[ElvisSpencer]

Hi all -

This is my first post on this site.  I am preparing a literature seminar on current concepts in reaction dynamics from a theoretical and experimental point of view.  I have a question about the concept of non-statistical dynamics.  Could someone help clarify this concept to me?  I've written down my understanding of this, and welcome your thoughts/criticism.  Thanks!

Potential energy surfaces can be calculated and then used in understanding geometries and energies of reacting chemical species.  Reactant molecules can traverse a number of different paths (or trajectories) on their way through transition structures, intermediate structures, and on to products.  The statistical approximation allows for estimation of rate constants without needing to specify which trajectory is selected, by assuming that the rate of intramolecular vibrational energy redistribution is a lot faster than passage through a transition structure.  In other words, although structures in the transition region that may arrive via different trajectories and possess different vibrational energies - these energies statistically randomize rapidly to produce an ensemble of geometries and energies.

I think non-statistical dynamics refers to situations in which transition structures with different energies do not randomize - but instead exit the transition region via different trajectories to form product(s).  Is this correct?

Thanks again .

[Juan R.]

The 'standard' explanation, which I just copy and paste:

Nonstatistical dynamics can be summarised as follows. Most reactive intermediates are created with selective excitation of a small subset of their available vibrational modes. In thermal reactions there can be two sources of this selectivity: for reactions in which the intermediate sits on an energetic plateau or in a very shallow minimum, the selectivity arises primarily from the need to localize the excess energy of the reactant(s) in the reaction coordinate for formation of the intermediate. For reactions in which the intermediate occupies a relatively deep local minimum on the potential energy surface (PES), the largest contributor will be the potential energy (PE) to kinetic energy (KE) conversion that accompanies the progress from the first transition state to the intermediate. This conversion deposits energy in modes that are, in large measure, determined by the geometry differences of the stationary points for an intermediate and the transition structure from which it was formed. For photochemical reactions, the selectivity commonly arises from the PE to KE conversion that accompanies passage through a conical intersection.

The proposal of selective excitation is not, by itself, at odds with the standard statistical approximation to reaction kinetics. The distinction arises in what one thinks happens to these selectively excited species. Statistical models, by their very nature, assume that intramolecular vibrational energy redistribution (IVR) occurs much faster than conversion of the intermediate to any product, and hence that selective excitation has no mechanistic consequence.

Now, this above 'nomenclature' and the whole discourse in traditional chemical reaction literature are in conflict with most modern understanding.

Dynamics is a branch of mechanics. And statistical dynamics (there exists a textbook with this exact title by Radu Balescu, although it is devoted to classical theory only) is an extension of dynamics to study irreversibility, chaos, and fluctuations. This includes a mathematical extension of the Hilbert space used in quantum mechanics, for instance.

Dynamics (e.g. Newtonian laws, Schrödinger dynamics, etc.) is recovered from statistical dynamics in those simple cases when the statistical aspects are of no importance. E.g. the Schrödinger equation arises as approximation from a more general quantum equation of motion (see section III in paper cited below).

In this perspective, terms as "nonstatistical dynamics" used in chemical reaction literature are an oximoron. I find interesting when some chemist claims to make "MD simulation of nonstatistical dynamics", when "MD has also been termed statistical mechanics by numbers", which translates to "I am doing a statistical simulation of something nonstatistical", if was to be taken literally.

In my experience the literature on chemical reactions dynamics is outdated, non-rigorous, and sometimes plain wrong. Some traditional mistakes regarding irreversibility, chaos, and reductionism are corrected by I. Prigogine in his last paper Chemical Kinetics and Dynamics in

http://onlinelibrary.wiley.com/doi/10.1111/j.1749-6632.2003.tb06091.x/full

Note: Recent research seems to suggest that Prigogine theory can be obtained from a more general theory in Liouville space. See "A foundation for the Brussels-Austin theory" in

http://www.canonicalscience.org/publications/canonicalsciencetoday/20100531.html