Energy potential, surfaces

The complete intemiolecular potential energy surface depends upon the intemiolecular distance and up to five angles, as discussed in section Al.5,1.3. 

Hu C H and Thakkar A J 1996 Potential energy surface for interactions between N2 and He ab initio calculations, analytic fits, and second virial coefficients J. Chem. Phys. 104 2541 

Figure Al.4.6. A cross-section of the potential energy surface of PH. The coordinate p is defined in figure Al.4.5.

It is the relationship between the bound potential energy surface of an adsorbate and the vibrational states of the molecule that detemiine whether an adsorbate remains on the surface, or whether it desorbs after a period of time. The lifetime of the adsorbed state, r, depends on the size of the well relative to the vibrational energy inlierent in the system, and can be written as 

LeRoy R J and Hutson J M 1987 Improved potential energy surfaces for the interaction of H2 with Ar, Kr and Xe J. Chem. Phys. 86 837 

For a molecule that has no observable tiumelling between minima on the potential energy surface (i.e., for a 

LeRoy R J and Carley J S 1980 Spectroscopy and potential energy surfaces of van der Waals molecules Adv. Chem. Phys. 42 353 

Figure Al.6.10. (a) Schematic representation of the three potential energy surfaces of ICN in the Zewail experiments, (b) Theoretical quantum mechanical simulations for the reaction ICN ICN [I--------------

Because of the general difficulty encountered in generating reliable potentials energy surfaces and estimating reasonable friction kernels, it still remains an open question whether by analysis of experimental rate constants one can decide whether non-Markovian bath effects or other influences cause a particular solvent or pressure dependence of reaction rate coefficients in condensed phase. From that point of view, a purely 

Jeziorski B, Moszynski R and Szalewicz K 1994 Perturbation theory approach to intermolecular potential energy surfaces of van der Waals complexes Chem. Rev. 94 1887 

CN] —> I + CN. Wavepacket moves and spreads in time, with its centre evolving about 5 A in 200 fs. Wavepacket dynamics refers to motion on the intennediate potential energy surface B. Reprinted from Williams S O and lime D G 1988 J. Phys. Chem.. 92 6648. (c) Calculated FTS signal (total fluorescence from state C) as a fiinction of the time delay between the first excitation pulse (A B) and the second excitation pulse (B -> C). Reprinted from Williams S O and Imre D G, as above. 

This section discusses how spectroscopy, molecular beam scattering, pressure virial coeflScients, measurements on transport phenomena and even condensed phase data can help detemiine a potential energy surface. 

Rosker M J, Rose T S and Zewail A 1988 Femtosecond real-time dynamics of photofragment-trapping resonances on dissociative potential-energy surfaces Ghem. Phys. Lett. 146 175-9 

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. 

The result is that, to a very good approxunation, as treated elsewhere in this Encyclopedia, the nuclei move in a mechanical potential created by the much more rapid motion of the electrons. The electron cloud itself is described by the quantum mechanical theory of electronic structure. Since the electronic and nuclear motion are approximately separable, the electron cloud can be described mathematically by the quantum mechanical theory of electronic structure, in a framework where the nuclei are fixed. The resulting Bom-Oppenlieimer potential energy surface (PES) created by the electrons is the mechanical potential in which the nuclei move. Wlien we speak of the internal motion of molecules, we therefore mean essentially the motion of the nuclei, which contain most of the mass, on the molecular potential energy surface, with the electron cloud rapidly adjusting to the relatively slow nuclear motion. 

The theory coimecting transport coefficients with the intemiolecular potential is much more complicated for polyatomic molecules because the internal states of the molecules must be accounted for. Both quantum mechanical and semi-classical theories have been developed. McCourt and his coworkers [113. 114] have brought these theories to computational fruition and transport properties now constitute a valuable test of proposed potential energy surfaces that 

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