Bond order potential is a class of empirical (analytical) interatomic potentials which is used in molecular dynamics and molecular statics simulations. Examples include the Tersoff potential, the EDIP potential, the Brenner potential, the Finnis–Sinclair potentials, ReaxFF, and the second-moment tight-binding potentials.

They have the advantage over conventional molecular mechanics force fields in that they can, with the same parameters, describe several different bonding states of an atom, and thus to some extent may be able to describe chemical reactions correctly. The potentials were developed partly independently of each other, but share the common idea that the strength of a chemical bond depends on the bonding environment, including the number of bonds and possibly also angles and bond lengths. It is based on the Linus Pauling bond order concept and can be written in the form

, but the strength. In case of only one atomic bond (like in a diatomic molecule and the potential turns completely repulsive (as illustrated in the figure to the right).

Alternatively, the potential energy can be written in the embedded atom model form

is the electron density contains no angular dependence).

A more detailed summary of how the bond order concept can be motivated by the second-moment approximation of tight binding and both of these functional forms derived from it can be found in.

The original bond order potential concept has been developed further to include distinct bond orders for sigma bonds and pi bonds in the so-called BOP potentials.

Extending the analytical expression for the bond order of the sigma bonds to include fourth moments of the exact tight binding bond order reveals contributions from both sigma- and pi- bond integrals between neighboring atoms. These pi-bond contributions to the sigma bond order are responsible to stabilize the asymmetric before the symmetric (2x1) dimerized reconstruction of the Si(100) surface.

Also the ReaxFF potential can be considered a bond order potential, although the motivation of its bond order terms is different from that described here.

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