Bond order potential

The Tersoff potential [Tersoff 1988] is based on a model known as the empirical bond-order potential. This potential can be written in a form very similar to the Finnis-Sinclair potential ... 

The key term is which is the bond order between the atoms i and j. This parameter depends upon the number of bonds to the atom i the strength of the bond between i and j decreases as the number of bonds fo fhe atom i increases. The original bond-order potential [Abell 1985] is mathematically equivalent to the Finnis-Sinclair model if the bond order by is given by ... 

An expression of the type (7.101), which gives the bond order explicitly in terms of the positions of the neighbouring atoms, is called a bond order potential (BOP). Angularly dependent bond order potentials were first derived heuristically for the elemental semiconductors by TersofF (1988). We will see in the next chapter that a many-body expansion for the bond order may be derived exactly within the model. 

Fig. 8.20 Convergence of the bcc-fcc d bond energy (full curve) and hcp-fcc d bond energy (dashed curve) with respect to the number of terms in the bond order potential expansion. The left, middle and right panels correspond to keeping terms up to fourth, sixth and eighteenth moments respectively. (From Aoki (1993).)...

As in the MD method, PES for KMC can be derived from first-principles methods or using empirical energy functionals described above. However, the KMC method requires the accurate evaluation of the PES not only near the local minima, but also for transition regions between them. The corresponding empirical potentials are called reactive, since they can be used to calculate parameters of chemical reactions. The development of reactive potentials is quite a difficult problem, since chemical reactions usually include the breaking or formation of new bonds and a reconfiguration of the electronic structure. At present, a few types of reactive empirical potentials can semi-quantitatively reproduce the results of first-principles calculations these are EAM and MEAM potentials for metals and bond-order potentials (Tersoff and Brenner) for covalent semiconductors and organics. 

A. Lagana, G.O. de Aspuru, E. Garcia, The largest angle generalization of the rotating bond order potential Three different atom reactions, /. Chem. Phys. 108 (10) (1998) 3886-3896. 

In Sec. 2, we review the reactive empirical bond order potentials that we have developed over the last decade which possess these essential characteristics. Our model systems and computational techniques are also described. Simulations using the first of our models to exhibit classic detonation behavior are discussed in Sec. 3, where results involving both detonation and initiation are presented. In Sec. 4, the results of our molecular dynamics simulations are compared in detail with the predictions of continuum theory. Then, in Sec. 5, we review some simulations that raise... 

To overcome this limitation we developed a series of potentials in the late 1980 s and early 1990 s that have become known as reactive empirical bond order (REBO) potentials. These potentials are based on the empirical bond order potential form introduced by Tersoff to describe the static properties of silicon but were tailored by us to incorporate a modicum of chemistry. In Sec. 2.1, after introducing the REBO potential form, we describe our simple models for energetic materials that are based on these potentials. In Sec. 2.2, we provide an overview of the approach taken to implement our simulations of shock-induced chemistry and detonations. 

Many body potentials e.g. Sutton-Chen, Tersoff, " Brenner can be used to describe metals and other continuous solids such as silicon and carbon. The Brenner potential has been particularly successful with fullerenes, carbon nanotubes and diamond. Erhart and Albe have derived an analytical potential based on Brenner s work for carbon, silicon and silicon carbide. The Brenner and Tersolf potentials are examples of bond order potentials. These express the local binding energy between any pair of atoms/ions as the sum of a repulsive term and an attractive term that depends on the bond order between the two atoms. Because the bond order depends on the other neighbours of the two atoms, this apparently two-body potential is in fact many-body. An introduction and history of such potentials has recently been given by Finnis in an issue of Progress in Materials Science dedicated to David Pettifor. For a study of solid and liquid MgO Tangney and Scandolo derived a many body potential for ionic systems. 

The more sophisticated potentials used in the nanowire study point to an important consideration in modeling such systems. Simple potentials are parameterized under bulk homogeneous conditions and may give poor descriptions of the inhomogeneous environment near a crack tip. In an effort to employ a classical potential that is responsive to a rapidly changing environment, Omeltchenko and coworkers ° simulated a graphite sheet modeled by more than a million particles. The authors used a reactive bond order potential developed by Brenner. In this approach, the total potential energy can be written as follows ... 

The energy partition method described here is essentially the same as Pettifor s bond order potential(12,13). He and his coauthors utilize it to analyze chemical bonds of variety of materials quantitatively 14). 

Molecular dynamics studies of diatomic model detonations were first carried out by Karo and Hardy in 1977 [14]. They were soon followed by other groups [15, 16]. These early studies employed predissociative potentials, in which the reactant dimer molecules are metastable and can dissociate exothermically. More realistic models, combining an endothermic dissociation of reactants with an exothermic formation of product molecules, were introduced by White and colleagues at the Naval Research Laboratory and U.S. Naval Academy, first using a LEPS (London-Eyring-Polanyi-Sato) three-body potential for nitric oxide [17], and later a Tersoff-type bond-order potential [18] for a generic AB model, loosely based on NO [19, 20]. 

