Infatuation Rules
Infatuation Rules
Photo: Samson Katt
Bond energy is a measure of the bond strength of a chemical bond, and is the amount of energy needed to break the atoms involved in a molecular bond into free atoms.
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Read More »For bonds of order between 1 and 3 (for C bound to C, C to O, and O to O), there is quite a good log–log correlation between the bond energy (D e ) and bond order (n), i.e., (2.36) D e = D e, s n p where D e, s is the energy of the single bond between a particular pair of atoms. In addition, Johnston made use of an equation originally suggested by Pauling relating n to bond length: (2.37) r = r s − 0.26 ln n so that combining these two equations gave (2.38) ln ( D e / D e, s ) = p ( r s − r ) / 0.26 In order to use this equation to evaluate partial bond energies where r > r s , the additional assumption was made that this relationship is not only valid for n ≫ 1 but also holds as n approaches zero. As a consequence, the parameter p was evaluated, by substituting for D e and r in equation (2.38) the Lennard–Jones parameters ε LJ and r m , for the noble-gas pair belonging to the same horizontal rows of the Periodic Table as the partially bound species in question; so (2.39) p = 0.26 ln ( D e , s / ε LJ ) / ( r m − r s ) The use of the Lennard–Jones parameters was justified on the grounds that the force constants calculated from these potentials appeared to obey Badger's rule quite well, and the values of ε LJ and r m also fitted a smooth (but not linear) extrapolation of bond energy versus bond length for C–C and N–N bonds. As no information on the Lennard–Jones potentials for mixed pairs of noble-gas atoms, for example He + Ne, was available at the time the BEBO method was proposed, ε LJ and r m were evaluated, for these cases, using the combining rules: (2.40a) r m ( He − Ne ) = 0.5 { r m ( He − He ) + r m ( Ne − Ne ) } and (2.40b) ε LJ ( He − Ne ) = { ε LJ ( He − He ) ε LJ ( Ne − Ne ) } 1 2 Combination of equations (2.34) and (2.36) and addition of D e, BC , so that the potential energy is referred to separated A + BC rather than A + B + C, yields (2.41) V ( x ) = D e, BC − D e, BC n p BC − D e, AB ( 1 − n ) p AB + V rep ( r CA ) = D e, BC ( 1 − n p BC ) − D e, AB ( 1 − n ) p AB + V rep ( r CA ) where n and (1 − n) are the BC and AB bond orders. Using Pauling's relationship (2.37) and the fact that r CA = r AB + r BC for collinear configurations, r AB , r BC and V ( x ) can be evaluated at values of n from 1 to 0. The maximum value of V ( x ) corresponds to the predicted energy barrier for the reaction. To determine activation energies for comparison with experimental results, use should be made of transition state theory (Chapter 4). At the time the BEBO method was proposed, it was claimed to predict activation energies within about 2 kcal/mole (∼8 kJ mol−1) for most H atom-transfer reactions, but since then more instances have been discovered where the agreement is poorer. Partly because of this, a number of modifications and re-evaluations of the BEBO method have been carried out since it was first proposed. Quite recently, attention was drawn25 to the fact that equations (2.40a) and (2.40b) predict values of r m and ε LJ for mixed noble-gas atom pairs, differing significantly from those which have been accurately determined from measurements of elastic scattering in molecular beam experiments (see Table 2.4). If the latter data are used in equation (2.38) to find values of the parameter p, the predicted activated energies are changed considerably for the worse. For example, for the H + H 2 reaction, the calculated energy barrier ( V ∗ ) is lowered from 41.4 to 27.6 kJ mol−1. Even more recently, however, this gloomy prognosis has been disputed26, it being pointed out that other small modifications of the BEBO technique, especially adjusting the numerical factor in equation (2.37) to 0.28, restores and even improves the success of the method.
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Read More »What the various evaluations clearly, if inadvertently, demonstrate is the sensitivity of the BEBO predictions to the values chosen for the p parameters, since relatively large changes in the predicted barrier heights are brought about by an alteration of only a few percent in these factors. Since it is extremely doubtful whether the numerical factor in Pauling's relationship remains constant for a variety of partially bound pairs, the earlier quantitative agreement of the BEBO predictions with experimental data must be seen as slightly fortuitous. The BEBO method provides a fine example of soundly based empiricism, and it has already assisted a generation of kineticists to acquire a clear understanding of the nature of atom-transfer reactions. However, it now seems unlikely that additional insight is to be gained by further tinkering with the basic equations. Furthermore, it appears doubtful if a straightforward BEBO calculation can provide a more reliable prediction of an unknown activation energy than the educated guess of an experienced kineticist who has access to data on related reactions. An alternative use of the BEBO expression is to have a single value of p in equation (2.41) which can be adjusted, like Δ in the LEPS equation, to bring the predicted and observed activation energies into coincidence. However, the use that can be made of this potential is limited, since the BEBO procedure does not generate even an energy surface, let alone a full hypersurface.
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