Potential energy surfaces techniques

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. 

In this chapter, we look at the techniques known as direct, or on-the-fly, molecular dynamics and their application to non-adiabatic processes in photochemistry. In contrast to standard techniques that require a predefined potential energy surface (PES) over which the nuclei move, the PES is provided here by explicit evaluation of the electronic wave function for the states of interest. This makes the method very general and powerful, particularly for the study of polyatomic systems where the calculation of a multidimensional potential function is an impossible task. For a recent review of standard non-adiabatic dynamics methods using analytical PES functions see [1]. 

Results using this technique are better for force helds made to describe geometries away from equilibrium. For example, it is better to use Morse potentials than harmonic potentials to describe bond stretching. Some researchers have created force helds for a specihc reaction. These are made by htting to the potential energy surface obtained from ah initio calculations. This is useful for examining dynamics on the surface, but it is much more work than simply using ah initio methods to hnd a transition structure. 

The reaction coordinate is one specific path along the complete potential energy surface associated with the nuclear positions. It is possible to do a series of calculations representing a grid of points on the potential energy surface. The saddle point can then be found by inspection or more accurately by using mathematical techniques to interpolate between the grid points. 

This type of calculation does reliably find a transition structure. However, it requires far more computer time than any of the other techniques. As such, this is generally only done when the research requires obtaining a potential energy surface for reasons other than just finding the transition structure. 

Rather than using transition state theory or trajectory calculations, it is possible to use a statistical description of reactions to compute the rate constant. There are a number of techniques that can be considered variants of the statistical adiabatic channel model (SACM). This is, in essence, the examination of many possible reaction paths, none of which would necessarily be seen in a trajectory calculation. By examining paths that are easier to determine than the trajectory path and giving them statistical weights, the whole potential energy surface is accounted for and the rate constant can be computed. 

If we require similar information regarding the ground state potential energy surface in a polyatomic molecule the electronic emission specttum may again provide valuable information SVLF spectroscopy is a particularly powerful technique for providing it. 

Computer simulation techniques offer the ability to study the potential energy surfaces of chemical reactions to a high degree of quantitative accuracy [4]. Theoretical studies of chemical reactions in the gas phase are a major field and can provide detailed insights into a variety of processes of fundamental interest in atmospheric and combustion chemistry. In the past decade theoretical methods were extended to the study of reaction processes in mesoscopic systems such as enzymatic reactions in solution, albeit to a more approximate level than the most accurate gas-phase studies. 

Chapter 3, Geometry Optimizations, describes how to locate equilibrium structures of molecules, or, more technically, stationary points on the potential energy surface. It includes an overview of the various commonly used optimization techniques and a consideration of optimizing transition strucmres as well as minimizations. 

The case of water is particularly convenient because the required high Ka states may be detected in the solar absorption spectrum. However, it is difficult to observe the necessary high vibrational angular momentum states in molecules, which can only be probed by dispersed fluorescence or stimulated emission techniques. On the other hand, it is now possible to perform converged variational calculations on accurate potential energy surfaces, from which one could hope to verify the quantum monodromy and assess the extent to which it is disturbed by perturbations with other modes. Examples of such computed monodromy are seen for H2O in Fig. 2 and LiCN in Fig. 12. 

A disadvantage of this technique is that isotopic labeling can cause unwanted perturbations to the competition between pathways through kinetic isotope effects. Whereas the Born-Oppenheimer potential energy surfaces are not affected by isotopic substitution, rotational and vibrational levels become more closely spaced with substitution of heavier isotopes. Consequently, the rate of reaction in competing pathways will be modified somewhat compared to the unlabeled reaction. This effect scales approximately as the square root of the ratio of the isotopic masses, and will be most pronounced for deuterium or... 

Vibrationally mediated photodissociation (VMP) can be used to measure the vibrational spectra of small ions, such as V (OCO). Vibrationally mediated photodissociation is a double resonance technique in which a molecule first absorbs an IR photon. Vibrationally excited molecules are then selectively photodissociated following absorption of a second photon in the UV or visible [114—120]. With neutral molecules, VMP experiments are usually used to measure the spectroscopy of regions of the excited-state potential energy surface that are not Franck-Condon accessible from the ground state and to see how different vibrations affect the photodissociation dynamics. In order for VMP to work, there must be some wavelength at which vibrationally excited molecules have an electronic transition and photodissociate, while vibrationally unexcited molecules do not. In practice, this means that the ion has to have a... 

OsB (5), and one can only find estimates of the potential energy surface around Esa (6 = 0) by stabilization techniques [48]. 

In addition to the natural improvements expected in the accuracy of the measurements, and the increased scope in the types of systems examined, new techniques go beyond the issue of thermochemistry to allow for very detailed studies of reaction dynamics. The investigation by Zewail and co-workers of the reactivity of planar COT" on the femtosecond time scale is likely only the beginning. Time-resolved photoelectron spectroscopy, for example, has recently been used to map the potential energy surfaces for the dissociation of simple ions IBr and l2. " Although applications in the field of organic reactive molecules are likely far off, they are now possible. 

However, even the best experimental technique typically does not provide a detailed mechanistic picture of a chemical reaction. Computational quantum chemical methods such as the ab initio molecular orbital and density functional theory (DFT) " methods allow chemists to obtain a detailed picture of reaction potential energy surfaces and to elucidate important reaction-driving forces. Moreover, these methods can provide valuable kinetic and thermodynamic information (i.e., heats of formation, enthalpies, and free energies) for reactions and species for which reactivity and conditions make experiments difficult, thereby providing a powerful means to complement experimental data. 

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