John S. Hutchinson

Nonlinear resonances and vibrational energy flow in model hydrocarbon chains

Intramolecular energy transfer in hydrocarbons is modeled with an anharmonic HC bond coupled to a chain of harmonically coupled carbon atoms. The HC stretch is initially excited to various vibrational states and the flow of energy from the HC bond is observed. It is found that, at sufficiently high excitation, vibrational energy flow is irreversible and occurs on a time scale of roughly 100 fs, independent of chain length. This corresponds very well to experimentally observed spectral bandwidths. By analyzing the motion in a set of natural dynamical modes, it is shown that this energy transfer is due to sequential nonlinear resonances in the chain. Analytic modeling of the mode–mode couplings then provides a simple approximate description of the energy transfer process.

Quantum dynamics of energy transfer between bonds in coupled Morse oscillator systems

The quantum dynamic flow of energy between coupled anharmonic bonds is calculated and analyzed for ABA triatomics with a massive central atom. The time dependence of quantum ‘‘normal mode’’ states is found to be classical in nature, but for states which are classically local, purely quantum energy flow between bonds occurs. We show that the mechanism for this quantum energy flow between local modes can be understood as an indirect state‐to‐state flow of probability, involving normal mode intermediary states. In particular, there is a regime in which rapid energy flow—which is classically forbidden—occurs from nonclassical states in the quantum case. Criteria are presented for the existence of purely quantum, and classically impossible, flow of energy between oscillators. Initially prepared states are accordingly classified as normal mode states, quantum local mode states, or nonclassical states, according to the extent and rate of bond–bond energy flow, the sensitivity of the process to small asymmetries,...

Quantum dynamic analysis of energy transfer in model hydrocarbons

Abstract The quantum dynamic flow of energy out of an initially excited CH bond in a model hydrocarbon is calculated numerically. The results are interpreted in terms of a state-to-state flow of probability and contrasted to classical trajectory, ensemble averages. We show that quantum energy flow has a direct classical interpretation in terms of sequential non-linear resonances. We also present evidence for and the mechanism of significant short-time non-classical effects in the quantum energy flow.

A model for impulsive mode–mode energy transfer in highly vibrationally excited molecules

The classical dynamics of mode–mode vibrational energy transfer are investigated for a coupled Morse oscillator system by explicitly integrating Hamiltonian’s equations in action–angle coordinates. This method permit the identification of specific oscillator phase relationships which dictate the extent and timing of large‐scale, nonperiodic energy transfer; we term this ‘‘impulsive energy transfer.’’ In previous classical trajectory studies, such impulsive events have been related to the dynamics of isomerization immediately prior to reaction. A qualitative understanding of the required phase relationships for impulsive energy transfer is gained via the Chirikov hindered rotor analysis, usually applied to resonant energy flow. The implications of the model are illustrated in a three mode isomerization system.

Local-mode overtones. Ultrashort pulse excitation, intramolecular relaxation and unimolecular reactions

The dynamics of the preparation of local-mode overtone states in model systems have been considered where the excitation competes with relaxation of the initial state into either a reaction continuum or an intramolecular quasi-continuum. The overtone excitation process is many orders of magnitude slower than either vibrational relaxation or unimolecular decay, so that the prepared state is actually not localized. We demonstrate that when a continuum or quasi-continuum is present the prepared state is a sensitive function of the duration of the excitation pulse. Correspondingly, the absorption spectrum depends on the pulse duration, particularly when the pulse length is comparable to the IVR or reaction time. As such, ultrashort laser pulses are capable of probing the detailed intramolecular vibrational dynamics associated with decay of localized excitations. In the case of intramolecular relaxation into a quasi-continuum of vibrational bath states, the pulse-length-dependent spectrum reveals a sequential appearance of states which contribute to IVR. We have labelled these states as IVR resonances. In the case of unimolecular decay into a reactive continuum, the photochemical yield can be a non-monotonic function of the pulse length. This indicates the simultaneous competition amongst ultrashort pulse excitation, intramolecular dynamics and unimolecular reaction.

Oscillator phase and the reaction dynamics of HN3 : A model for correlated motion

The reaction coordinate for a unimolecular dissociation reaction is intrinsically anharmonic, therefore the period of vibration depends upon the energy in the bond. Consequently, the final few vibrations leading up to and including reaction can occur over very different time scales, depending upon the amount of vibrational energy in the reaction coordinate. In recent studies, we have compared ensembles of reactive trajectories and have observed correlations in molecular motions during reaction leading up to the transition state. If the comparison is made in time, differences in the periods of the reaction coordinate vibration can obscure these correlations. However, if the reactions are compared vibration by vibration (i.e., coherently) clear patterns of vibrational motions emerge in the reaction dynamics. In this paper, we introduce a new application of the Hilbert transform to assign oscillator phases to the motions of anharmonic oscillators, which permits coherent comparison of trajectories. We also demonstrate by several examples that, when compared coherently, reaction dynamics of HN3 exhibit order which is not evident in time series comparisons. These orderly patterns of motions reflect the intramolecular conditions necessary for reaction to occur. We propose a model to account for the observed correlated motion in terms of the requirements for intramolecular energy transfer. As a consequence of the constraints of energy transfer, the phases of several oscillators have clearly defined relative values. Physically this corresponds to a correlation in the vibrations of several modes such that (for example) two key bonds always extend simultaneously during the course of reaction. Since the motions of atoms preceding reaction are not random, but rather follow a specific pattern, a restricted set of reactant states immediately precede reaction.