Research School of Chemistry **Machine** VP

**Co-Investigators** Harold W Schranz

Research School of Chemistry

**Intramolecular Vibrational Energy Redistribution and Reaction Dynamics in
Excited Molecules**

An understanding of chemical reaction dynamics is essential to the more
complete understanding of physiochemical phenomena in combustion, industrial
and atmospheric systems. Crucial to this development is a detailed
understanding of how and on what timescale energy moves about a molecule, a
process known as *intramolecular vibrational energy redistribution
(IVR*).

Chemical reaction dynamics plays a central role in the modelling of a wide range of complex chemical phenomena. Areas of major current relevance include ozone depletion in the stratosphere, tropospheric air pollution, plasma processing of electronic devices, combustion and oxidation processes, and high-energy chemistry.

Chemical reaction systems generally consist of a network of interlinked elementary reactions which are classified on the basis of their molecularity (the number of molecules required in a single reaction). The vast bulk can be classified as unimolecular, bimolecular or termolecular.

The focus of the proposed project will be on unimolecular and related reactions in the gas phase. This topic automatically encompasses the closely related classes of termolecular reactions and complex bimolecular reactions. There will also be close links to reactions on surfaces (e.g. silicon chemical vapour deposition) and to matrix isolation studies. In fact, results arising from this work will also have significance for reactions occurring in clusters and in solution.

**What are the basic questions addressed?**

The objective of this project is to yield detailed answers to the fundamental question: How and on what timescale does energy move around within a molecule?

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

We have completed a series of simulations of intramolecular vibrational energy transfer in symmetric sequentially bonded tetra-atomic molecules of the ABBA type. These studies have concentrated on the coupling of the torsion motion with higher frequency bond stretching and bending motions. (CPU time ratios of better than 10:1 vector:scalar are the norm for these studies.)

These model studies have enabled us to identify the most important terms in the
Hamiltonian for energy transfer between such modes of motion. We have found
that 4:1 (ratio of frequencies) resonant energy transfer from torsion to
bending motion can occur under favourable conditions. However, Fermi resonance
(2:1 frequency matching) is a much stronger mechanism (as one might expect) and
dominates energy transfer unless the modes in question do not have any other
mode within several tens of cm^{-1} of a 2:1 ratio. The symmetry of
these systems places important restrictions on the pathways available for
energy transfer. The strength of these mechanisms can be estimated from the
form of the Hamiltonian in internal coordinates, and verified by simulation.
Interestingly, the frequency of torsional motion as a function of energy has
been found to exhibit a plateau region. Thus, frequency matching with other
modes can occur over an energy range of 1000-2000 cm^{-1}, even when
the fundamental frequency is of the order of 100 cm^{-1}.

Quantum simulations corresponding to the classical studies have also been completed. The quantum dynamics code is restricted to a subset of the six internal modes, as the classical simulations have shown the practical restriction of coupling produced by a combination of symmetry and `order of smallness' in the anharmonic terms in the Hamiltonian. These quantum studies have elucidated the roles of both resonant and non-resonant interactions between the torsional motion and other modes on the energy levels and IVR rates (Fig. 1).

Fig. 1 Facile IVR out of an excited torsion for a two-mode model of CH3OOCH3 near a 2:1 resonance

Current classical simulations will concentrate on a comparison of isomerisation rates as calculated by simulation and statistical theories, to quantify the effect of particular energy transfer pathways on the rate of this simple chemical reaction. In the absence of molecular rotation, initial studies on H2S2 indicate that energy redistribution between the SS stretch, symmetric HSS bending and torsion does have a significant impact on the isomerisation rate. The coupling of these vibrations to molecular rotation should also provide an interesting insight into the mechanism of this simple isomerisation. These calculations are highly vectorised (>70% vectorisation) and not highly memory intensive. The results of these calculations are presently being analysed and more extensive runs are envisaged.

A potential energy surface for benzene which incorporates the dominant
couplings has been constructed on the basis of *ab initio* data. The
surface is being employed for a full dimensional classical mechanical molecular
dynamics study of IVR. Comparisons are intended with recent experimental
observations regarding the extent and timescale of IVR involving the ring
modes. The linewidths found experimentally 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}. Preliminary calculations (Fig. 2) are consistent with the
experiments and reveal an initially rapid decay followed by slow IVR at longer
times.

Fig.
2. IVR out of [[nu]]6 for an initial [[nu]]6^{2}[[nu]]1^{5}
excitation of benzene

**What computational techniques are used and why is a supercomputer
required?**

For the classical simulations, large numbers of classical trajectories need to be generated by integrating the classical equations of motion. In the quantum studies, large matrices need to be diagonalized and the results used to propagate the quantum wavepacket in time. Both types of calculations are numerically intensive, the former requiring large amounts of CPU time and the latter requiring large amounts of RAM (typically in excess of 300 MB).

**Publications**

*Nonlinear resonance and torsional dynamics: model simulations of HOOH
and CH3OOCH3,* Harold W Schranz and Michael A Collins, J. Chem. Phys.,
**98**, 1132-1148 (1993) .

*Quantum simulations of nonlinear resonance and torsional dynamics,
*Michael A Collins and Harold W Schranz, J. Chem. Phys., **100**, 2089
(1994).

*Phase space analysis of nonlinear resonance and torsional dynamics,
*Harold W Schranz and Michael A Collins, J. Chem. Phys., **101**, 307
(1994).

*Intramolecular vibrational energy redistribution and torsional
isomerization: a model classical and quantum study*, H W Schranz and M A
Collins, First Electronic Computational Chemistry Conference CD-ROM, ARInternet
(1995), in press.