BEBO method

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. 

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. 

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... 

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 a priori calculation of activation energies or potential energy surfaces for radical—molecule reactions is still beyond the present scope of quantum mechanics despite the use of large computers [382]. One of the more successful of several empirical or semi-empirical attempts to calculate activation energies of H-abstraction reactions is the bond energy-bond order (BEBO) method developed by Johnston [382]. There are no adjustable parameters involved but rather empirical relations of a non-kinetic type. For the general situation... 

Introducing certain approximations into the BEBO method, Clark and Dove have recently calculated Arrhenius plots for the reactions (30)... 

The kinetics of the hypothetical hydrogen transfer reactions P+HA PH +A with A=H, Li, Na, K, Be, Mg, B, Al, C, Si, N, O, S, F, Cl, Br, I at 1000 K was computed using the bond energy bond order (BEBO) method and the activated complex theory or the simple collision theory [13]. However, the values reported have partially been questioned [14]. 

PHa + H- Products. The exothermic bimolecular H-abstraction reaction PHa + H PH + Ha, for which AH = -97 kJ/mol [7] or -22.1 kcal/mol was given [12], possibly is the main channel for the formation of PH [13], observed during the flash photolysis of PH3 (and explained by PHa disproportionation) [14]. The reaction was also proposed for the PH3 photolysis at different pressure ranges [15,16] and for the PH3 + H [17] and PH3 + NaO [18] reactions. A rate constant of k = 6.2x10" exp(-318/T) was estimated with a modified bond-energy bond-order (BEBO) method (see [19]) using empirical corrections (to obtain agreement with the experimental data in the case of the PH3 + H reaction) [20]. 

Probably this derives from an assumed proportionality between force constants and bond dissociation energies. It is not a necessary feature of the BEBO method. 

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 BEBO method has been quite successful in calculating the activation energies of a large number of atom-transfer reactions, but reveals some difficulties with reactions involving dramatic ZPE differences. For example, it predicts the structure Cl-H-Cl to be a stable molecule rather than a transition state of the Cl+HCl atom exchange. We will not pursue the BEBO method any further, but make use of its definition of the reaction coordinate to express the sum of bond extensions as... 

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... 

The BEBO method involves consideration of a collinear model for the transfer of a hydrogen atom from atom A to atom B, which can be represented... 

When the above procedure is done for the first time, the activation energy calculated from Eq. (3.60) will not be the same as the experimental value. One can adjust p and p in the BEBO method or A in the LEPS method to get these to agree, after which the preexponential factor according to TST is fixed. 

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