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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
| | The name of the writer is Jayson. Distributing production has been his occupation for some time. North Carolina is where we've been living for years and will never move. To climb is something I truly appreciate performing.<br><br>Here is my website ... free psychic; [http://Www.octionx.sinfauganda.Co.ug/node/22469 my homepage], |
| | 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
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| | 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
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| | |
| <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> | |
| 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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The name of the writer is Jayson. Distributing production has been his occupation for some time. North Carolina is where we've been living for years and will never move. To climb is something I truly appreciate performing.
Here is my website ... free psychic; my homepage,