Potential Energy Surface

A potential energy surface is generally used within the adiabatic or Born–Oppenheimer approximation in quantum mechanics and statistical mechanics to model chemical reactions and interactions in simple chemical and physical systems. The "(hyper)surface" name comes from the fact that the total energy of an atom arrangement can be represented as a curve or (multidimensional) surface, with atomic positions as variables. The best visualization for a layman would be to think of a landscape, where going North-South and East-West are two independent variables (the equivalent of two geometrical parameters of the molecule), and the height of the land we are on would be the energy associated with a given value of such variables.

There is a natural correspondence between potential energy surfaces as they exist (as polynomial surfaces) and their application in potential theory, which associates and studies harmonic functions in relation to these surfaces.

For example, the Morse potential and the simple harmonic potential well are common one-dimensional potential energy surfaces (potential energy curves) in applications of quantum chemistry and physics.

These simple potential energy surfaces (which can be obtained analytically), however, only provide an adequate description of the very simplest chemical systems. To model an actual chemical reaction, a potential energy surface must be created to take into account every possible orientation of the reactant and product molecules and the electronic energy of each of these orientations.

Typically, the electronic energy is obtained for each of tens of thousands of possible orientations, and these energy values are then fitted numerically to a multidimensional function. The accuracy of these points depends upon the level of theory used to calculate them. For particularly simple surfaces (such as H + H2), the analytically derived LEPS (London-Eyring-Polanyi-Sato) potential surface may be sufficient. Other methods of obtaining such a fit include cubic splines, Shepard interpolation, and other types of multidimensional fitting functions.

Once the potential energy surface has been obtained, several points of interest must be determined. Perhaps the most important is the global minimum for the energy value. This global minimum, which can be found numerically, corresponds to the most stable nuclear configuration. Other interesting features are the reaction coordinate (the path along the potential energy surface that the atoms "travel" during the chemical reaction), saddle points or local maxima along this coordinate (which correspond to transition states), and local minima along this coordinate (which correspond to reactive intermediates).

Single-point energy is the potential energy of a molecule for a given arrangement of the atoms in the molecule. The single point energy is simply a numeric value of the potential energy surface.

Outside of physics and chemistry, "potential energy" surfaces may be associated with a cost function, which may be explored in order to minimize the function.

Other articles related to "energy, potential energy, potential energy surface, potential":

Obesity
... Obesity is most commonly caused by a combination of excessive food energy intake, lack of physical activity, and genetic susceptibility, although a few cases are caused primarily by genes, endocrine disorders ... due to a slow metabolism is limited on average obese people have a greater energy expenditure than their thin counterparts due to the energy required to maintain an ... quality can be improved by reducing the consumption of energy-dense foods such as those high in fat and sugars, and by increasing the intake of dietary fiber ...
Transformations of Energy
... One form of energy can often be readily transformed into another with the help of a device- for instance, a battery, from chemical energy to electric energy a dam gravitational potential energy to kinetic ... Similarly, in the case of a chemical explosion, chemical potential energy is transformed to kinetic energy and thermal energy in a very short time ... At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum ...
Semi-rigid Molecule - Potential Energy Surface
... The potential, derived from these forces, is a function of the Cartesian nuclear coordinates R1.. ... The potential function is known as force field or potential energy surface written as V(R1.. ... Often a more accurate representation of the potential V is obtained by the use of internal curvilinear coordinates, so-called valence coordinates ...
Vinylcyclopropane Rearrangement - Mechanism
... rearrangement was discovered, it was established that the activation energy for the vinylcyclopropane rearrangement is around 50 kcal/mol ... seemed likely it was shortly recognized that the activation energy to break the carbon-carbon bond in unsubstituted cyclopropane was with 63 kcal/mol exactly 13 kcal/mol higher in energy than the parent activation ... Furthermore their analysis revealed potential experiments that would allow to distinguish between a concerted or stepwise mechanism ...
Transition State Theory - Development - Potential Energy Surfaces
... The concept of potential energy surface was very important in the development of TST ... progress of a chemical reaction could be described as a point in a potential energy surface with coordinates in atomic momenta and distances ... In 1931, Eyring and Michael Polanyi constructed a potential energy surface for the reaction below ...

Famous quotes containing the words surface, potential and/or energy:

    How easily it falls, how easily I let drift
    On the surface of morning feathers of self-reproach:
    How easily I disperse the scolding of snow.
    Philip Larkin (1922–1986)

    While each child is born with his or her own distinct genetic potential for physical, social, emotional and cognitive development, the possibilities for reaching that potential remain tied to early life experiences and the parent-child relationship within the family.
    Bernice Weissbourd (20th century)

    Viewed narrowly, all life is universal hunger and an expression of energy associated with it.
    Mary Ritter Beard (1876–1958)