Bond separation energies

There was less agreement between calculated and experimental energy values. The use of 6-3IG, the best procedure in energy calculations of three-membered rings, yielded a value too low by more than 40 kJ moF in the case of diazirine bond separation energy was calculated as -45 kJ moF the experimental value is +0.4 kJ moF . Vibrational correction and extrapolation to 0 K would reduce this difference by several kJ moF . 

TABLE 29. Bond separation energies (in kcal mol ) for SnH3—Y — SnH3- + Ya ... 

The value of Aif (F2NOF) derived from bond separation energies of this reaction was 55.7 kj mol-1. This compared with the empirical MNDO calculation of -85.8 kj mol-1 (172). 

A bond separation reaction takes any molecule comprising three or more heavy (non-hydrogen) atoms into the set of simplest (two-heavy-atom) molecules containing the same bonds. The only requirement is that bonding must be defined in terms of a single valence (Lewis) structure or set of equivalent valence structures. This in turn guarantees that the bond separation energy is unique. ... 

Bond separation energies from Hartree-Fock models with STO-3G, 3-2IG, 6-3IG and 6-311+G basis sets, local density models, BP, BLYP, EDFl and B3LYP density functional models and MP2 models all with 6-3IG and 6-311+G basis sets and MNDO, AMI and PM3 semi-empirical models are compared with values based on G3 energies and on experimental thermochemical data in Table 6-13. These have been abstracted from a much larger collection found in Appendix A (Tables A6-36 to A6-43). A summary of mean absolute deviations from G3 values in calculated bond separation energies (based on the full data set) is provided in Table 6-14. 

Local density models yield bond separation energies of similar quality to those from corresponding (same basis set) Hartree-Fock models. Bond separation energies for isobutane and for trimethylamine, which were underestimated with Hartree-Fock models, are now well described. However, local density models do an even poorer job than Hartree-Fock models with benzene and with small-ring compounds. 

With the exception of semi-empirical models, all models provide very good descriptions of relative nitrogen basicities. Even STO-3G performs acceptably compounds are properly ordered and individual errors rarely exceed 1 -2 kcal/mol. One unexpected result is that neither Hartree-Fock nor any of the density functional models improve on moving from the 6-3IG to the 6-311+G basis set (local density models are an exception). Some individual comparisons improve, but mean absolute errors increase significantly. The reason is unclear. The best overall description is provided by MP2 models. Unlike bond separation energy comparisons (see Table 6-11), these show little sensitivity to underlying basis set and results from the MP2/6-3IG model are as good as those from the MP2/6-311+G model. 

A bond separation reaction is uniquely defined. Therefore, a bond separation energy is a molecular property . Given that a bond separation reaction leads to products, the heats of formation of which are either known experimentally or can be determined from calculations, combining a calculated bond separation energy with experimental (or calculated) heats of formation, gives rise to a unique value for the heat of formation. For example, a heat of formation for methylhydrazine may be obtained from the thermochemical cycle. 

It has previously been documented (Chapter 6) that Hartree-Fock, density functional and MP2 models generally provide excellent descriptions of the energetics of bond separation energies, while semi-empirical models are not successful in this regard (Tables 6-10 and A6-36 to A6-43). Use of bond separation energies from these models (but not from semi-empirical models) together with... 

Bond separation reactions and heats of formation obtained from bond separation energies suffer from two serious problems. The first is that bond types in reactants and products for some types of processes may not actually be the same or even similar . The bond separation reaction for benzene is an obvious example. Here to reactant (benzene) incorporates six equivalent aromatic carbon-carbon bonds, midway between single and double bonds, while the products (three ethanes and three ethylenes) incorporate three distinct carbon-carbon single bonds and three distinct carbon-carbon double bonds. 

The second problem is even more serious. The number of product molecules in a bond separation reaction increases with the size of the reactant, and (presumably) so too does the overall magnitude of error in the calculated bond separation energy. Whereas errors in bond separation energies (and in heats of formation derived from bond separation reactions) are close to acceptable limits ( 2 kcal/ mol) for small molecules (see discussion in Chapter 6), it is likely that will rapidly move outside of acceptable limits with increasing molecular size. 

An isodesmic reaction92 is a formal reaction, in which the number of electron pairs as well as formal chemical bond types are conserved while the relationships among the bonds are altered. A subclass of the isodesmic reactions is the class of bond separation energies, in which all formal bonds of a molecule are separated into two-heavy-atom molecules containing the same type of bonds. Stoichiometric balance is achieved for the bond separation energies by adding an appropriate number of one-heavy-atom hydrides to the left side of the reaction92. 

SCHEME 11. Isodesmic bond separation energies (kcalmol ) calculated at the HF/3-21G level93... 

K. Raghavachari, B. B. Stefanov, and L. A. Curtiss, /. Chem. Phys., 106, 6764 (1997). Accurate Thermochemistry for Larger Molecules Gaussian-2 Theory with Bond Separation Energies. 

TABLE 31. Bond lengths (pm), rotation barriers around the central M —M bond, A/irot (kcal mol 1), and bond separation energies AE (kcal mol 1), in H2M=M H—M H=MH2a... 

TABLE 3.18 Mean Absolute Deviation (kcal mol of the Computed Bond Separation Energy Compared with Experiment... 

The bond separation energies reflect the stabilization or destabiUzation that results when the separated bonds between heavy atoms are brought together in the three-membered ring. 

For the three-membered ring molecules, the bond separation energies depend primarily on three factors ... 

In some cases e.g. cyclopropane), one of these factors e.g. ring strain) is likely to be much more important than the other two. In other cases, all three factors may have a significant influence on the bond separation energy. 

Experimental heats of formation are available for five of the three-membered rings calculated and experimental bond separation energies for these molecules are compared in Table 5. Three sets of calculated values are listed corresponding to the STO-3G, 4-31G and 6-31G basis sets. The theoretical bond separation energies should be compared with experimental values at 0 °K corrected for zero-point vibration these are quoted in the last column of the table. However, since the data e.g. vibrational frequencies) required to obtain such experimental values are not always available, we also give experimental bond separation energies at 0 °K and 298 °K without the vibrational corrections in order to point out the approximate magnitude of such corrections. 

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