Potential energy surface atomic reaction systems

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. 

In highly exothermic reactions such as this, that proceed over deep wells on the potential energy surface, sorting pathways by product state distributions is unlikely to be successful because there are too many opportunities for intramolecular vibrational redistribution to reshuffle energy among the fragments. A similar conclusion is likely as the total number of atoms increases. Therefore, isotopic substitution is a well-suited method for exploration of different pathways in such systems. 

For both statistical and dynamical pathway branching, trajectory calculations are an indispensable tool, providing qualitative insight into the mechanisms and quantitative predictions of the branching ratios. For systems beyond four or five atoms, direct dynamics calculations will continue to play the leading theoretical role. In any case, predictions of reaction mechanisms based on examinations of the potential energy surface and/or statistical calculations based on stationary point properties should be viewed with caution. 

In general three position variables will be needed to specify the potential energy of the reaction system. These may be the X-Y, Y-Z, and X-Z internuclear distances or two internuclear distances and the included angle. Even in this relatively simple case, four dimensions would be required for generation of the potential energy surface. However, if we restrict our attention to linear configurations of these atoms, it is possible... 

For a system containing a larger number of atoms, the general picture of the potential energy surface and the transition state also applies. For example, in the second reaction step in the mechanism of ethane pyrolysis in Section 6.1.2,... 

In some situations we have performed finite temperature molecular dynamics simulations [50, 51] using the aforementioned model systems. On a simplistic level, molecular dynamics can be viewed as the simulation of the finite temperature motion of a system at the atomic level. This contrasts with the conventional static quantum mechanical simulations which map out the potential energy surface at the zero temperature limit. Although static calculations are extremely important in quantifying the potential energy surface of a reaction, its application can be tedious. We have used ah initio molecular dynamics simulations at elevated temperatures (between 300 K and 800 K) to more efficiently explore the potential energy surface. 

This model has obvious shortcomings. For example, the interaction with the solvent in the initial state is straightforward since the proton is in the ionic form, whereas in the final state, the proton is the nonionic adsorbed H atom and its interaction with the solvent should be negligible. No consideration of this fact was made in the potential of the final state Uf m Eq. (43). However, this treatment incorporates the basic feature of the proton transfer reaction interaction with the solvent, tunneling as well as classical transition of the proton, and the effect of the electric field on the potential energy surfaces of the system. 

At the most fundamental level one follows the time development of the system in detail. The reactants are started in a specific initial (quantum) state and the equation of motion are propagated to give the final state. The equation of motion of the system is the time dependent Schroinger equation, or, if the atoms involved are heavy enough (not H or Li) Newtons equation. The starting point is the adiabatic potential energy surface on which the process takes place. For some reactions electronic excitations during the reaction are important and must be included in addition to the electronically adiabatic dynamics. 

Figure 14. (a) Potential-energy surfaces, with a trajectory showing the coherent vibrational motion as the diatom separates from the I atom. Two snapshots of the wavepacket motion (quantum molecular dynamics calculations) are shown for the same reaction at / = 0 and t = 600 fs. (b) Femtosecond dynamics of barrier reactions, IHgl system. Experimental observations of the vibrational (femtosecond) and rotational (picosecond) motions for the barrier (saddle-point transition state) descent, [IHgl] - Hgl(vib, rot) + I, are shown. The vibrational coherence in the reaction trajectories (oscillations) is observed in both polarizations of FTS. The rotational orientation can be seen in the decay of FTS spectra (parallel) and buildup of FTS (perpendicular) as the Hgl rotates during bond breakage (bottom). 

In reactions involving electronically excited states, the interaction of two potential energy surfaces is likely to be involved. This interaction is reasonably well understood and easy to visualize in the case of potential curves for diatomic systems, but for systems containing more than two atoms, the situation is considerably less tractable. One tries to develop a description, starting from the observed kinetics of a reaction and using whatever spectroscopic data may be available. 

The most important systems studied by the flow method are H+X2, H+HX and X+HX where X represents a halogen atom. These reactions are of prime interest because they are three-atom systems. Thus, there is hope that they may be treated successfully in terms of potential energy surfaces. They have been studied in considerable detail, both experimentally and theoretically, by Polanyi and his coworkers over the past decade. The studies have been aimed at determining the initial distribution of product molecules in the available vibrational and rotational levels, at finding the amount of reaction energy that goes into internal excitation and at establishing a satisfactory theoretical model. 

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