rotating parent molecules. The depolarization of the A k q is described by a set of rotational depolarization factors that depend on the angle of rotation of the molecular axis g. We evaluate these rotational depolarization factors for the case of dissociating diatomic molecules and demonstrate that they are in complete agreement with the results of Kuznetsov and Vasyutinskii [J. Chem. Phys., 2005, 123, 034307] obtained from a fully quantum mechanical approach of the same problem, showing the effective equivalence of the two approaches. We further evaluate the set of rotational depolarization factors for the case of dissociating polyatomic molecules that have three (near) equal moments of inertia, thus extending these calculations to polyatomic systems. This ideal case yields insights for the dissociation of polyatomic molecules of various symmetries when we compare the long lifetime limit with the results obtained for the diatomic case. In particular, in the long lifetime limit the depolarization factors of the A k 0 (odd k), Re(A k 1 ) (even k) and Im(A k 1 ) (odd k) for diatomic molecules vanish; in contrast, for polyatomic molecules the depolarization factors for the A k 0 (odd k) reduce to a value of 1/3, whereas for the Re(A k 1 ) (even k) and Im(A k 1 ) (odd k) they reduce to 1/5.