Computational Molecular Kinetics concerns itself with the simulation of the rates of reactive molecular processes - whether this be individually or coupled into complex multi-component systems. For individual reactions, the theories of elementary chemical processes may be applied, supported by adequate quantum chemical data concerning the stabilities of the molecular species involved and the nature of the potential energy surface (barrier height, reaction pathways, etc). For complex systems (combustion, hypersonic reactive flows, solid state materials, soft materials, biomolecular systems), different combinations of methods must be applied. Sometimes direct molecular dynamics simulations can be a powerful approach. Sometimes individual reaction rate data must be coupled into a master equation, a computational fluid dynamics solver, or some other reaction network simulator. Whatever the case, it is fair to say that the output of a kinetic simulator - which aims at prediction of system evolution in real time - often depends critically on the quality of the input (kinetic and thermodynamic) data. Computational molecular kinetics provides an essential source of such data that is complementary to experimental approaches.

The detailed quantum simulation of chemical reactions is the most exact and complete approach to molecular kinetics - but it is also computationally very difficult and the numerical demands scale exponentially with the number of atoms in the system.  For larger molecular systems (perhaps five to hundreds of atoms) statistical theories have proven an economical and very powerful way of predicting reaction rates approximately.  Our group has been involved for many years in the development of improved statistical theories for chemical reaction rates - particularly for unimolecular and complex-forming bimolecular reactions  involving barrierless bond fragmentation processes, where the transition state is not well characterised by traditional methods. This work, which is ongoing, is summarized by Smith in a recent invited chapter: “Recent Developments in Statistical Rate Theory for Unimolecular and Complex-Forming Reactions”, pp291-328 in Modern Trends in Chemical Reaction Dynamics, vol I, Xueming Yang and Kopin Liu eds. (World Scientific, Singapore, 2004).

By way of illustration of the complexities of even relatively simple combustion reactions, the figure below (reproduced from Kislov et al. 2004) shows the various species potentially involved in the dissociation of benzene. Master equation simulations, with input kinetic data calculated via statistical theory, was used to map out the likely product states arising for different laser excitation energies in order to correlate with photo-dissociation studies of this reaction.

Van der Waals clusters are ubiquitous in the interstellar medium and the earth’s atmosphere.   Supposing chemical equilibrium exists, methods exist for computing partition functions for such clusters and subsequently predicting equilibrium constants, equilibrium concentrations and so forth. Environments such as these are quite often not equilibrated, however. How long a van der Waals cluster survives after the initial association of the two component monomers then becomes a function of whether a stabilising event has time to occur before the cluster falls apart. The lifetime of a van der Waals cluster is inversely proportional to its dimerisation rate constant; and a density of states calculation is necessary to establish a dimerisation rate constant. The cluster density of states is dominated by the loose, highly anharmonic motions in the van der Waals modes (i.e., the relative "tumbling" or loose "vibrations" between the two monomers). Quantum calculation of such large, anharmonic state densities is not currently feasible due to the numerical demands, and a generic and economical method for computing them as a function of the total energy and angular momentum of the cluster has yet to be implemented.  This problem - efficient and accurate calculation of anharmonic densities of states for van der Waals clusters - has been one focus in the Molecular Kinetics group. The new algorithm we have developed computes the classical density of states of van der Waals interactions between monomers over the entire manifold of total energy and angular momenta whilst maintaining speed of computation. It opens the way to the estimation of reliable bounds on cluster lifetimes via unimolecular rate theory.

Even apparently simple chemical reactions can be surprisingly complex when one looks under the carpet!! One example is afforded by the complex isomerisation / dissociation pathways in the figure above for benzene photodissociation.  Briefly, when molecules of even moderate complexity such as benzene are activated with a lot of energy, many different kinds of bond rearrangements and bond breakage become possible, leading to sometimes bewildering kinetics. Direct computational simulation via a master equation is typically the best way to approach such systems. Individual rates for the different molecular rearrangements or fragmentations are computed using unimolecular rate theory (see Gilbert and Smith 1989), and this kinetic data is then fed into a linear or non-linear reaction simulator which effectively solves the time-dependent master equation in order to predict the time evolution of the system. Collisional relaxation as well as reaction processes are explicitly incorporated into the master equation, since in many cases there is no time for thermal equilibrium of the individual populations to be attained during the reaction - everything is coupled up on the same timescale and hence must be explicitly incorporated.

The figure below illustrates the real time evolution that is predicted for the populations of three different molecular isomers (as a function of their internal vibrational energy) during the reaction of singlet methylene (¹CH₂) with acetylene (C₂H₂).

The CCMS molecular kinetics group have been at the forefront of international research in the area of developing high-performance simulation algorithms for complex combustion reactions which can comprise of tens of thousands of coupled rate equations. These new algorithms are designed to exploit state-of-the-art iterative matrix algorithms together with new types of pre-conditioners to facilitate time propagation algorithms scaling with the square of the number N of coupled reactions as opposed to traditional methods which scale with N³. The great advantage of these new methods lies in the fact that they are much faster than alternative stochastic simulation approaches.