Potential energy surface hopping

B. N. Fu, B. C. Shepler, and J. M. Bowman. Three-state trajectory surface hopping studies of the photodissociation dynamics of formaldehyde on ab initio potential energy surfaces, J. Am. Chem. Soc., 133 7957-7968 (2011). 

Figure 65. Potential-energy surface for first excited singlet state of linear Hj1. Cut through surface at large R coincides with potential curve of at small R2 and with H2 curve at large R2 (see Fig. 63). There is a seam connecting this surface to that shown in Fig. 64, along which potential surface hopping can occur.2...

The universality of the relaxation time near the crossover temperature also originates in the dynamic nature of supercooled liquids. The idea here is that supercooled liquids have collective excitations. These elementary excitations have characteristics of phonons [119-122]. Furthermore, there is a unique temperature at which the lifetime for the elementary excitation becomes comparable to the lifetime of hopping dynamics on the potential energy surface [119]. Analysis indicates that the value of crossover relaxation time at this characteristic temperature is < ) x 10-7 5 s, where < ) varies between 1 and [ 119]. 

In addition to the consideration of equilibrium problems, the treatment of thermal excitations is also important to the investigation of kinetics. An intriguing insight into kinetics is that in many cases, the tools for treating thermal excitations to be described in this chapter can be used to consider driven processes such as diffusion. As will be noted in chap. 7, models of kinetics are tied to the idea that as a result of the random excursion of atoms from their equilibrium positions, a system may occasionally pass from one well in the multi-dimensional potential energy surface to another. Indeed, this eventuality has already been rendered pictorially in fig. 3.22 where we saw an adatom hopping from one energy well to the next in its... 

The trajectory surface hopping method is an additional extension of the classical trajectory method. Potential energy surfaces are constructed for each electronic state involved in the collision. In addition, a function has to be obtained that defines the locus of points at which hops between surfaces can occur. Still another function is necessary which gives the probability of such jumps as a function of nuclear positions and velocities.28 Diatomics-in-molecules surfaces approximated the two lowest singlet potential surfaces of H3. The surfaces have been shown30 to be in good agreement with accurate ab initio calculations by Conroy.31... 

The trajectory surface hopping model of ion-molecule reaction dynamics has realized an impressive agreement between theory and experiment in this reaction, i.e. H+ + H2, and it provides the experimentalist with a realistic and workable theory to use in the comparison with and interpretation of experimental results. As reliable potential energy surfaces become available for other ion-molecule systems, we can expect further tests of this theory and its applicability to more complicated reactions. 

Nonetheless, the probability of the hop from potential energy surfaces is not 1. As a consequence, different product distribution and kinetic isotopic effects can also be observed. When very strong spin-orbit coupling between the different states is involved, the reaction behaves like any other, that is, on a single adiabatic potential energy hypersurface whose spin character varies smoothly from reactants to products. 

---