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Potential energy is the energy by virtue of an object's position relative to other objects. [6] Potential energy is often associated with restoring forces such as a spring or the force of gravity. The action of stretching a spring or lifting a mass is performed by an external force that works against the force field of the potential.
In simplest terms, a potential energy surface or PES is a mathematical or graphical representation of the relation between energy of a molecule and its geometry. The methods for describing the potential energy are broken down into a classical mechanics interpretation (molecular mechanics) and a quantum mechanical interpretation.
The forces acting between atoms can be obtained by differentiation of the total energy with respect to atom positions. That is, to get the force on atom one should take the three-dimensional derivative (gradient) of the potential with respect to the position of atom :
A potential energy surface (PES) or energy landscape describes the energy of a system, especially a collection of atoms, in terms of certain parameters, normally the positions of the atoms. The surface might define the energy as a function of one or more coordinates; if there is only one coordinate, the surface is called a potential energy ...
The Lennard-Jones potential is a simple model that still manages to describe the essential features of interactions between simple atoms and molecules: Two interacting particles repel each other at very close distance, attract each other at moderate distance, and eventually stop interacting at infinite distance, as shown in the Figure.
The gravitational potential (V) at a location is the gravitational potential energy (U) at that location per unit mass: =, where m is the mass of the object. Potential energy is equal (in magnitude, but negative) to the work done by the gravitational field moving a body to its given position in space from infinity.
Depending on the material and the degree of detail desired, a variety of energy levels will be plotted against position: E F or μ: Although it is not a band quantity, the Fermi level (total chemical potential of electrons) is a crucial level in the band diagram. The Fermi level is set by the device's electrodes.
A graph of the potential energy of a bistable system; it has two local minima and .A surface shaped like this with two "low points" can act as a bistable system; a ball resting on the surface can only be stable at those two positions, such as balls marked "1" and "2".