We present an overview of the current status of transition-state theory and its generalizations. We emphasize (i) recent improvements in available methodology for calculations on complex systems, including the interface with electronic structure theory, (ii) progress in the theory and application of transition-state theory to condensed-phase reactions, and (iii) insight into the relation of transition-state theory to accurate quantum dynamics and tests of its accuracy via comparisons with both experimental and other theoretical dynamical approximations.

Current status of transition-state theory

Theories of intramolecular vibrational energy transfer

Coupled nonlinear Hamiltonian systems are known to exhibit regular (quasiperiodic) and chaotic classical motions. In this and the preceding paper by Jaffe and Reinhardt, we find substantial short time regularity even in the chaotic regions of phase space for what appears to be a large class of systems. This regularity is demonstrated by the behavior of approximate constants of motion calculated by Pade summation of the Birkhoff–Gustavson normal form expansion and is attributed to remnants of destroyed invariant tori in phase space. The remnant toruslike manifold structures are used to suggest justification for use of Einstein–Brillouin–Keller semiclassical quantization procedures for obtaining quantum energy levels even in the absence of complete tori and to form a theoretical basis for the calculation of rate constants for intramolecular mode–mode energy transfer. These results are illustrated in a thorough analysis of the Henon–Heiles oscillator problem. Possible generality of the analysis is shown by b...

Approximate constants of motion for classically chaotic vibrational dynamics - Vague tori, semiclassical quantization, and classical intramolecular energy flow

A semiclassical model for tunneling from one classically allowed region on a potential energy surface to another is described. The principal feature of this model, compared to earlier (more ‘‘rigorous’’) multidimensional semiclassical tunneling theories, is that it can be implemented in a straightforward way within the framework of a standard classical trajectory simulation. Applications to several examples of unimolecular isomerization and unimolecular dissociation show that the model is capable of providing excellent results over a wide range of conditions (i.e., coupling strengths, different symmetries of couplings, etc.)

A semiclassical tunneling model for use in classical trajectory simulations

New quantum chemistry calculations (with a triple zeta plus polarization basis set, and a single and double configuration interaction) have been carried out to determine the equilibrium points and the transition state for the vinylidene (H2C=C:)→acetylene (HC≡CH) isomerization. A classical barrier height (i.e., with no zero point energy effects) of 6.3 kcal/mol is obtained, and application of the Davidson correction for unlinked clusters reduces this to 5.4 kcal/mol. Our best estimate is that the true classical barrier lies in the range 2–4 kcal/mol. The dynamics of the vinylidene/acetylene isomerization is described with the framework of the reaction path Hamiltonian. The lifetime of vinylidene (in its ground vibrational state) with respect to this process is calculated to be 0.24 to 4.6 ps for a classical barrier of 2 to 4 kcal/mol. This lifetime decreases by a factor of ∼2 if one quantum of the CH2 scissors mode of vinylidene is excited, but is predicted to increase somewhat if a quantum of the C–C str...

Vinylidene: Potential energy surface and unimolecular reaction dynamics

Essentially exact quantum mechanical calculations are carreid out to determine the energies and lifetimes of the quasibound states for a system of two (nonlinearly) coupled oscillators (one of which is harmonic, the other being able to dissociate). For weak coupling the system displays mode specificity, i.e., the unimolecular rate constants are not a monotonic function of the total energy, but increased coupling and frequency degeneracy tends to destroy mode specificity. A somewhat surprising result is that for a given coupling the degree of mode specificity is roughly independent of the energy, in marked contrast to the fact that there is an energetic threshold for the onset of ’’stochastic trajectories’’ of the corresponding classical system: i.e., there seems to be no relation between statistical/mode‐specific behavior of the unimolecular rate constants and stochastic/regular classical trajectories. In order to be able to treat more physically relevant models—i.e., those with more than two degrees of f...

