Reactive empirical bond-order potential

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... 

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... 

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... 

Monte Carlo and molecular dynamics for statistical thermodynamics, potential energy functions and applications, discovery of applicability of potential energy functions, reactive empirical bond order potentials... 

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 ... 

Brenner DW, Shenderova OA, Harrison JA, Stuart SJ, Ni B, Sinnott S (2002) A second generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys. Cond. Matt. 14 783-802... 

Reactive Empirical Bond Order (REBO) Potentials... 

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. 

We have chosen to study the latter, reactive empirical bond-order (REBO) potential, introduced by Brenner et al. [20]. The binding energy of an 7V-atom system is given by... 

In Section 3, we showed that large-scale molecular-dynamics (MD) simulations could be used to study the effect of impacts upon perfect crystals of high-explosive diatomic molecules whose interactions are modeled by the reactive empirical bond-order (REBO) potential. We showed that perfect crystal shock simulations lead to detonation above a threshold impact velocity, with characteristics that satisfy the ZND theory of detonations. To see if the threshold for initiation of chemical reaction can be lowered, we also introduced a variety of defects into our samples. 

The main remaining limitation of these kinds of potentials is the lack of terms to represent chemical reactions. Some recent progress along these lines, particularly in the field of energetic materials, has been recently reviewed.[138] The most important developments have been achieved so far using reactive empirical bond order (REBO) potentials introduced by Brenner and coworkers.[139] The REBO potentials have been used mainly for simulations of shockwave propagation in simple diatomic or triatomic molecular crystals however, it is likely that these kinds of potentials will soon be extended to more complex systems. A reactive potential based on somewhat different bond order concepts has been used to calculate the initial shock-wave induced chemical events in RDX.[140] To date, to our knowledge, REBO potentials have not been applied to ionic crystals. 

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... 

Silvestre et al. [39] 2011 The second generation reactive empirical bond order (REBO) potential (5,5)(7,7) — — Comparison between budding behavior of SWCNTs with Doimell and Sanders shell theories and MD results... 

Ansari et al. [78] 2012 Adaptive Inteimo-lecular Reactive Empirical Bond Order (AIREBO) potential (8,8) 8.3-39.1 Vibration characteristics and comparison between different gradient theories as well as different beam assumptions in predicting the free vibrations of SWCNTs... 

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. 

Another fairly new method, using the electrostatic molecular potential, will not be discussed here since it is the subject of another contribution to this volume 50>. I will now consider methods that have had the widest application in the theoretical study of chemical reactivity, in order of increasing complexity a) molecular mechanics b) extended Htickel method c), d) empirical self-consistent field methods such as CNDO and MINDO e) the simplest ab initio approach f) the different S.C.F. methods, possibly including configuration interaction g) valence bond methods, and h) the dynamical approach, including the calculation of trajectories 61>. 

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