On the use of action‐angle variables for direct solution of classical nonreactive 3D (Di) atom–diatom scattering problems

Rotational Energy Transfer in Highly Excited States of Lithium Dimer: Experiment and Modeling

We report level-resolved rate coefficients for collision-induced rotational energy transfer in the ⁷Li₂^*-Ne system, with ⁷Li₂^* in the highly electronically excited E(3)¹Σ_g⁺(v_i = 4, j_i = 31) and F(4)¹Σ_g⁺(v_i = 10, j_i = 31) states. The distributions of rate coefficients are strikingly different from those previously measured for the A(1)¹Σ_u⁺(v_i = 2-24, j_i = 30) state of the same molecule, falling off much more rapidly with increasing rotational quantum number change |Δj|. The reason for the difference was explored by means of an inverse Monte Carlo approach employing classical trajectories and a model potential, which was adjusted to give agreement with experiment. The modeling strongly suggests that the E and F state interaction potentials are much more nearly isotropic than that of the A state. The resulting dramatic reduction in rate coefficient, especially for large |Δj|, may be relevant in the relaxation of gases at high temperatures.

Crossing the dividing surface of transition state theory. III. Once and only once. Selecting reactive trajectories

The purpose of the present work is to determine initial conditions that generate reacting, recrossing-free trajectories that cross the conventional dividing surface of transition state theory (i.e., the plane in configuration space passing through a saddle point of the potential energy surface and perpendicular to the reaction coordinate) without ever returning to it. Local analytical equations of motion valid in the neighborhood of this planar surface have been derived as an expansion in Poisson brackets. We show that the mere presence of a saddle point implies that reactivity criteria can be quite simply formulated in terms of elements of this series, irrespective of the shape of the potential energy function. Some of these elements are demonstrated to be equal to a sum of squares and thus to be necessarily positive, which has a profound impact on the dynamics. The method is then applied to a three-dimensional model describing an atom-diatom interaction. A particular relation between initial conditions is shown to generate a bundle of reactive trajectories that form reactive cylinders (or conduits) in phase space. This relation considerably reduces the phase space volume of initial conditions that generate recrossing-free trajectories. Loci in phase space of reactive initial conditions are presented. Reactivity is influenced by symmetry, as shown by a comparative study of collinear and bent transition states. Finally, it is argued that the rules that have been derived to generate reactive trajectories in classical mechanics are also useful to build up a reactive wave packet.

Crossing the dividing surface of transition state theory. II. Recrossing times for the atom-diatom interaction

We consider a triatomic system with zero total angular momentum and demonstrate that, no matter how complicated the anharmonic part of the potential energy function, classical dynamics in the vicinity of a saddle point is constrained by symmetry properties. At short times and at not too high energies, recrossing dynamics is largely determined by elementary local structural parameters and thus can be described in configuration space only. Conditions for recrossing are given in the form of inequalities involving structural parameters only. Explicit expressions for recrossing times, valid for microcanonical ensembles, are shown to obey interesting regularities. In a forward reaction, when the transition state is nonlinear and tight enough, one-fourth of the trajectories are expected to recross the plane R = R* (where R* denotes the position of the saddle point) within a short time. Another fourth of them are expected to have previously recrossed at a short negative time, i.e., close to the saddle point. These trajectories do not contribute to the reaction rate. The reactive trajectories that obey the transition state model are to be found in the remaining half. However, no conclusion can be derived for them, except that if recrossings occur, then they must either take place in the distant future or already have taken place in the remote past, i.e., far away from the saddle point. Trajectories that all cross the plane R = R* at time t = 0, with the same positive translational momentum P(R*) can be partitioned into two sets, distinguished by the parity of their initial conditions; both sets have the same average equation of motion up to and including terms cubic in time. Coordination is excellent in the vicinity of the saddle point but fades out at long (positive or negative) times, i.e., far away from the transition state.

Crossing the dividing surface of transition state theory. I. Underlying symmetries and motion coordination in multidimensional systems

The objective of the present paper is to show the existence of motion coordination among a bundle of trajectories crossing a saddle point region in the forward direction. For zero total angular momentum, no matter how complicated the anharmonic part of the potential energy function, classical dynamics in the vicinity of a transition state is constrained by symmetry properties. Trajectories that all cross the plane R = R* at time t = 0 (where R* denotes the position of the saddle point) with the same positive translational momentum P(R*) can be partitioned into two sets, denoted "gerade" and "ungerade," which coordinate their motions. Both sets have very close average equations of motion. This coordination improves tremendously rapidly as the number of degrees of freedom increases. This property can be traced back to the existence of time-dependent constants of the motion.

Nearly resonant multidimensional systems under a transient perturbative interaction

We analyze the response of a classical system with N>or=2 internal degrees of freedom satisfying R<or=(N-1) approximated resonance conditions to an external perturbative transient interaction. Under certain assumptions on the system internal frequencies and on the coupling interaction, we show the precise N-R adiabatic invariants and obtain an estimate of the span of the domain defined by the intersecting resonances. The results are illustrated considering a system of three anharmonic oscillators transiently coupled by an explicitly time-dependent interaction, and applied to the low energy vibro-rotationally inelastic collisions between two diatomic molecules.

Role of diffusion in excitation energy transfer and migration

Effect of diffusion on excitation energy transfer and migration in a dye pair sodium fluorescein (donor) and Rhodamine-6G (acceptor) has been studied for different viscosities by both steady state and time domain fluorescence spectroscopic measurements. The donor-donor interaction appears to be weaker as compared to donor-acceptor interaction and thus favors direct Forster-type energy transfer. Interestingly, at low viscosity (water in this case) transfer appears to be controlled by material diffusion/energy migration. Further, acceptor dynamics reveals the fact that direct Forster transfer dominates in viscous media.