Potential energy surface
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A potential energy surface (PES) is a theoretical concept used to describe the energy of a system, especially a collection of atoms, in terms of certain parameters, normally the positions of the atoms. The surface might be in 1 or more dimensions. It is helpful to use the analogy of a landscape: for a system with two degrees of freedom (e.g. two bond lengths), the value of the energy (the height of the land) is a function of the bond lengths (the position on the ground).
The PES concept finds application in fields such as chemistry and physics, especially in the theoretical sub-branches of these subjects. It can be used to theoretically explore properties of structures composed of atoms, for example, finding the minimum energy shape of some molecule and computing the rates of a chemical reaction.
Outside of chemistry and physics, potential energy surfaces may be associated with some quantity unrelated to energy, such as some cost function which is to be minimized.
These simple potential energy surfaces (which can be obtained analytically), however, only provide an adequate description of the very simplest chemical systems.
Computing Potential Energy Surfaces
To model a chemical reaction, it must be possible to calculate the energy for every arrangement of the atoms that one is interested in. For particularly simple surfaces some analytically derived expressions can be appropriate (such as for H + H2, the London-Eyring-Polanyi-Sato potential).
Often, for more complicated systems, calculation of the energy of a particular arrangement of atoms can be to computationaly expensive for large scale repesentations of the surface to be feasible. For these systems it is normal to calculate only the points
One possibility is to obtain the energy for each of tens of thousands of possible orientations and the obtained points are used by an interpolation algorithm, for example Shepard interpolation, to fill in the gaps.
Applications of a Potential Energy Surface
Once it is possible to evaluate the necessary points on a PES, the points can be further classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. Stationary points, that is, those points with a zero gradient, have some physical meaning: energy minima correspond to physically stable chemical species and saddle points correspond to transition states, the highest energy point on the reaction pathway, that is, the lowest energy pathway connecting a chemical reactant to a chemical product. See geometry optimization for more information.