Exploring molecular vibrational motions with periodic orbits

A periodic orbit bifurcation analysis of vibrationally excited isotopologues of sulfur dioxide and water molecules: symmetry breaking substitutions

Theoretical predictions and assignment of highly excited vibrational states and their organization is one of the most important challenges in molecular spectroscopy. A systematic procedure to investigate such problems is locating the principal families of periodic orbits that emanate from the stationary points of the molecule and then following their evolution with the total energy. This results in constructing continuation/bifurcation diagrams that assist in locating the critical bifurcation energies and to discover new types of vibrational modes. Another parameter that may influence the dynamics of a molecule is isotopic mass substitution. In this article, we investigate the effect of symmetry breaking by isotopic mass substitution of triatomic molecules with C(2v) symmetry in classical and quantum dynamics. Sulfur dioxide and water molecules in their ground electronic state are studied by employing accurate potential energy surfaces. Continuation/bifurcation diagrams of periodic orbits are constructed by varying the energy and the mass of one oxygen atom of sulfur dioxide and one hydrogen atom of a water molecule. The transition from normal-to-local mode vibrations is studied in terms of a pitchfork to a center-saddle elementary bifurcation of periodic orbits. The results presented in this article aim to help the assignment of experimentally obtained spectra.

Chaotic scattering in a molecular system

We study the classical dynamics of bound state and scattering trajectories of the chlorine atom interacting with the HO molecule using a two-dimensional model in which the HO bond length is held fixed. The bound state system forms the HOCl molecule and at low energies is predominantly integrable. Below dissociation a number of bifurcations are observed, most notably a series of saddle-center bifurcations related to a 2:1 and at higher energies 3:1 resonance between bend and stretch motions. At energies above dissociation the classical phase space becomes dominated by a homoclinic tangle which induces a fractal distribution of singularities in all scattering functions. The structure of the homoclinic tangle is examined directly using Poincaré surfaces of section as well as indirectly through its influence on the time delay of the scattered chlorine atom and the angular momentum of the scattered HO molecule.

Resonances of CH2(ãA11) and their roles in unimolecular and bimolecular reactions

Low-lying resonances of the CH2(a 1A1) system (J=0) in an accurate ab initio potential energy surface are studied using a filter-diagonalization method. The width of these resonances fluctuates by more than two orders of magnitude and on average increases with the energy. Analysis of the resonance states concludes that the unimolecular decay of the excited molecular system near the dissociation threshold is neither mode specific nor statistical state specific. This is apparently due to remnant regularity embedded in the largely chaotic classical phase space, as evidenced by periodic orbit analysis. As a result, the Rice-Ramsperger-Kassel-Marcus and statistical adiabatic channel models overestimate the average unimolecular decay rate. The implications of the resonances for the bimolecular C(1D)+H2 reaction are also discussed.

The Huggins band of ozone: A theoretical analysis

The Huggins band of ozone is investigated by means of dynamics calculations using a new (diabatic) potential energy surface for the 3 (1)A'(1B2) state. The good overall agreement of the calculated spectrum of vibrational energies and intensities with the experimental spectrum, especially at low to intermediate excitation energies, is considered as evidence that the Huggins band is due to the two C(s) potential wells of the 1B2 state rather than the single C2v well of the 2 (1)A'(1A1) state. The vibrational assignment of the "cold bands," based on the nodal structure of wave functions, on the whole supports the most recent experimental assignment [J. Chem. Phys. 115, 9311 (2001)]. The quantum mechanical spectrum is analyzed in terms of classical periodic orbits and the structure of the classical phase space.

Octupolar perturbation of a single ion in a Penning trap

We investigate the classical dynamics of a single ion trapped in a Penning trap perturbed by a octupolar electrostatic perturbation that introduces nonlinearities in the motion. We show that the dynamics is controlled by a single external parameter that combines the influence of the electric and magnetic fields. Through the variation of this parameter, we explore the evolution of the phase space structure of the system by the numerical continuation of the families of periodic orbits.

HCP CPH ISOMERIZATION: Caught in the Act

▪ Abstract  In this overview we discuss the vibrational spectrum of phosphaethyne, HCP, in its electronic ground state, as revealed by complementary experimental and theoretical examinations. The main focus is the evolution of specific spectral patterns from the bottom of the potential well up to excitation energies of approximately 25,000 cm−1, where large-amplitude, isomerization-type motion from H–CP to CP–H is prominent. Distinct structural and dynamical changes, caused by an abrupt transformation from essentially HC bonding to mainly PH bonding, set in around 13,000 cm−1. They reflect saddle-node bifurcations in the classical phase space—a phenomenon well known in the nonlinear dynamics literature—and result in characteristic patterns in the spectrum and the quantum-number dependence of the vibrational fine-structure constants. Two polar opposites are employed to elucidate the spectral patterns: the exact solution of the Schrödinger equation, using an accurate potential energy surface and an effective or resonance Hamiltonian (expressed in a harmonic oscillator basis set and block diagonalized into polyads), which is defined by parameters adjusted to fit either the measured or the calculated vibrational energies. The combination of both approaches—together with classical mechanics and semiclassical analyses—provides a detailed spectroscopic picture of the breaking of one bond and the formation of a new one.