Molecular collisions potential energy surface

The use of supercomputers has allowed us to test the sensitivity of accurate quantal molecular energy transfer probabilities in diatom-diatom collisions to the choice of potential energy surface, even at total energies great enough to allow both diatoms to be vibrationally excited. 

Experiments have also played a critical role in the development of potential energy surfaces and reaction dynamics. In the earliest days of quantum chemistry, experimentally determined thermal rate constants were available to test and improve dynamical theories. Much more detailed information can now be obtained by experimental measurement. Today experimentalists routinely use molecular beam and laser techniques to examine how reaction cross-sections depend upon collision energies, the states of the reactants and products, and scattering angles. 

Molecular dynamic studies used in the interpretation of experiments, such as collision processes, require reliable potential energy surfaces (PES) of polyatomic molecules. Ab initio calculations are often not able to provide such PES, at least not for the whole range of nuclear configurations. On the other hand, these surfaces can be constructed to sufficiently good accuracy with semi-empirical models built from carefully chosen diatomic quantities. The electric dipole polarizability tensor is one of the crucial parameters for the construction of such potential energy curves (PEC) or surfaces [23-25]. The dependence of static dipole properties on the internuclear distance in diatomic molecules can be predicted from semi-empirical models [25,26]. However, the results of ab initio calculations for selected values of the internuclear distance are still needed in order to test and justify the reliability of the models. Actually, this work was initiated by F. Pirani, who pointed out the need for ab initio curves of the static dipole polarizability of diatomic molecules for a wide range of internuclear distances. 

The most satisfactory treatment of the reactions of interest in this chapter is in terms of classical trajectories on potential energy surfaces. They provide a detailed consideration of the reactive interaction (for which the kinematic models are limiting cases7), and provide ample scope for the theoretician to apply his intuition in explaining reactive molecular collisions. Reactions are naturally divided into those which take place on a single surface, usually leading to vibrational excitation, and those which involve two or more surfaces, often leading to electronic excitation. 

Most of these theoretical investigations have been carried out using methyl compounds as the substrate. For example, the Sn2 reaction between OFT and methyl chloride has been investigated for non-linear and linear collisions using ab initio molecular dynamics calculations.105 The potential energy surface was calculated at the MP2/6-311-I— -G(2df,2pd) level of theory and the collision energy was set at 25 kcal mor1. The results for 495 trajectories indicated that the reactants pass from the initial encounter complex to the transition state in 0.02 ps and to the product encounter... 

The first unambiguous observation of a reactive resonance in a collision experiment was recently made for the F+HD -HF+D reaction [96-98]. This reaction was one isotopomer of the F+H2 system studied in the landmark molecular beam experiments of Lee and coworkers in 1985 [86, 87], Unlike the F+H2 case, no anomalous forward peaking of the product states was reported, and the results for F+HD were described as the most classical-like of the isotopes considered. Furthermore, a detailed quantum mechanical study [99] of F+HD->-HF+D reaction on the accurate Stark-Wemer potential energy surface (SW-PES) [100] failed to locate resonance states. Therefore, it was surprising that the unmistakable resonance fingerprints emerged so clearly upon re-examination of this reaction. 

Kuntz, P.J. (1976). Features of potential energy surfaces and their effect on collisions, in Dynamics of Molecular Collisions, Part B, ed. W.H. Miller (Plenum Press, New York). 

The concept of potential-energy surface (or just potentials) is of major importance in spectroscopy and the theoretical study of molecular collisions. It is also essential for the understanding of the macroscopic properties of matter (e.g., thermophysical properties and kinetic rate constants) in terms of structural and dynamical parameters (e.g., molecular geometries and collision cross sections). Its role in the interpretation of recent work in plasmas, lasers, and air pollution, directly or otherwise related to the energy crisis, makes it of even greater value. 

Although the concept of potential has a classical meaning, it is in the Born-Oppenheimer approximation that it finds significance in the context of the present work. Born and Oppenheimer22 recognized that for the great majority of molecular collisions with chemical interest, the nuclei move much more slowly than the electrons, and hence their motions can be treated as separable. The concept of potential-energy surface stems from this separation. 

It seems, therefore, with the current renewal of theoretical interest in atomic and molecular collision problems, reactive scattering, and predissociation phenomena, that it is worthwhile to examine the VB theory as a useful model that is capable of yielding accurate potential energy surfaces. 

A large number of elementary molecular collision processes proceeding via (or in) excited electronic states are known at present. A prominent feature of all these is that as a rule they can not be interpreted (even at a very low kinetic energy of nuclei) in terms of the motion of a representative point over a multidimensional potential-energy surface. The breakdown of the Born-Oppenheimer approximation, which manifests itself in the so-called nonadiabatic coupling of electronic and nuclear motion, induces transitions between electronic states that remain still well defined at infinitely large intermolecular distances. 

Fig. 38. The probability to exit on the reactive side (of the upper electronic potential energy surface as a function of the relative velocity in a near collinear CH3I + CH3I collision, see inset. The results are shown for three impact parameters as indicated. The arrow indicates the nominal energy threshold for accessing the upper electronic surface. Computed by the quantal FMS method. The reactive side includes both the formation of molecular products (CH3CH3 +12 as well as CH3 + CH3 + I2 etc.).

The exact mechanism arises in the process of inverse pre-dissociation, as discussed in detail by Herzberg (1966). During an atom-molecule collision, the reactants interact with one another subject to the relevant potential energy surface. The lifetime of this excited intermediate is on the order of molecular vibrational periods, or 10 s. The lifetime is a complex function of the chemical reaction dynamics, which in turn depends on the number of available states. In this specific instance, there is a state dependence for the isotopically substimted species. Ozone of pure has a Cav symmetry and has half the rotational complement of the asymmetric isotopomers. As a result, it was suggested that the extended lifetime for the asymmetric species leads to a greater probability of stabilization. While these assumptions are valid for a gas phase molecular reaction, they do not sufficiently account for the totality of the experimental ozone isotopic observations. Reviews by Weston (1999) and Thiemens (1999) have detailed the physical-chemical reasons. 

The moments and polarizabilities of molecules can be determined by indirect means. In collision experiments, the nature of the interaction is governed by the potential energy surface, itself a function of the molecular properties of the colliding partners. Usually the potential energy is written in a multipole expansion whereby the electrical properties are displayed in the long-range terms [38]. The potential that is generated must satisfy simultaneously... 

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