Energy surface addition

In those cases where the dynamics cannot be adequately described by motion on a single adiabatic potential-energy surface, additional dynamical assumptions must be made. The pioneering technique is the trajectory surface hopping (TSH) method (55,56) of Tully and co-workers. In these calculations, the classical trajectories are integrated on an adiabatic potential energy surface (typically generated by diatomics in molecules, DIM... 

There are significant differences between tliese two types of reactions as far as how they are treated experimentally and theoretically. Photodissociation typically involves excitation to an excited electronic state, whereas bimolecular reactions often occur on the ground-state potential energy surface for a reaction. In addition, the initial conditions are very different. In bimolecular collisions one has no control over the reactant orbital angular momentum (impact parameter), whereas m photodissociation one can start with cold molecules with total angular momentum 0. Nonetheless, many theoretical constructs and experimental methods can be applied to both types of reactions, and from the point of view of this chapter their similarities are more important than their differences. 

In addition to the dependence of the intennolecular potential energy surface on monomer vibrational level, the red-shifting of the monomer absorption as a fiinction of the number of rare gas atoms in the cluster has been studied. The band origin for the Vppp = 1 -t— 0 vibration in a series of clusters Ar -HF, with 0 < n < 5, was measured and compared to the HF vibrational frequency in an Ar matrix (n = oo). The monomer vibrational frequency Vp p red shifts monotonically, but highly nonlinearly, towards the matrix value as sequential Ar atoms are added. Indeed, roughly 50% of the shift is already accounted for by n = 3. 

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. 

In his search of the Si2H4 potential energy surface, the original researcher, Krishnan Raghavachari, found the following minima (in addition to the reactants) ... 

Much additional work on HF-HF potentials, as discussed elsewhere (37.38). is directed very specifically at that part of the potential energy surface that governs the binding energy, geometry, and internal dynamics of the (HF) dimer near its... 

Ab initio molecular orbital calculations are being used to study the reactions of anionic nucleophiles with carbonyl compounds in the gas phase. A rich variety of energy surfaces is found as shown here for reactions of hydroxide ion with methyl formate and formaldehyde, chloride ion with formyl and acetyl chloride, and fluoride ion with formyl fluoride. Extension of these investigations to determine the influence of solvation on the energy profiles is also underway the statistical mechanics approach is outlined and illustrated by results from Monte Carlo simulations for the addition of hydroxide ion to formaldehyde in water. 

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