Potential energy surface structure

There is also the possibility of distonic, superelectrophilic bis-carbo-nium ions. Despite the fact that such species may be important in the superacid-catalyzed cracking reactions of aliphatic hydrocarbons, there have been very few studies of such systems. The structures and energies of small distonic alkonium dications have been studied using ab initio calculations.24 For diprotonated -butane (C4Hi22+) two structures were located as stable minima on the potential energy surface. Structure 63 is formed by a protonation of the two terminal C-H bonds, resulting in a pair of two electron-three center bonds. The other structure (64) arises from protonation of the terminal C-H bond and the most distant C-C bond. 

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. 

Schlegel H B 1995 Geometry optimization on potential energy surfaces Modern Electronic Structure Theory vo 2, ed D R Yarkony (Singapore World Scientific) pp 459-500... 

Jensen F 1994 Transition structure modeling by intersecting potential energy surfaces J. Comput. Chem. 15 1199... 

Keywords, protein folding, tertiary structure, potential energy surface, global optimization, empirical potential, residue potential, surface potential, parameter estimation, density estimation, cluster analysis, quadratic programming... 

Transition stale search algorithms rather climb up the potential energy surface, unlike geometry optimi/.ation routines where an energy minimum is searched for. The characterization of even a simple reaction potential surface may result in location of more than one transition structure, and is likely to require many more individual calculations than are necessary to obtain et nilibrinm geometries for either reactant or product. 

Molecular mechanics methods are not generally applicable to structures very far from equilibrium, such as transition structures. Calculations that use algebraic expressions to describe the reaction path and transition structure are usually semiclassical algorithms. These calculations use an energy expression fitted to an ah initio potential energy surface for that exact reaction, rather than using the same parameters for every molecule. Semiclassical calculations are discussed further in Chapter 19. 

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. 

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. 

Obtain the transition structure from the entire potential energy surface. It is questionable that there will be any case where this is the only option, but it should work as a desperate last resort. 

E. Kracka, T. H. Dunning, Jr., Advances in Molecular Electronic Structure Theory Calculation and Characterization of Molecular Potential Energy Surfaces T. H. Dunning, Jr. Ed., 129, JAI, Greenwich (1990). 

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