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Model studies of mode specificity in unimolecular reaction dynamics

Energies and lifetimes (with respect to tunneling) for metastable states of the Henon–Heiles potential energy surface [V(x,y) = 1/2x2−1/3x3+1/2y2+xy2] have been computed quantum mechanically (via the method of complex scaling). This is a potential surface for which the classical dynamics is known to change from quasiperiodic at low energies to ergodic‐like at higher energies. The rate constants (i.e., inverse lifetimes) for unimolecular decay as a function of energy, however, are seen to be well described by standard statistical theory (microcanonical transition state theory, RRKM plus tunneling) over the entire energy region. This is thus another example indicating that mode specificity in unimolecular reaction dynamics is not determined solely by the quasiperiodic/ergodic character of the intramolecular mechanics.

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Mode specificity in unimolecular reaction dynamics: The Henon-Heiles potential energy surface

Ion/molecule reaction products of cobalt cluster ions have been characterized using mass spectrometric techniques. Atomic and bare‐metal cluster ions were desorbed from foils by particle bombardment within a high‐pressure (0.1–0.2 Torr) ion source. Sputtered metal cluster ions react with O2 to produce abundant stoichiometric or nearly stoichiometric cobalt(II) oxide cluster ions. The positive cluster product ions consist of three types: oxygen‐deficient [Co(CoO)x]+ clusters, oxygen‐equivalent [(CoO)x]+ clusters, and (in less abundance) metal‐deficient [(CoO)xO]+ clusters. Tandem mass spectrometry and collision spectroscopy provide structural information about the more abundant cobalt cluster product ions. A major collision‐induced fragmentation pathway for the oxygen‐equivalent [(CoO)x]+ clusters is the loss of a CoO moiety to form [(CoO)x−1]+ fragments. A major collision‐induced fragmentation pathway for the oxygen‐deficient [Co(CoO)x]+ clusters is the loss of a cobalt atom to yield [(CoO)x]+ fragments. ...

The role of cluster ion structure in reactivity and collision‐induced dissociation: Application to cobalt/oxygen cluster ions in the gas phase

A semiclassical multichannel branching model is developed and applied to various dynamical phenomena in polyatomic molecular systems. The model is based on the reaction path Hamiltonian of Miller, Handy, and Adams [J. Chem. Phys. 72,99 (1980)] and also utilizes the semiclassical perturbation‐infinite order sudden approximation of Miller and Shi [J. Chem. Phys. 75, 2258 (1981)] for describing vibrational inelasticity along the reaction path. Specific applications of the model are made to state‐specific unimolecular decomposition, energy level splitting in multidimensional double‐well potentials, and to reaction probabilities along reaction paths with multiple transition states.

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A semiclassical multichannel branching model for describing state‐specific unimolecular decomposition and other dynamical processes in polyatomic molecular systems

A parameter‐free theoretical determination of the rotational state distribution of the CN fragment from photodissociation of ClCN at 193 nm is presented. The ground‐ and excited‐state potential energy surfaces are calculated at a grid of points corresponding to bent and linear geometries using density functional theory. The points are fit to a functional form similar to one used previously in model studies of the effects of bending forces during ICN photodissociation. Rotational state distributions are obtained by a modified quasiclassical method. Comparison of the results obtained at 0 and 300 K are in excellent agreement with experimental determination of the rotational state distribution of the CN fragment for ClCN photodissociation. The importance of the bending force in the excited state (which results in extensive population in the rotational states j=50–65 of the CN fragment) is discussed.

Boyd A. Waite

Papers

Model studies of mode specificity in unimolecular reaction dynamics

Mode specificity in unimolecular reaction dynamics: The Henon-Heiles potential energy surface

The role of cluster ion structure in reactivity and collision‐induced dissociation: Application to cobalt/oxygen cluster ions in the gas phase

A semiclassical multichannel branching model for describing state‐specific unimolecular decomposition and other dynamical processes in polyatomic molecular systems

The photodissociation of ClCN: A theoretical determination of the rotational state distribution of the CN fragment