CASPT2 /6-31G* calculations

In order to test the validity of these qualitative expectations, CASPT2/6-31G calculations on the ring expansion reactions of ortho, meta, and para-cyano-phenylnitrene (12a-c) were performed.96 Fig. 15 summarizes the results. In all three cases, the ring expansions were computed to be nearly thermoneutral, with the first step rate-determining. 

Indeed, CASPT2/6-31G calculations of Kemnitz et al. find that triplet phenyl nitrene is 26.4 kcal/mol lower in energy than the isomeric triplet m-pyridylcarbene. 

From the understanding, provided by the calculations, of the mechanism by which lb cyclizes, what can be predicted about how the rate of this reaction might be affected by substituents on the benzene ring The substiment effects would, in fact, be expected to be small, except for possible steric effects due to substituents in the ortho positions. If both ortho positions are substimted, one would expect to see a decrease in rate, relative to unsubstituted lb. On the other hand, if only one ortho position is substituted, cyclization should be about as fast as in unsubstituted lb but cyclization should preferentially occur at the unsubstituted ortho carbon. Additional (8/8)CASPT2/6-31G calculations by Bill Kamey in our group and subsequent experiments by the Platz group confirmed these qualitative predictions about the effects of ortho substituents. 

In agreement with the results of experiments on pyrolysis of l,l-bis(trimethyl-silyl)cyclopropane, additional (2/2)CASPT2/6-31G calculations predict that a rapid 1,2-silyl shift will occur in 12a, forming 13a. However, if cis- and trans-l,l-bis(trimethylsilyl)-2,3-dimethylcyclopropanes (11b and 11c) were pyrolyzed, then, as shown in Figure 22.10, the stereochemistry of ring opening could, presumably, still be inferred from the stereochemistry of the double bonds in the expected rearrangement products (13b and 13c). 

Prior to these experiments, CASPT2/6-31G calculations on the ring expansion reactions of para-cyanophenylnitrene (62a) were performed. Table 5.14 shows that the barrier computed for cyclization of para-cyanophenylnitrene (62a) is more than 1 kcal/mol higher than that for parent phenylni-trene 49. This prediction is in quantitative agreement with subsequent experiments (Table 5.7). 

Figure 7. Comparison of the energetics of the ring expansions of phenylcarbene ( A -la) and phenylnitrene (1A2-lb), calculated at the CASPT2(8,8)/6-31 G //CASSCF(8,8)/6-31 G level.57-61 The numbers in parentheses represent corrections for the known deficiencies of CASPT2/6-31G in computing the energies of singlet phenylnitrene61 and singlet phenylcarbene.55 The small differences in the energies in Fig. 5 are a consequence of the difference between the basis sets used in the two sets of calculations.

The qualitative predictions and experimental findings in the case of cyano substituents have been analyzed computationally by performing (8/8)CASSCF and CASPT2/6-31G ab initio calculations. Table 7 summarizes the results for the cyclization reactions of ortho-, meta-, para-, and... 

On the other hand, fluorine substitution at both ortho positions (21a) raises the CASPT2/6-31G barrier from 8.6 to 13.0 kcal mol The increase in the barrier height inhibits the rearrangement reaction and allows 21a to participate in intermolecular chemistry. Subsequent experiments determined that its activation barrier is 7.3-8.0 kcal mol (depending on the solvent). Calculations predict a... 

At the CASSCF(8,8)/6-31G level, 1 A"-4b is predicted to be a transition state for the enantiomerization of 3b. The CASPT2 calculated barrier for this process is ca. 21 kcal/mol (Fig. 12). This predicted value for the barrier to enantiomerization of 3b is essentially the same as that calculated for the racemization of 3a,55,57 which, as already noted, is approximately half of the experimental value of ca. 42 kcal/mol for racemization of allene.73... 

Figure 14. Energetics (in kcol/mol) of the ring expansions of fluoro-substituted phenylni-trenes, calculated at the CASPT2(8,8)/cc-pVDZ//CASSCF(8,8)/6-31G level.87-88 (a) Difluo-rinated nitrenes. (b) Monofluorinated nitrenes.

Another route to the formation of carbonyl oxides is the reaction of methylene (CH2) with dioxygen. This oxidative process involving methylene with O2 is one of the most important reactions in the combustion of unsaturated hydrocarbons. The reaction between CH2 (X Bi) 4- O2 has been studied by Anglada and BofilP in the gas phase by carrying out CASSCF and CASPT2 calculations with the 6-31G(d,p) and 6-31H-G(3df,2p) basis... 

Figure 11.3. Energetics of the ring expansion of singlet phenylnitrene calculated at the CASPT2 (8,8)/6-311G(2d,p)//CASSCF(8,8)/6-31G level. [Reproduced with permission from W. L. Karney and W. T. Borden, J. Am. Chem. Soc. 1997,119, 1378. Copyright 1997 American Chemical Society.]...

Fig. 14 Relative energies (in kcal/mol) of species involved in the ring expansions of singlet fluoro-substituted phenylnitrenes calculated at the CASPT2/cc-pVDZ// CASSCF(8,8)/6-31G level, (a) Difluorinated phenylnitrenes. (b) Monofluorinated phenylnitrenes.

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