Johnston and Parr

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. 

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. 

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]. 

Kinetic isotopic effect studies of this kind permit a test of the mass dependence predicted by transition state theory or other theories of bimolecular rate coefficients. A qualitative test of various potential energy surfaces can also be made using such data. Using the theory of Bigeleisen and Wolfsberg of kinetic isotopic effects and several methods of constructing potential energy surfaces (Wheeler et al, Sato, Johnston and Parr ) Timmons and Weston ° found no surface which predicted rates to within better than 40 % of the measured values taken as a whole. 

Murdoch [15] pointed out that the quantitative barrier expressions given by Lon-don-Eyring-Polanyi-Sato [16], Johnston and Parr [17], Marcus [6, 18], Murdoch... 

This expression is the same as that used by Johnston and Parr [63] in their bond-energy - bond-order (BEBO) method for describing potential energy surfaces of simple chemical reactions. It shows an exponential dependence of dissociation energy on change in ground-state distance. Stretching force constants k n) and equilibrium distance are related as follows... 

The equations for k(n) and D n) derived in this way have the same form as the Pauling definition of fractional bond order [24], Herschbach and Laurie s relationship between stretching force constant and bond distance [193], and Johnston and Parr s expressions for the bond-energy and bond-order relationships [25]. With reasonable values of p 2 A Dq 100 kcal mol and n = 1, dD(/"el/dre is about 400kcalmol thus reproducing the order of magnitude of the experimental slope for acetal hydrolysis. 

ISM is a unidimensional reactivity model based on the diabatic method originally proposed by Evans and Polanyi [18] and on the conservation of the bond order along the reaction coordinate of the bond-energy-bond-order (BEBO) first proposed by Johnston and Parr [19]. Eor a reaction of the type... 

The calculation of transition-state bond orders is much faciUtated by the insightful BEBO method of Johnston and Parr, where the bond order is conserved along the reaction coordinate... 

The RMBEBO formalism is cur own extended and modified version of the bond-energy-bond-order (BEBO) method of Johnston and Parr" and the reduced-variable-bond-energy-bond-order (RVBEBO) method of Mayer et The RMBEBO method predicts different saddle point... 

Johnston and Parr use an H-0 bond strength of 114.7 kcal/mol, as compared to the diatomic value of 106.6 kcal/mol. Except where indicated otherwise though we use the mass of the most common atomic isotope, as we do for the calculations with other kinds of surfaces. 

In view of the high cost of ab initio quantum mechanical calculations, simplified procedures have been used in attempts to capture the essential features of potential energy hypersurfaces by approximate means. We discuss two of these, the BEBO (bond-energy-bond-order) method (Johnston and Parr, 1963 Johnston, 1966) and the LEPS (London-Eyring-Polanyi-Sato) method (Sato, 1955). 

Johnston, H.S. and Parr, C. (1963) Activation energies from bond energies. 

H. S. Johnston and C. Parr. Activation energies from bond energies. I. Hydrogen transfer reactions. J. Am. Chem. Soc. 85, 1963, 2544-2551. 

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