Reaction dynamics: rules change with molecular size.

Calculating the rate at which a chemical reaction occurs from first principles is a formidable task. Formulated in the most general sense, the problem encompasses 1) the characterization of how the constituent atoms interact with each other, 2) solving the dynamical problem of how the reactants move from educt to product, and 3) finally determining the rate from integrating over the initial state distribution. Concerning problem (1), quantum chemical methods developed since the 1960s have made tremendous progress in that it is now possible to compute accurate energies (better than fractions of a kcalmol ) for a sufficiently large number of configurations in the product and educt channel(s) of the reaction. Nevertheless, even with several 10000s of accurate single-point energies, the utility of such a potential energy surface is limited if it cannot be evaluated for any arbitrary relative geometry of the reactants. Therefore, the points need to be accurately represented (fitted) by a continuous, multidimensional function in order to allow seamless evaluation of energies for arbitrary geometries. An alternative to such a procedure is to carry out “on the fly” studies whereby energies are determined from a quantum chemical calculation for the present configuration of interest. However, such an approach is usually only viable for the smallest molecular systems, for short time scales (several picoseconds) and for a statistically insignificant number of trajectories. Addressing the dynamical problem (point 2 above) requires a method to solve the classical or quantum mechanical equations of motion to follow the temporal evolution of a system given the interaction potential and suitable initial conditions. The quantum mechanical problem—in the form of the timedependent Schrçdinger equation—can nowadays be solved rigorously without dimensional reduction for a system of up to four atoms. Again, this leads to a computationally demanding exercise. Instead, classical or semiclassical approaches have repeatedly and successfully been demonstrated to provide valuable and generally qualitatively, in many cases even quantitatively, correct results. This requires, however, averaging over a sufficiently large, statistically significant number of initial conditions. After solving problem (2), the reaction rate can be determined by counting the number of productive processes (final state analysis). The above program is sufficiently involved that early on more qualitative but still physically rigorous theories were developed. Amongst the most successful theories are transitionstate theory and its variants. A particular advantage of atomistic molecular dynamics simulations is that at every instant in time the full information about all atoms in the system (i.e. positions and velocities) is available and can be analyzed in unprecedented detail. By averaging over a large number of such individual events, contact can be made with experiment. Another long-standing, albeit qualitative, framework are the Polanyi rules that predict that “a barrier predominantly along the coordinate of approach [...] is best traversed by motion in that same coordinate, namely, reagent translation, whereas a barrier predominantly along the coordinate of separation [...] is best traversed by motion in that coordinate, that is, vibration in the bond under attack.” These rules were derived from experiments on H2 colliding with Cl and F-atoms and therefore generalization to more complex molecules with more internal degrees of freedom (see Figure 1) may require adaptation of the rules. Recent experiments on Cl+CHD3!HCl+CD3 challenged the validity of the Polanyi rules for low collision energies. Specifically, it was found that vibrational excitation of the CH stretch in CHD3 was no more effective in driving the reaction than translational energy. In order to shed more light on the underlying dynamics the above computational tour-de-force was followed by J. M. Bowman and G. Czako. To this end they computed 16000 points on the fully-dimensional potential energy