Tersoff potential reactive empirical bond-order

In the early 1990s, Brenner and coworkers [163] developed interaction potentials for model explosives that include realistic chemical reaction steps (i.e., endothermic bond rupture and exothermic product formation) and many-body effects. This potential, called the Reactive Empirical Bond Order (REBO) potential, has been used in molecular dynamics simulations by numerous groups to explore atomic-level details of self-sustained reaction waves propagating through a crystal [163-171], The potential is based on ideas first proposed by Abell [172] and implemented for covalent solids by Tersoff [173]. It introduces many-body effects through modification of the pair-additive attractive term by an empirical bond-order function whose value is dependent on the local atomic environment. The form that has been used in the detonation simulations assumes that the total energy of a system of N atoms is ... 

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. 

To address this problem, Monte Carlo simulations [32] and MD smdies [33-37] have been carried out before, aU of them using reactive empirical bond-order (REBO) Tersoff-type [38,39] interatomic carbon-carbon potentials developed originally for studying the vapor deposition of diamond [40,41]. Unlike traditional molecular mechanics force fields, the REBO potential allows for the formation and dissociation of covalent chemical bonds by determination of next neighbors and on-the-fly switching... 

The most widely used family of reactive FFs is based on the concept of bond order it is assumed that the strength of a bond between two atoms is not constant, but depends on the local environment. Examples indude the Tersoff potential,the reactive empirical bond order (REBO and REB02) modd, the adaptive intermolecular reactive empirical bond order (AIREBO) model, the second-moment TB potentials, and the bond-based analytic bond order (BOP) potentials. These models allow for bond formation,... 

One particularly successful example of a Tersoff potential is the reactive empirical bond-order (REBO) potential developed by Brenner (26-29) to describe the covalent bonding interactions in carbon and hydrocarbon systems. Originally developed for use in simulating the chemical vapor deposition of diamond (26), the REBO potential has recently been extended to provide more accurate treatment of the energetic, elastic, and vibrational properties of solid carbon and small hydrocarbons (29). 

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. 

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