Bond-order function

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 bond-order function applies, not only to integral bond orders, but also to order zero, characteristic of all non-bonded interactions in a molecule. From these results it becomes possible, in principle, to define a force field, based on pairwise interaction, that should account for all structural and thermodynamic effects, apart from those related to orbital and spin angular momenta. The main purpose is not to produce yet another force field -the available products are more than adequate. What it does is to provide the much needed theoretical underpinning and reassurance that molecular mechanics is soundly based on first principles. 

J.C.A. Boeyens and D.J. Ledwidge, A Bond-Order Function for Metal-Metal Bonds, Inorg. Chem., 1983 (22) 3587-3589. 

E. Garcia, A. Lagana, A new bond-order functional form for triatomic-molecules a fit of the BETH potential-energy. Mot Phys. 56 (3) (1985) 629-639. 

For the case of an ideal lattice with only nearest-neighbor interactions, all bond lengths are identical and the bond-order function reduces to the inverse square root of coordination z. The cohesive energy can then be written as... 

Figure 3.31. Bond-order function F and bond-order correction energy per bond F/n for Rh. Values indicated by the circles are obtained from the atomic energies for fee, bee, simple eubie (se), and diamond cubic (dc) systems. In all systems the atoms are equally spaced at t-q, the equilibrium nearest-neighbor distance of Rh in an fee lattice. AEa = 5.48 eV, adapted from P. van Beurdenl .

An example of the bond-order function F is shown in Fig. 3.31. In Fig. 3.31 one notes the decreasing value of the bond order per bond T with increasing coordination number, as predicted according to the Bond Order Conservation theory. 

The first key development was the bond-order type of interatomic potential, such as the Abell potential. Because the bond-order function not only takes the distances among atoms into account but also their local atomic... 

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