Potential energy surfaces reaction dynamics

Donald G. Truhlar, Potential Energy Surfaces and Dynamics Calculations for Chemical Reactions and Molecular Energy Transfer, Plenum, New York, 1981. 

Before discussing the details of the product energy distributions for specific reactions, we shall try to identify the important factors that determine the disposal of energy in chemical reactions. Broadly, energy disposal is determined by the nature of the interactions (the reaction potential-energy surface), by dynamical or kinetic effects and by the initial states of the reagents. For a particular reaction, one effect may dominate or the system may be governed by a complex interaction of all three effects. 

Potential Energy Surfaces and Dynamics for Spectroscopy During Chemical Reactions [1]... 

Ultrafast spectroscopies have opened the door not only to understand early time dynamics of the intrinsically fast processes but also to control the outcome of the reaction in real time [59, 60]. Quantum control necessarily relies on very detailed a priori knowledge of the potential energy surface and dynamics of the system for designing pulse shapes and pulse sequences that wiU ultimately promote the molecules into the desired reaction path with minimal energy losses. 

Potential energy surfaces and dynamics calculations for chemical reactions and molecular energy transfer. 

The above discussion represents a necessarily brief simnnary of the aspects of chemical reaction dynamics. The theoretical focus of tliis field is concerned with the development of accurate potential energy surfaces and the calculation of scattering dynamics on these surfaces. Experimentally, much effort has been devoted to developing complementary asymptotic techniques for product characterization and frequency- and time-resolved teclmiques to study transition-state spectroscopy and dynamics. It is instructive to see what can be accomplished with all of these capabilities. Of all the benclunark reactions mentioned in section A3.7.2. the reaction F + H2 —> HE + H represents the best example of how theory and experiment can converge to yield a fairly complete picture of the dynamics of a chemical reaction. Thus, the remainder of this chapter focuses on this reaction as a case study in reaction dynamics. 

Chemical reaction dynamics is an attempt to understand chemical reactions at tire level of individual quantum states. Much work has been done on isolated molecules in molecular beams, but it is unlikely tliat tliis infonnation can be used to understand condensed phase chemistry at tire same level [8]. In a batli, tire reacting solute s potential energy surface is altered by botli dynamic and static effects. The static effect is characterized by a potential of mean force. The dynamical effects are characterized by tire force-correlation fimction or tire frequency-dependent friction [8]. 

B. H. Lengsfield and D. R. Yarkony, Nonadiabatic Interactions Between Potential Energy Surfaces Theory and Applications, in State-Selected and State to State Ion-Molecule Reaction Dynamics Part 2 Theory, M. Baer and C.-Y. Ng, eds., John Wiley Sons, Inc., New York, 1992, Vol, 82, pp. 1-71. 

In Chapter VI, Ohm and Deumens present their electron nuclear dynamics (END) time-dependent, nonadiabatic, theoretical, and computational approach to the study of molecular processes. This approach stresses the analysis of such processes in terms of dynamical, time-evolving states rather than stationary molecular states. Thus, rovibrational and scattering states are reduced to less prominent roles as is the case in most modem wavepacket treatments of molecular reaction dynamics. Unlike most theoretical methods, END also relegates electronic stationary states, potential energy surfaces, adiabatic and diabatic descriptions, and nonadiabatic coupling terms to the background in favor of a dynamic, time-evolving description of all electrons. 

Results using this technique are better for force helds made to describe geometries away from equilibrium. For example, it is better to use Morse potentials than harmonic potentials to describe bond stretching. Some researchers have created force helds for a specihc reaction. These are made by htting to the potential energy surface obtained from ah initio calculations. This is useful for examining dynamics on the surface, but it is much more work than simply using ah initio methods to hnd a transition structure. 

Molecular dynamics studies can be done to examine how the path and orientation of approaching reactants lead to a chemical reaction. These studies require an accurate potential energy surface, which is most often an analytic... 

Reality suggests that a quantum dynamics rather than classical dynamics computation on the surface would be desirable, but much of chemistry is expected to be explainable with classical mechanics only, having derived a potential energy surface with quantum mechanics. This is because we are now only interested in the motion of atoms rather than electrons. Since atoms are much heavier than electrons it is possible to treat their motion classically. Quantum scattering approaches for small systems are available now, but most chemical phenomena is still treated by a classical approach. A chemical reaction or interaction is a classical trajectory on a potential surface. Such treatments leave out phenomena such as tunneling but are still the state of the art in much of computational chemistry. 

At first sight, the easiest approach is to fit a set of points near the saddle point to some analytical expression. Derivatives of the fitted function can then be used to locate the saddle point. This method has been well used for small molecules (see Sana, 1981). An accurate fit to a large portion of the potential energy surface is also needed for the study of reaction dynamics by classical or semi-classical trajectory methods. 

Hirst DM (1985) Potential Energy Surfaces — Molecular Structure and Reaction Dynamics. Taylor and Francis, London, Philadelphia... 

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