Bond order conservation model

Analytical expressions for interactions can be regarded either as mathematical in origin or with a physical origin.The former have often a simple form and they hold for many if not all systems, but they may have many parameters. The latter are based on the mechanism that leads to the interactions, they have seldom a simple mathematical form, they generally hold only for a limited set of systems, but they may have only few parameters.An expansion in terms two-, three-, four-, and more-particle interactions (see Sections 3.2.1 and 3.2.2) is an example of a mathematical model for lateral interactions. As an example of a physical model we only present the bond-order-conservation model in Section 3.2.3 as this is the model that has been used most extensively in kMC simulations. 

Before leaving this section, we should mention the application of simple bond-order conservation models (Shustorovich 1985, 1986, 1987, 1988) to molecule-surface PESs. In this model, one assumes that each gas atom-surface atom bond is a simple Morse potential, yielding the total interaction between A-S as ... 

A second approach which may be attractive for more complex surface systems involves the application of the Bond Order Conservation model that was developed by Shustorovich and co-workers . The BOC model treats the interaction between the adsorbate and the surface atom through the use of a Morse potential. The total heat of adsorption is then described by summing all interactions. The BOC model is based on the concept that the bonding potential for every atom in the system is conserved. The heat of adsorption for an atomic species A is described by the following expression ... 

In regard to the second problem, correlation of the fractional bond order and pyramidalization, the newer crystallographic and computational evidence consistently supports the original model, albeit a modification of its quantitative aspects is clearly necessary. Similarly, the simple relations invoking bond-order conservation during bond breaking and forming proved useful also in the more recent studies. 

E. Shustorovich. Chemisorption phenomena analytical modeling based on perturbation theory and bond-order conservation. Surf. Sci. Rep. 6, 1 (1986). 

Recently, semiempirical methods based on DFT calculations have been developed for catalyst screening. These methods include linear scaling relationships [41, 42] to transfer thermochemistry from one metal to another and Brpnsted-Evans-Polanyi (BEP) relationships [43 7]. Here, these methods and also methods for estimation of the surface entropy and heat capacity are briefly discussed. Because of their screening capabilities, semiempirical methods can be used to produce a first-pass microkinetic model. This first-pass model can then be refined using more detailed theory aided by analytical tools that identify key features of the model. The empirical bond-order conservation (BOC) method, which has shown good success in developing microkinetic models of small molecules, has recently been reviewed [11] and will not be covered here. 

In modeling reactions, in general, and catalytic reactions, in particular, the kineticist must draw on as many tools at his disposal as possible. Some of the most important concepts that are routinely used to derive, simplify and evaluate complicated rate expressions are 1) Transition-state theory 2) The steady-state approximation 3) Bond-order conservation calculations for surface species 4) A rate determining step 5) A most abundant reaction intermediate and 6) Criteria to evaluate parameters in derived rate expressions. Let us examine these topics prior to their utilization in deriving and evaluating reaction models and rate equations. 

Elementary rate constants can be estimated also using semi-empirical methods, which are not as accurate as quantum mechanical approaches, being able at the same time to reduce the computational costs of model development. One of such computationally inexpensive semi-empirical approaches appHcable to small molecules, is the bond-order conservation (BOG) or unity bond index—quadratic exponential potential (UBI—QEP) technique of Shustorovich and Sellers. This method ensures thermodynamic consistency... 

H. Sellers. A bond order conservation-Morse potential model of adsorbate-surface interactions Dissociation of H2, 02, and F2 on the liquid mercury surface. J. Chem. Phys. 99,1993, 650-655. 

There have been a number of investigations of the formulation of the problem of electron transfer accompanied by atom transfer particularly with regard to the simultaneous movement of the proton (which, in view of its small mass, may in fact be an atypical case). A possible model for such processes would assume a conservation of bond order along the reaction coordinates (Johnston, 1960). It is of interest that the results of such calculations are similar to those for electron transfer for weak coupling, although the interpretation of the process and parameters (such as a) are different. 

FIGURE 8.15 Conservation of the overall entropic bond multiplicity J °(P) = 1 bit in the 2-AO model of the chemical bond, combining the conditional entropy (average noise, bond covalency) S P) = H(P) and the mutual information (information capacity, bond ionicity) P(P) = 1 - H P). In MO theory, the direct bond order of Wiberg is represented by the (broken line) parabola M yP) = 4P(1 -P) = 4PQ. 

The Wiberg index has thus been recovered as the overall IT descriptor of the chemical bond in the 2-AO model, with its covalent (Sab) and ionic (/ ) contributions being established at the same time. It follows from Figure 8.17 that these IT covalency/ionicity components compete with one another while conserving the Wiberg bond order as the overall information measure of chemical bond multiplicity... 

---