Efficient Calculation of Statistical and Dynamical Reaction Rates for Large Dimensional Molecular Systems

Principal Investigator

Harold W. Schranz

Research School of Chemistry

Knowledge of how quickly chemical reactions occur is an essential ingredient in the rigorous modelling of combustion, industrial and atmospheric reaction systems. This project focuses on the development of new methods for the accurate prediction of rate constants for chemical reaction. Crucial to this development is a more complete understanding of how and on what timescale energy moves about a molecule (IVR) and between molecules (collisional energy transfer).


s10 - VPP, PC

What are the results to date and the future of the work?

An initial classical study considered the nonlinear resonant interaction resulting from kinematic coupling between the torsion mode and other modes in sequentially bonded ABBA type tetra-atomic molecules. It was found that the nonlinear resonant interactions were most likely to involve the symmetric bending mode. This finding stimulated our later detailed quantum and classical dynamical studies which were facilitated by employing a reduced dimensional model. The observed rate of torsional isomerisation was compared to the predictions of Transition State Theory. Thus, the importance of statistical or dynamical behaviour was related to the observed extent of intramolecular vibrational energy redistribution (IVR).

· IVR involving the ring modes in S0 benzene

Our IVR studies are being extended to larger molecular systems. A collaboration is being pursued with Dr. Warren Lawrance, Flinders University, South Australia. An ab initio potential energy surface for benzene which incorporates the dominant potential couplings was employed for a full dimensional classical mechanical molecular dynamics study. Comparisons were made with experiments regarding the extent and timescale of IVR involving the ring modes.

Fig. 1. IVR out of n6 for an initial n62n15 excitation

The linewidths found experimentally by the the Lawrance group were instrument limited at 1 cm-1 for a range of excited ring modes for excitations of between 1200 and 8200 cm-1 yielding an upper limit on the IVR rate of 0.094 ps-1. Trajectory calculations reveal an initially rapid decay followed by slow IVR at longer times (Fig. 1). Future analysis of energy transfer amongst the ring modes in benzene will be connected more closely with the experiments by accounting for higher potential couplings using information from recent ab initio calculations.

· Studies of energy transfer and isomerisation

Further classical and quantum simulations will concentrate on a comparison of isomerisation rates as calculated by simulation and statistical theories (Fig. 2), to quantify the effect of particular energy transfer pathways on the rate of isomerisation.

Fig. 2. Isomerisation of methyl isocyanide

- Appendix A

Isomerisation is of interest as it is a prototypical example of a simple chemical reaction which is of relevance in chemical, physical and biological contexts, e.g. conformational isomerisation of proteins. Unlike dissociation reactions, the reaction coordinate is not a distance but an angle and this may lead to some novel effects. Further time dependent information will be extracted about nature of the reaction process and how sensitive it is to the extent and rate of intramolecular energy transfer. We would like to find out what details of the potential energy surface determine the dynamics of the reaction and relate this to recent experiments.

· Collisional Energy Transfer in Highly Excited Molecules

A new project is proposed on the study of collisional energy transfer in highly excited molecules. One of the aims of this project is to develop a useful method to incorporate quantum effects in classical simulations. This component will involve a binational collaboration with Prof. John Barker of the University of Michigan who has proposed a simple model for incorporating quantum effects in the transition probability governing energy transfer. To create the input for this statistical model requires classical trajectory simulations and calculation of quantum corrections by semiclassical methods. Comparison with the simpler but ad hoc constraint procedures will also be of interest in exploring the classical-quantum correspondence. A further related component is a proposed study of how collisional energy transfer is affected by the transition from the dilute gas to liquid phase regime, of much current experimental interest.

· Vectorised statistical rate calculations

The energy and angular momentum resolved rate constant k(E,J) is difficult to calculate by ordinary integration techniques An exciting new and general method is proposed which takes advantage of our recently derived procedures for efficiently sampling the phase space of a reactant molecule. Vector implementations of the Markov walk over the configuration space are planned (Fig. 3).

a. Scalar implementation of statistical method b. Vector implementation of statistical method

Fig. 3. Schematic representation of Markov walk over configuration space

By comparing the predictions of the above statistical method with dynamical calculations the relevance of statistical theories and the importance of nonstatistical effects can be clarified. In particular, the dependence of mode specific product yield enhancement on the type of chemical reaction and on the initial molecular states will be revealed.

What computational techniques are used?

For the classical dynamical simulations, large numbers of trajectories need to be generated by integrating the classical equations of motion. In the statistical studies, long Markov walks need to be performed in order to properly sample the high dimensional phase space of the reactant molecule. Both types of calculations are numericallly intensive, the former requiring large amounts of CPU time but vectorizes well. A further type of calculation performed are quantum dynamical simulations of energy transfer. The current method does not vectorize well, due to the highly complex nature of the matrix elements, but use of supercomputers such as the Fujitsu VPP300 and the SGI Power Challenge is essential as memory requirements exceed that available on workstations at the RSC.


Ming, L., Nordholm, S., Schranz, H. W., On the Estimation of Anharmonic Densities of States of Molecules, Chem. Phys. Lett., 248, 1996, 228-236.

Schranz, H. W., Mode to Mode Energy Flow Amongst the Ring Modes of Benzene, THEOCHEM, 368, 1996, 119-124.

Schranz, H. W., Sewell, T. D., Statistical and Dynamical Behaviour in the Unimolecular Reaction Dynamics of Polyatomic Molecules, THEOCHEM, 368, 1996, 125-131.

Schranz, H. W., Sewell, T. D., Nordholm, S., Statistical and Dynamical Behaviour in the Isomerisation of Methyl Isocyanide, in Femtochemistry: Ultrafast Chemical and Physical Processes in Molecular Systems (Ed. M. Chergui) pp 202-205, World Scientific, Singapore (1996).

Schranz, H. W., Collins, M. A., Intramolecular vibrational energy redistribution and torsional isomerization: a model classical and quantum study, in Femtochemistry: Ultrafast Chemical and Physical Processes in Molecular Systems (Ed. M. Chergui) pp 206-209, World Scientific, Singapore (1996).

- Appendix A