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| '''Bond order potential''' is a class of empirical (analytical) potentials which is used in [[molecular dynamics]] and [[molecule|molecular]] statics simulations. Examples include the [[Jerry Tersoff|Tersoff]] potential,<ref name="Tersoff88">{{cite journal
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| | first = J.
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| | last = Tersoff
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| | authorlink = | coauthors = | year = 1988
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| | month = | title = | journal = Phys. Rev. B
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| | volume = 37
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| | issue = | pages = 6991
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| | id = | url = | doi=10.1103/PhysRevB.37.6991|bibcode = 1988PhRvB..37.6991T }}</ref> the Brenner potential,<ref>{{cite journal
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| | first = D. W.
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| | last = Brenner | |
| | authorlink =| coauthors = | year = 1990
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| | month = | title = | journal = Phys. Rev. B
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| | volume = 42
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| | issue = 15
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| | pages = 9458
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| | id =| url = | doi=10.1103/PhysRevB.42.9458 | bibcode=1990PhRvB..42.9458B}}</ref> the Finnis-Sinclair potentials,
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| <ref>{{cite journal
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| | first = M. W.
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| | last = Finnis
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| | authorlink =| coauthors = | year = 1984
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| | month = | title = A simple empirical N-body potential for transition metals
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| | journal = Phil. Mag. A
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| | volume = 50
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| | issue = 1
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| | pages = 45
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| | id =| url =| doi = 10.1080/01418618408244210
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| |bibcode = 1984PMagA..50...45F }}</ref> ReaxFF,<ref>ReaxFF: A Reactive Force Field for Hydrocarbons, Adri C. T. van Duin, Siddharth Dasgupta, Francois Lorant, and William A. Goddard III, J. Phys. Chem. A, 2001, 105 (41), pp 9396–9409</ref>
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| and the second-moment tight-binding potentials.
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| <ref>{{cite journal
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| | first = F.
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| | last = Cleri
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| | authorlink = | coauthors = V. Rosato
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| | year = 1993
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| | month = | title = Tight-binding potentials for transition metals and alloys
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| | journal = Phys. Rev. B
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| | volume = 48
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| | issue = | pages = 22
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| | id = | url =| doi = 10.1103/PhysRevB.48.22 | bibcode=1993PhRvB..48...22C
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| }}</ref>
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| They have the advantage over conventional [[molecular mechanics]] [[Force field (chemistry)|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 reaction]]s 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 [[molecular geometry|angles]] and [[bond length]]. It is based on the [[Linus Pauling]] [[bond order]] concept
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| <ref name="Tersoff88"/>
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| ,<ref>{{cite journal
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| | first = G. C.
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| | last = Abell
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| | authorlink = | coauthors = | year = 1985
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| | month = | title = | journal = Phys. Rev. B
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| | volume = 31
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| | issue = | pages = 6184
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| | id = | url =|bibcode = 1985PhRvB..31.6184A |doi = 10.1103/PhysRevB.31.6184 }}</ref>
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| and can be written in the form | |
| | |
| <math>
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| V_{ij}(r_{ij}) = V_{repulsive}(r_{ij}) + b_{ijk} V_{attractive}(r_{ij})
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| </math>
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| This means that the potential is written as a simple pair potential depending on the distance between two atoms <math>r_{ij}</math>, but the [[bond strength|strength]] of this bond is modified by the environment of the atom <math>i</math> via the <math>b_{ijk}</math>term. Alternatively, the [[energy]] can be written in the form
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| | |
| <math>
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| V_{ij}(r_{ij}) = V_{pair}(r_{ij}) - D \sqrt{\rho_i}
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| </math>
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| where <math>\rho_i</math> is the [[electron density]] at the location of atom <math>i</math>. These two forms for the energy can be shown to be equivalent.
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| <ref>{{cite journal
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| | first = D.
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| | last = Brenner
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| | authorlink = | coauthors = | year = 1989
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| | month = | title = | journal = Phys. Rev. Lett.
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| | volume = 63
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| | issue = | pages = 1022
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| | id = | url =|bibcode = 1989PhRvL..63.1022B |doi = 10.1103/PhysRevLett.63.1022 }}</ref>
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| 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
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| <ref>{{cite journal
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| | first = K.
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| | last = Albe
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| | authorlink = | coauthors = K. Nordlund
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| | year = 2002
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| | month = | title = | journal = Phys. Rev. B
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| | volume = 65
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| | issue = | pages = 195124
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| | id = | url =}}</ref>
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| 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.
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| .<ref>{{cite journal
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| | first = D. G.
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| | last = Pettifor
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| | authorlink = | coauthors = I. I. Oleinik
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| | year = 1999
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| | month = | title = Analytic bond-order potentials beyond TersofF Brenner. I. Theory
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| | journal = Phys. Rev. B
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| | volume = 59
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| | issue = | pages = 8487
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| | id = | url =| doi = 10.1103/PhysRevB.59.8487
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| |bibcode = 1999PhRvB..59.8487P }}</ref>
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| 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.<ref name="Kuhlmann07">{{cite journal
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| | first = V.
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| | last = Kuhlmann
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| | authorlink = | coauthors = K. Scheerschmidt
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| | year = 2007
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| | month = | title = σ-bond expression for an analytic bond-order potential: Including π and on-site terms in the fourth moment
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| | journal = Phys. Rev. B
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| | volume = 76
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| | issue = 1
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| | pages = 014306
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| | id = | url =| doi = 10.1103/PhysRevB.76.014306
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| |bibcode = 2007PhRvB..76a4306K }}</ref>
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| 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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| == References ==
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| <references/>
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| {{DEFAULTSORT:Bond Order Potential}}
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| [[Category:Computational chemistry]]
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| [[Category:Computational physics]]
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