Bond Order Potential

Bond order potential is a class of empirical (analytical) potentials which is used in molecular dynamics and molecular statics simulations. Examples include the Tersoff 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 length. It is based on the Linus Pauling bond order concept, and can be written in the form

V_{ij}(r_{ij}) = V_{repulsive}(r_{ij}) + b_{ijk} V_{attractive}(r_{ij})

This means that the potential is written as a simple pair potential depending on the distance between two atoms, but the strength of this bond is modified by the environment of the atom via the term. Alternatively, the energy can be written in the form

V_{ij}(r_{ij}) = V_{pair}(r_{ij}) - D \sqrt{\rho_i}

where is the electron density at the location of atom . These two forms for the energy can be shown to be equivalent.

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.

Famous quotes containing the words bond, order and/or potential:

    “Camillo. Prosperity’s the very bond of love,
    Whose fresh complexion and whose heart together
    Affliction alters.
    Perdita. One of these is true:
    I think affliction may subdue the cheek,
    But not take in the mind.”
    —William Shakespeare (1564–1616)

    “Russian forests crash down under the axe, billions of trees are dying, the habitations of animals and birds are layed waste, rivers grow shallow and dry up, marvelous landscapes are disappearing forever.... Man is endowed with creativity in order to multiply that which has been given him; he has not created, but destroyed. There are fewer and fewer forests, rivers are drying up, wildlife has become extinct, the climate is ruined, and the earth is becoming ever poorer and uglier.”
    —Anton Pavlovich Chekhov (1860–1904)

    “The germ of violence is laid bare in the child abuser by the sheer accident of his individual experience ... in a word, to a greater degree than we like to admit, we are all potential child abusers.”
    —F. Gonzalez-Crussi, Mexican professor of pathology, author. “Reflections on Child Abuse,” Notes of an Anatomist (1985)