Bond dissociation energy limitations

A more useful quantity for comparison with experiment is the heat of formation, which is defined as the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. The heat of formation can thus be calculated by subtracting the heats of atomisation of the elements and the atomic ionisation energies from the total energy. Unfortunately, ab initio calculations that do not include electron correlation (which we will discuss in Chapter 3) provide uniformly poor estimates of heats of formation w ith errors in bond dissociation energies of 25-40 kcal/mol, even at the Hartree-Fock limit for diatomic molecules. 

We will now look at how different types of wave functions behave when the O-H bond is stretched. The basis set used in all cases is the aug-cc-pVTZ, and the reference curve is taken as the [8, 8J-CASSCF result, which is slightly larger than a full-valence Cl. As mentioned in Section 4.6, this allows a correct dissociation, and since all the valence electrons are correlated, it will generate a curve close to the full Cl limit. The bond dissociation energy calculated at this level is 122.1 kcaPmol, which is comparable to the experimental value of 125.9 kcal/mol. 

Bond energy considerations indicate that the initiation reaction (4.2.2) should be quite slow because its activation energy must be quite high (at least equal to the bond dissociation energy). If one were dealing with an open sequence reaction mechanism, such a step would imply that the overall reaction rate would also be low because in these cases the overall reaction becomes approximately equal to that of the rate limiting step. In the case of a chain reaction, on the other hand, the overall reaction rate is usually much faster because the propagation steps occur many times for each time that an initiation step occurs. 

Finally, it is worth noting that all of the research described here is greatly facilitated when accurate values are available for metal-ligand bond dissociation energies. Only limited data of this type is presently available and further work along these lines is certainly warranted. 

More than just a few parameters have to be considered when modelling chemical reactivity in a broader perspective than for the well-defined but restricted reaction sets of the preceding section. Here, however, not enough statistically well-balanced, quantitative, experimental data are available to allow multilinear regression analysis (MLRA). An additional complicating factor derives from comparison of various reactions, where data of quite different types are encountered. For example, how can product distributions for electrophilic aromatic substitutions be compared with acidity constants of aliphatic carboxylic acids And on the side of the parameters how can the influence on chemical reactivity of both bond dissociation energies and bond polarities be simultaneously handled when only limited data are available ... 

Examples of silver(l) alkyl and alkenyl (including aryl) complexes have been known from as early as 1941 6-9 however, the number of examples is fairly limited with respect to that of the heavier congeners, copper(l) and gold(l). Such a phenomenon can readily be attributed to the relatively low stability of this class of complexes, both photochemically and thermally. Simple homoleptic alkyl and alkenyl complexes of silver(i) are known to be very unstable under ambient temperature and light, and successful isolation of this class is fairly limited and mainly confined to those involving perfluoroorganics.10 The structures and the metal-carbon bond-dissociation energies for... 

C-H and N-H bond dissociation energies (BDEs) of various five- and six-membered ring aromatic compounds (including 1,2,5-oxadiazole) were calculated using composite ab initio CBS-Q, G3, and G3B3 methods. It was found that all these composite ab initio methods provided very similar BDEs, despite the fact that different geometries and different procedures in the extrapolation to complete incorporation of electron correlation and complete basis set limit were used. A good quantitive structure-activity relationship (QSAR) model for the C-H BDEs of aromatic compounds... 

The apparent first-order rate coefficient is 1.5x 1010 exp(—28,200/RT ) sec-1. This expression has undoubtedly been obtained for a pressure-dependent region. If, as an extreme case, it is assumed that the unimolecular process occurred in the second-order region and if approximately one half of the classical degree of vibrational freedom are active, an upper limit of kx — 1.5 x 1015 exp(—46,000/Rr) sec-1 is obtained. The mean Pb-CH3 bond dissociation energy in tetramethyl lead19,142 is 37.6 kcal.mole-1. Dx should therefore be about 40 kcal.mole-1. 

Under standard conditions, both molecules exist in their lowest vibrational energy levels. These are known as their zero-point vibrational states, in which the value of the vibrational quantum number is zero. The fact that molecules in their zero-point vibrational states possess vibrational energy is a consequence of the Uncertainty Principle this would be violated if the internuclear distance was unchanging. The dissociation limits for both species are identical the complete separation of the two atoms, which is taken as an arbitrary zero of energy. The difference between the zero of energy and the zero-point vibrational energy in both cases represents the bond dissociation energies, respectively, of H2+ and H2. 

This, initially surprising, finding has been shown (143) to originate in the difference in O-H bond dissociation energies between the organic and inorganic pairs listed in Table VII. The lower limit of the value for CraqOH2+ (bde > 373 kJ/mol) was estimated (143) from the reduction potential of the CraqO )Cra couple ( L6 V), Ka for Craq (10 4 M ), and the oxidation potential for H (2.29 V). 

In our second example we look at the reduction of chlorinated ethenes at a nickel electrode and at the surfaces of two zero-valent metals [Fe(0), Zn(0)]. To gain insight into the rate-limiting process(es) in these cases, we consider how the relative overall reduction rates (relative to PCE) of PCE, TCE, and the three DCE isomers (see Fig. 14.15 for structures) vary as a function of two common descriptors used in QSARs, the one-electron reduction potential (EJ Fig- 14.17a) and the bond dissociation energy (DR X Fig. 14.176). In all these systems, the reduction rates were found to be significantly slower than diffusion of the compounds to the respective surfaces. Therefore, the large differences in the relative reactivities of the compounds between the systems reflect differences in the actual reaction at the metal surface. 

The limited stabilization of a radical by partial fluorination is reflected in the corresponding bond-dissociation energies (sec Table 10) 87 however, increasing degrees of fluorination. such as the introduction of a trifluoromethyl group into a molecule, destabilize the radical (vide supra) 02 104 Even a single fluorine in the /J-position is destabilizing. 

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