Potential Energy Hyper Surface PES

Computational methods typically employ the Born-Oppenheimer approximation in most electronic structure programs to separate the nuclear and electronic parts of the Schrodinger equation that is still hard enough to solve approximately. There would be no potential energy (hyper)surface (PES) without the Born-Oppenheimer approximation -how difficult mechanistic organic chemistry would be without it ... 

Within the Born-Oppenheimer approximation, the results of molecular collisions depend on the motion of the nuclear particles (atoms) on the potential energy (hyper) surface (PES) that describes how the electronic energy of the... 

A point of lowest tnaxitnutn energy on a valley (reaction path) connecting two minima on the potential energy (hyper)surface (PES). In mathematical terms, the stationary point on the PES in which the Hessian matrix has only one negative eigenvalue is assigned to the saddle point of the first rank, a transition structure. 

In the case of a polyatomic molecule with N atoms (N > 2), V j depends on 3N — 6 variables determining the configuration of the nuclei. The function Vu(R) therefore represents a surface in (3N — 5)-dimensional space (a hypersuiface). This potential energy (hyper)surface Vkj R), or PES, for the motion of the nuclei represents one of the most important ideas in chemistry. 

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