Reactive bond order potential

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 ... 

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. 

The results of molecular dynamics simulations are critically dependent on the quality of the force field. In principle, any potential that accurately describes SWNT should have terms that reflect the curvature of the tube. However, curvature effects are largely ignored in force fields published in the literature.20-23 Some potentials, such as those based on reactive bond-order formalism, correctly account for the local curvature in describing the covalent bonding interactions.24-26 But the adsorption... 

In order to include curvature-dependence in both the covalent and non-bonding interactions, we used the adaptive intermolecular reactive bond-order (AIREBO) potential,24 with modified van der Waals interactions. This potential uses the same bonding interactions as Brenner s REBO potential,25,26 both of which correctly account for local curvature dependence in the covalent bonding interactions. Chemisorption is thus treated accurately, but there is no explicit or implicit curvature dependence in the Lennard-Jones (L-J) parameters used to describe the non-bonded van der Waals interactions (physisorption). Consequently, we modified the Lennard-Jones parameters to make them explicitly dependent on the curvature of the nanotube. 

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. 

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... 

Aromatic substitution reactions are often complicated and multistep processes. A correlation, however, in many cases can be found between the charged attacking species and the electron density distribution in the molecule attacked during electrophilic and nucleoph c substitution. No such correlation is expected in radical substitution where the attacking particles are neutral, rather a correlation between the reactivities of separate bonds and a free valency index of the bond order. This allows the prediction of the most reactive bonds. Such an approach has been used by researchers who applied quantum calculations to estimate the reactivities of the isomeric thienothiophenes and to compare them with thiophene or naphthalene. " Until recently quantum methods for studying reactivities of aromatics and heteroaromatics were developed mainly in the r-electron approximation (see, for example, Streitwieser and Zahradnik ). The M orbitals of a sulfur atom were shown not to contribute substantially to calculations of dipole moments, polarographic reduction potentials, spin-density distribution, ... 

A mathematical analysis of all four isomeric thiadiazoles by the simple molecular orbital method has provided molecular diagrams of the free base and conjugate acid of each thiadiazole, with electron densities, bond orders, and free valencies. On this basis, predictions have been made concerning the reactivities of the six non-equivalent carbon atoms, the basicities of the nitrogen atoms, and the delocalization energies in these molecules. The 5-position in free 1,2,4-thiadiazole should possess maximum reactivity in nucleophilic substitution reactions. The treatment also accounts for the order of the polarographic half-wave potentials and the position of the absorption maxima in the ultraviolet region of the spectra of 1,2,4- and 1,3,4-thiadiazoles.4... 

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 ... 

Another reactive force field that is dependent on bond-order was developed by van Duin, Dasgupta, Loran, and Goddard [183] for hydrocarbons. The configurational energy is described as the sum of energy contributions from internal modes as well as non-bonding van der Waals and Coulombic interactions, but the parameters of the functions that describe each contribution is dependent upon the bond order of atoms involved in each description. It is assumed that the bond order between an atom pair is dependent on the interatomic separation. While this model has been used to predict bond dissociation energies, heats of formation and structures of simple hydrocarbons, it was not applied to predict condensed phase properties. However, the form of the potential should allow for condensed phase studies. 

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... 

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>. 

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. 

In 1988, Tersoff [7] introduced an analytical expression for a many-body potential energy function based on bond order, which was able to accommodate reactive dynamies in a straightforward manner. In this formalism, the interaction energy Eij between a pair of atoms i and j is given by... 

---