Potential energy surfaces predictions

Results of calculations of the potential energy surface predict the existence of weakly bound intermediate complexes. This implies a complex, multi-step reaction mechanism. The profile of the potential energy surface of the reaction systems is shown in Fig. 19. 

Aspartic acid (R=—CH2-COOH, m.p. >300°C) is a natural amino acid with a carboxyl group in the side chain. Ab initio searches in the potential energy surface predict up to 14 low energy conformers to lie within 800 cm [135]. Investigation of the microwave spectmm of laser ablated aspartic acid yields the identification of six conformers (see Fig. 17). The relative population ratios follow the order la-I > Ib-I Ila-I > la-ll nb-I > Illpb-I. Conformer la-1 is the most abundant conformer in the molecular beam, in poor agreement with the ab initio calculations which predict la-I to be ca. 300 cm above the global minimum. This fact can be attributed to relaxation processes between conformers [108-110, 135]. 

Empirical methods are of two types those that permit potential energy surfaces to be calculated and those that only allow activation energies to be estimated. Laidler has reviewed these. A typical approach is to establish a relationship between experimental activation energies and some other quantity, such as heats of reaction, and then to use this correlation to predict additional activation energies. In Section 5.3 we will encounter a different type of empirical potential energy surface. 

Geometry optimizations usually attempt to locate minima on the potential energy surface, thereby predicting equilibrium structures of molecular systems. Optimizations can also locate transition structures. However, in this chapter we will focus primarily on optimizing to minima. Optimizations to minima are also called minimizations. 

Theoretical predictions of potential energy surfaces and reaction paths can sometimes yield quite surprising results. In this section, we ll consider an example which illustrates the general approach toward and usefulness of studying potential energy surfaces in detail. 

The search for a conical intersection is also successful. The predicted structure is at the left. The predicted energies of the two states—the ground state and the first excited state—differ by about 0.00014 Hartrees, confirming that they are degenerate at these points on the two potential energy surfaces. ... 

The hrst step in theoretical predictions of pathway branching are electronic structure ab initio) calculations to define at least the lowest Born-Oppenheimer electronic potential energy surface for a system. For a system of N atoms, the PES has (iN — 6) dimensions, and is denoted V Ri,R2, - , RiN-6)- At a minimum, the energy, geometry, and vibrational frequencies of stationary points (i.e., asymptotes, wells, and saddle points where dV/dRi = 0) of the potential surface must be calculated. For the statistical methods described in Section IV.B, information on other areas of the potential are generally not needed. However, it must be stressed that failure to locate relevant stationary points may lead to omission of valid pathways. For this reason, as wide a search as practicable must be made through configuration space to ensure that the PES is sufficiently complete. Furthermore, a search only of stationary points will not treat pathways that avoid transition states. 

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. 

The study of multiple pathways leading to a single product channel provides a stringent test of our understanding of the potential energy surface and the calculations that use it to predict reaction outcomes. Although there are not many examples to date of pathway competitions, the increasing prominence of such systems, coupled with advances in experiment and theory that facilitate their study, promises a rich future in this normally hidden facet of reaction mechanisms. 

The F + H2 — HF + FI reaction is one of the most studied chemical reactions in science, and interest in this reaction dates back to the discovery of the chemical laser.79 In the early 1970s, a collinear quantum scattering treatment of the reaction predicted the existence of isolated resonances.80 Subsequent theoretical investigations, using various dynamical approximations on several different potential energy surfaces (PESs), essentially all confirmed this prediction. The term resonance in this context refers to a transient metastable species produced as the reaction occurs. Transient intermediates are well known in many kinds of atomic and molecular processes, as well as in nuclear and particle physics.81 What makes reactive resonances unique is that they are not necessarily associated with trapping... 

Experimental probes of Born-Oppenheimer breakdown under conditions where large amplitude vibrational motion can occur are now becoming available. One approach to this problem is to compare theoretical predictions and experimental observations for reactive properties that are sensitive to the Born-Oppenheimer potential energy surface. Particularly useful for this endeavor are recombinative desorption and Eley-Rideal reactions. In both cases, gas-phase reaction products may be probed by modern state-specific detection methods, providing detailed characterization of the product reaction dynamics. Theoretical predictions based on Born-Oppenheimer potential energy surfaces should be capable of reproducing experiment. Observed deviations between experiment and theory may be attributed to Born-Oppenheimer breakdown. 

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