Despite this progress several areas require further development. For example, we have evidenced that only a limited number of force fields are presently available for treatment of ionic salts, It will be very beneficial that this gap will be filled and general, transferable sets of force fields for different classes of ionic systems will be available as is the case with other classes of energetic materials such as nitramines systems. We have also pointed out in this chapter that current classical force fields developed for ionic crystals are limited to description of nonreactive processes. Development of reactive force fields such as reactive empirical bond order potentials for the case of ionic systems will represent a major forward step for simulation of reactions and of combustion and denotation processes. 

Fullerenes and carbon onions can be produced by various processes [2-6]. TEM pictures show a wide shape diversity of these particles polyhedral, spherical, highly defected fullerenes with various sizes and number of layers. The spherical structures may contain many defects like (Stone-Wales [7]). In this study we deal with icosahedral regular fullerenes [8] and with very Stone-Wales defective structures that lead to spherical particles [9]. These structures have been optimized with second-generation reactive empirical bond order potential energy (REBO2) [10]. The static dielectric properties are calculated using the RMD... 

Figure 6 Left the two-center terms in the bond-order potential for different local coordinations, and right their influence on the effective pair potential, z is the local coordination.

D. W. Brenner Mater. Res. Soc. Bull., B21, 36 (1996). Chemical Dynamics and Bond-Order Potentials. 

Shibuta, et al. Bond-Order Potential for Transition Metal Carbide Cluster for the Growth Simulation of a Single-Walled Carbon Nanotube. Department of Materials Engineering, The University of Tokyo 2003. 

Pettifor, D., Oleinik, I. Analytic bond-order potentials beyond Tersoff-Brenner. i. Theory. Phys. Rev. B 59, 8487-8499 (1999). doi 10.1103/PhysRevB.59.8487... 

Where is the force acting on the i-th atom or particle at time t and is obtained as the negative gradient of the interaction potential U, m. is the atomic mass and the atomic position. The interaction potentials together with their parameters, describe how the particles in a system interact with each other (so-called force field). Force field may be obtained by quantum method (e g., Ab initio), empirical method (e g., Lennard-Jones, Mores, and Bom-Mayer) or quantum-empirical method (e.g., embedded atom model, glue model, bond order potential). 

A combination of a second generation reactive empirical bond order potential and vdW interactions 0.55,0.73, 0.74,0.76 Predicting Young s modulus by four MD approaches for an armchair (14,14) type SWCNT and investigating effect of defects in the form of vacancies, van der Waals (vdW) interactions, chirality, and diameter... 

The first theoretical work providing information on the Debye temperature (Go) of intermetallic clathrates dates back to the year 1999 [33]. Molecular dynamics calculations for the carbon-framework of type-I and type-II clathrates used a Lennard-Jones potential (later on also for Si-based clathrates [34]). 0d for Ci36 [35] and for Siiae [34] were estimated from the calculated elastic constant Cn applying the empirical relation Qd = —11.3964 + 0.3475 x C — 1.6150 x 10 X Cj 1. Moriguchi et al. [36] used an empirical bond-order potential developed by Tersofif for the calculation of several thermodynamic properties, including the heat capacity, for the type-I and type-II Si networks. From the heat capacity data in the temperature range from 0 to 150 K 6d was extracted applying the Debye-model. The heat capacity, Cy, was calculated by the density functional theory (DFT),... 

The form of interatomic potential suggested by Tersoff [25] is an example of the wider family of bond-order potentials [26]. The total energy is written as a sum of pair like terms. 

The resulting potential is, in fact, a many-body potential, as the bond-order terms depend on the local environment. Bond-order potentials can also be derived from a... 

Figure 2. Isoenergetic contours of the Xt+FJT — XtF+iT Bond-Order potential energy surface. The Contours are drawn at 0.2, 0.5,1.5 and 3.7 eV. The potential energy surface above 3.7 eV has been shaded. The distance from the center of the plot is a measure of 0 whereas the azimuthal an e xa is measured from the positive z-axis. a) Stereographic projection at p = 5.14oo. b) Stereographic projection at p = IO.Ooq.

Two-body potentials are typically a good approximation of neutral atoms such as noble gases, which are dominated by attractive van der Waals forces at separations and with strong repulsion at close distances due to Pauli s exclusion principle. The electronic distributions of other systems, such as covalently bonded materials, are modeled more accurately by more complicated environmentally dependent semiempirical potentials. These include bond-order potentials like Tersoff [11], Brenner [12], and ReaxFF [13] and embedded atom model (EAM) [14] potentials, which are particularly applicable to metallic systems. 

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