Bond order potential

Bond order potentials are a class of empirical (analytical) potentials used e.g. in molecular dynamics and molecular statics simulations. Examples include the Tersoff potentialcite journal
first = J.
last = Tersoff
authorlink =
coauthors =
year = 1988
month =
title =
journal = Phys. Rev. B
volume = 37
issue =
pages = 6991
id =
url =
] , the Brenner potential [cite journal
first = D. W.
last = Brenner
authorlink =
coauthors =
year = 1990
month =
title =
journal = Phys. Rev. B
volume = 42
issue = 15
pages = 9458
id =
url =
] , the Finnis-Sinclair potentials [cite journal
first = M. W.
last = Finnis
authorlink =
coauthors =
year = 1984
month =
title =
journal = Phil. Mag. A
volume = 50
issue = 1
pages = 45
id =
url =
doi = 10.1080/01418618408244210] and the second-moment tight-binding potentials. [cite journal
first = F.
last = Cleri
authorlink =
coauthors = V. Rosato
year = 1993
month =
title = Tight-binding potentials for transition metals and alloys
journal = Phys. Rev. B
volume = 48
issue =
pages = 22
id =
url =
doi = 10.1103/PhysRevB.48.22] They have the advantage over e.g. conventional molecular mechanics force fields 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 (number of bonds and possibly also angles and distances) of an atom.This concept is based on the Linus Pauling bond order concept [cite journal
first = G. C.
last = Abell
authorlink =
coauthors =
year = 1985
month =
title =
journal = Phys. Rev. B
volume = 31
issue =
pages = 6184
id =
url =
] cite journal
first = J.
last = Tersoff
authorlink =
coauthors =
year = 1988
month =
title =
journal = Phys. Rev. B
volume = 37
issue =
pages = 6991
id =
url =
] ,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 $r\_\{ij\}$, but the strength of this bond is modified by the environment of the atom i via the $b\_\{ijk\}$term. Alternatively, the energy can be written in the form

$V\_\{ij\}(r\_\{ij\})\; =\; V\_\{pair\}(r\_\{ij\})\; -\; D\; sqrt\{\; ho\_i\}$

where $ho\_i$ is an 'electron density' at the locationof atom i. These two forms for the energy can be shown to beequivalent. [cite journal
first = D.
last = Brenner
authorlink =
coauthors =
year = 1989
month =
title =
journal = Phys. Rev. Lett.
volume = 63
issue =
pages = 1022
id =
url =
]

A more detailed summary of how the bond order concept can be motivatedby the second-moment approximation of tight binding and both ofthese functional forms derived from it can be found in [cite journal
first = K.
last = Albe
authorlink =
coauthors = K. Nordlund
year = 2002
month =
title =
journal = Phys. Rev. B
volume = 65
issue =
pages = 195124
id =
url =
]

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 [cite journal
first = D. G.
last = Pettifor
authorlink =
coauthors = I. I. Oleinik
year = 1999
month =
title = Analytic bond-order potentials beyond TersofF Brenner. I. Theory
journal = Phys. Rev. B
volume = 59
issue =
pages = 8487
id =
url =
doi = 10.1103/PhysRevB.59.8487] .Also the ReaxFF potential can be considered a bond-order potentialalthough the motivation of its bond order terms is different fromthat described here.

References