Potential energy surface frequencies

Table L Reactant, product, and saddle point properties of ab initio [126], SE [127], and improved [135] OH + H2 potential energy surfaces [frequencies in cm" distances in bohr, angles in degrees, and energies in kcal/mol relative to the reactants of reaction (Rl)] (adapted from [135]).

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. 

To calculate N (E-Eq), the non-torsional transitional modes have been treated as vibrations as well as rotations [26]. The fomier approach is invalid when the transitional mode s barrier for rotation is low, while the latter is inappropriate when the transitional mode is a vibration. Hamionic frequencies for the transitional modes may be obtained from a semi-empirical model [23] or by perfomiing an appropriate nomial mode analysis as a fiinction of the reaction path for the reaction s potential energy surface [26]. Semiclassical quantization may be used to detemiine anliamionic energy levels for die transitional modes [27]. 

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. 

One group has successfiilly obtained infonnation about potential energy surfaces without measuring REPs. Instead, easily measured second derivative absorption profiles are obtained and linked to the fiill RRS spectrum taken at a single incident frequency. In this way, the painstaking task of measuring a REP is replaced by carefiilly recording the second derivative of the electronic absorption spectrum of the resonant transition [, 59],... 

The fitting parameters in the transfomi method are properties related to the two potential energy surfaces that define die electronic resonance. These curves are obtained when the two hypersurfaces are cut along theyth nomial mode coordinate. In order of increasing theoretical sophistication these properties are (i) the relative position of their minima (often called the displacement parameters), (ii) the force constant of the vibration (its frequency), (iii) nuclear coordinate dependence of the electronic transition moment and (iv) the issue of mode mixing upon excitation—known as the Duschinsky effect—requiring a multidimensional approach. 

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]. 

The combination is in this case an out-of-phase one (Section I). This biradical was calculated to be at an energy of 39.6 kcal/mol above CHDN (Table ni), and to lie in a real local minimum on the So potential energy surface. A normal mode analysis showed that all frequencies were real. (Compare with the prebenzvalene intermediate, discussed above. The computational finding that these species are bound moieties is difficult to confimi experimentally, as they are highly reactive.)... 

HyperChem can calculate transition structures with either semi-empirical quantum mechanics methods or the ab initio quantum mechanics method. A transition state search finds the maximum energy along a reaction coordinate on a potential energy surface. It locates the first-order saddle point that is, the structure with only one imaginary frequency, having one negative eigenvalue. 

Because of the nature of the computations involved, firequency calculations are valid only at stationary points on the potential energy surface. Thus, frequency calculations must be performed on optimized structures. For this reason, it is necessary to run a geometry optimization prior to doing a frequency calculation. The most convenient way of ensuring this is to include both Opt and Freq in the route section of the job, which requests a geometry optimization followed immediately by a firequency calculation. Alternatively, you can give an optimized geometry as the molecule specification section for a stand-alone frequency job. 

Another use of frequency calculations is to determine the nature of a stationary point found by a geometry optimization. As we ve noted, geometry optimizations converge to a structure on the potential energy surface where the forces on the system are essentially zero. The final structure may correspond to a minimum on the potential energy surface, or it may represent a saddle point, which is a minimum with respect to some directions on the surface and a maximum in one or more others. First order saddle points—which are a maximum in exactly one direction and a minimum in all other orthogonal directions—correspond to transition state structures linking two minima. 

We are interested in exploring the C3H5F potential energy surface. We will begin hy running optimization and frequency jobs on these three isomers of 1-fluoropropenc... 

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. 

---