BEBO

A number of other analytic potential functions such as Rotated-Morse-Curve-Spline (RMCS), Bond-Energy-Bond-Order (BEBO) have been used for fitting of ab initio surfaces. 

The bond-energy bond-order (BEBO) method developed by Johnston and Parr (1963), in spite of its nonkinetic basis, represents a broadly applicable empirical approach to estimating activation energies of metathesis reactions. 

Computational details of the BEBO method are discussed in Johnston (1966) and Brown (1981). As is evident from the foregoing discussion, although the BEBO method represents a general method to estimate activation energies, it is strictly apphcable to bimolecular metathesis reactions. In addition, in spite of its computational rigor, the BEBO method often does not lead to the determination of activation energies that are more accurate than the other empirical methods discussed earlier. 

A full calculation of a kinetic isotope effect requires estimates of force constants in the transition structure. These are available from ab initio PE calculations, but also from an empirical method based on the bond energy bond order (BEBO) assumption [38], which often provides more useful qualitative feedback for the experimentalist than high-level methods (see Chapter 7). 

Lippincott and Schroeder [1955, 1957] introduced a semiempirical two-dimensional PES and fitted their parameters from experimental data. Further studies in this direction were carried out by Savel ev and Sokolov [1975] and Sokolov and Savel ev [1977], Lautie and Novak [1980], Saitoh et al. [1981], and Emsley [1984]. These studies have shown that an adequate two-dimensional PES can be constructed from Morse functions of diatomic fragments XH and HY and repulsive functions representing the XY interaction. The values of rXH ar,d wXH and isotope effects as a function of R are in agreement with the experimental ones for OH O, OH-N, and NH-- N fragments. The dependencies rXH(/ ) and a>XH(R) collected by Novak [1974] are shown in Figure 6.1. The method of Lippincott and Schroeder [1957] is one of the versions of the general semiempirical method of bond energy-bond order (BEBO) developed by Johnston and Parr [1963] to construct a two-dimensional PES. 

BEBO Bond energy—bond order. A semiempirical relationship that relates the energy of a bond to its bond order. This relationship is used for semiempirical construction of potential energy surfaces. 

Finally, one should mention that some version of bond-order conservation, known as the bond-energy/bond-order (BEBO) method, has been applied to chemisorption bonding and surface reactivity by Weinberg and... 

Merrill 157). The basic assumptions and mathematical formalism of the BOC-MP and BEBO methods are quite different, however. Most important, in the BEBO method, following Lewis and Pauling, the bond order x is defined as the number of shared electron pairs, so that x may be smaller than, equal to, or larger than unity, reflecting fractional, single, or multiple A-B bonding, respectively. Furthermore, the BEBO method makes use of the power function E x) = -Q0xp, where p is some empirical constant. 

An alternative equation, also derived by Marcus18, is from Johnston s19 BEBO calculation of activation energies. It is specifically useful for these H atom transfer processes. This is Eq. (5), with the terms as above. 

BEBO-based Marcus equation or the hyperbolic relation which is not based on theory but is easier to use and gives about the same answer. The reduction in isotope effect predicted by the Westheimer transition state symmetry arguments is harder to correlate, yet the wide range of isotope effects virtually requires this explanation, in contrast to the case in proton transfers. 

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More elaborate and more reliable procedures that can be used for estimates of rate coefficients of free-radical reactions are the bond energy-bond order method (BEBO) of Johnston and Parr [13] and the curve-crossing approach of Pross [14]. 

It is plausible that the variation in ff, in this homologous series of reactions is caused by the existence of a barrier along the reaction coordinate, the barrier height being negatively correlated with <7,. Mok and Polanyi have found using LEPS surfaces and the BEBO method that as the barrier height decreases, the location of the... 

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