Isomerization dynamics of a buckled nanobeam

We analyze the dynamics of a model of a nanobeam under compression. The model is a two mode truncation of the Euler-Bernoulli beam equation subject to compressive stress. We consider parameter regimes where the first mode is unstable and the second mode can be either stable or unstable, and the remaining modes (neglected) are always stable. Material parameters used correspond to silicon. The two mode model Hamiltonian is the sum of a (diagonal) kinetic energy term and a potential energy term. The form of the potential energy function suggests an analogy with isomerisation reactions in chemistry. We therefore study the dynamics of the buckled beam using the conceptual framework established for the theory of isomerisation reactions. When the second mode is stable the potential energy surface has an index one saddle and when the second mode is unstable the potential energy surface has an index two saddle and two index one saddles. Symmetry of the system allows us to construct a phase space dividing surface between the two "isomers" (buckled states). The energy range is sufficiently wide that we can treat the effects of the index one and index two saddles in a unified fashion. We have computed reactive fluxes, mean gap times and reactant phase space volumes for three stress values at several different energies. In all cases the phase space volume swept out by isomerizing trajectories is considerably less than the reactant density of states, proving that the dynamics is highly nonergodic. The associated gap time distributions consist of one or more `pulses' of trajectories. Computation of the reactive flux correlation function shows no sign of a plateau region; rather, the flux exhibits oscillatory decay, indicating that, for the 2-mode model in the physical regime considered, a rate constant for isomerization does not exist.Comment: 42 pages, 6 figure

Dynamical tunneling in molecules: Quantum routes to energy flow

Dynamical tunneling, introduced in the molecular context, is more than two decades old and refers to phenomena that are classically forbidden but allowed by quantum mechanics. On the other hand the phenomenon of intramolecular vibrational energy redistribution (IVR) has occupied a central place in the field of chemical physics for a much longer period of time. Although the two phenomena seem to be unrelated several studies indicate that dynamical tunneling, in terms of its mechanism and timescales, can have important implications for IVR. Examples include the observation of local mode doublets, clustering of rotational energy levels, and extremely narrow vibrational features in high resolution molecular spectra. Both the phenomena are strongly influenced by the nature of the underlying classical phase space. This work reviews the current state of understanding of dynamical tunneling from the phase space perspective and the consequences for intramolecular vibrational energy flow in polyatomic molecules.Comment: 37 pages and 23 figures (low resolution); Int. Rev. Phys. Chem. (Review to appear in Oct. 2007

A Quantum Mechanical Study of Ozone Isotope Effect

The rate of ozone recombination, O2 + O + M → O3 + M, is strongly sensitive to the masses of the participating oxygen isotopes—the effect ultimately leading to the unconventional fractionations of ozone isotopomers in the Earth atmosphere. The mass dependence for asymmetric molecules is reconstructed, within the strong collision approximation, from the partial widths of narrow resonances of O3 and demonstrated to stem from the contributions of highly rotationally excited ozones

Comment on: ‘Theory of the photodissociation of ozone in the Hartley continuum: Potential energy surfaces, conical intersections, and the photodissociation dynamics’

We demonstrate in this Comment that the quantum mechanical absorption spectrum of the Hartley band of ozone, calculated using the diabatic B state potential energy surface constructed from the ab initio data of the title paper, is strongly structured. This result, which is in agreement with previous theoretical studies of the Hartley band, contradicts the findings of Baloïtcha and Balint-Kurti and questions the accuracy of their calculations

Comment on: ‘Theory of the photodissociation of ozone in the Hartley continuum; effect of vibrational excitation and O(¹D) atom velocity disribution.’

In this Comment we present quantum mechanical absorption spectra of the Hartley band originating from the four vibrationally excited levels of the ground electronic state. The calculations are performed using the diabatic B-state potential energy surface and the transition dipole moment vector constructed from the ab initio data of the title paper. The calculated spectra are multimodal (for the symmetric stretch pre-excitation) and strongly structured (for the symmetric stretch and bending pre-excitations). These results agree with the previous theoretical analysis and with the predictions of a simple model based on the reflection principle, but contradict the findings of Baloïtcha amd Balint-Kurti thus questioning the accuracy of their calculations