Reactive Models

More realistic models were subsequently developed to incorporate many-body effects and realistic reaction mechanisms. Implementation of these in reduced dimensionality, small-scale simulations demonstrated the importance of the inclusion of these effects [161,162] however, the complexity of the functions and accompanying computational requirements prevent their use in large-scale molecular dynamics simulations in the condensed phase. 

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  

The range for both the intramolecular interaction term and the bond-order function is very small (in most models 3 A) and attenuates to zero at the intramolecular cutoff distance through a switching function fc. 

The intermolecular potential term is represented by a simple Lennard-Jones function that is attenuated at short interatomic distances by a cubic spline so that at small (covalent) intemuclear distances, the description of the interaction is that of the intramolecular term only. The original form of 

A subsequent molecular dynamics study using the REBO potential was used to demonstrate how information on reaction mechanisms gleaned from MD simulations can be used to design an explosive with specific performance properties [169]. Because the first step of the initiation reactions requires that a critical degree of compression must be attained in order for the material to atomize, there is an implication that a REBO crystal can be tailored in such a way that this critical degree of compression cannot be reached. Rice et al. [169] used molecular dynamics and REBO crystals that included heavy inert 

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The early kinetic models for copolymerization, Mayo s terminal mechanism (41) and Alfrey s penultimate model (42), did not adequately predict the behavior of SAN systems. Copolymerizations in DMF and toluene indicated that both penultimate and antepenultimate effects had to be considered (43,44). The resulting reactivity model is somewhat compHcated, since there are eight reactivity ratios to consider. 

Huang W, Weber W (1997) A distributed reactivity model for sorption by soils and sediments. 10. Relationships between desorption, hysteresis, and the chemical characteristics of organic domains. Environ Sci Technol 31 2562-2569... 

A gas-phase reactivity model that assumes molecules react as a result of the collision of reactant molecules. The basic idea is that the kinetic energy of the impacting molecules exceeds the activation energy required for reaction. Classical mechanics is used to estimate the fraction of the collisions with enough energy to allow re-... 

Because of the observation of a fast equilibrium between the C-titanium complexes 19A and 19C and the N-titanium ylides 19B, the reactivity model depicted in Scheme 1.3.16 was proposed in order to account for the regio- and diastereose-lectivity observed in the reaction of 19 with aldehydes. This model, which is based on the assumption of the operation of the Curtin-Hammett principle (that is, the reactions of 19A, 19B, and 19C with aldehydes are significantly slower than their isomerization), features the six-membered cyclic chair-like transition states... 

Weber, W.J., P.M. McGinley, and L.E. Katz. 1992. A distributed reactivity model for sorption by soils and sediments-1 Conceptual basis and equilibrium assessments. Environ. Sci. Technol. 26 1955-1962. 

This conversion is a clean reactivity model for the Mo enzyme trimethylamine A-oxide reductase. The molybdenum(VI) bis(oxido) complex has a distorted octahedral geometry [181],... 

Figure 16 A tentative answer to the question on reactive modeling snapshots of dimensionless ozone concentration at time of No. 30 s and related time-averaged radial profiles at different heights (experiment Ouyang et ai, 1995 Ug = 3.8 m/s,...

The reactive modeling was only performed for the furnace chamber limited to computing cost. Still a monodisperse solid phase was... 

Abstract. In this chapter we discuss approaches to solving quantum dynamics in the condensed phase based on the quantum-classical Liouville method. Several representations of the quantum-classical Liouville equation (QCLE) of motion have been investigated and subsequently simulated. We discuss the benefits and limitations of these approaches. By making further approximations to the QCLE, we show that standard approaches to this problem, i.e., mean-field and surface-hopping methods, can be derived. The computation of transport coefficients, such as chemical rate constants, represent an important class of problems where the QCL method is applicable. We present a general quantum-classical expression for a time-dependent transport coefficient which incorporates the full system s initial quantum equilibrium structure. As an example of the formalism, the computation of a reaction rate coefficient for a simple reactive model is presented. These results are compared to illuminate the similarities and differences between various approaches discussed in this chapter. 

A description of the method of molecular dynamics simulations and its applications to energetic materials research is provided. We present an overview of the development of both reactive and non-reactive interaction potentials used to describe the energetic materials in different phases. Limitations as well as performances of the current models are indicated, including recent advances in reactive model development. Applications of the method to both gas and condensed phases of energetic materials are given to illustrate current capabilities. 

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