Phenylnitrene calculations

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.

In this chapter we describe experimental studies on the ring expansion reactions of phenylcarbene and phenylnitrene and the calculations that have been performed in order to try to explain the experimental results. Our aim is to show how theory can rationalize these observations and can also serve to stimulate additional experiments by predicting their outcome. We will attempt to demonstrate that an understanding of the fundamental differences between the electronic structures of phenylcarbene and phenylnitrene can explain the many differences in the chemistry of these reactive intermediates. 

Our calculations on the ring expansion of the lowest singlet state of phenylnitrene ( A2-lb) to azacycloheptatetraene (3b) predict a two-step mechanism that is analogous to that for the rearrangement of la to 3a and which involves the bicyclic azirine intermediate 2b.61 The CASPT2 energetics are depicted in Fig. 5, and the CASSCF optimized geometries of the stationary points are shown in Fig. 6. 

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.

As discussed in Section HI, calculations on the ring expansions of phenylcar-bene (la) and phenylnitrene (lb) suggest that singlet lb is thermodynamically... 

Wentrup s experimental work on carbene-to-nitrene rearrangements10 suggested that calculations on phenylnitrene (lb) and the isomeric pyridylcarbenes might provide some useful relative energies. Kemnitz et al. carried out calculations on lb and 3-pyridylcarbene (lc).77 The latter molecule was used to provide a link between the energies of not only phenylcarbene (la) and phenylnitrene (lb), but also between CH2 and NH. 

Our calculations showed that the first step, cyclization of the nitrene to an azabicyclo[4.1.0]heptatriene, is rate-determining. Our calculated barriers for cyclization of four fluorinated derivatives of lb are given in Table 6.87 The CASPT2/cc-pVDZ barrier of 13.4 kcal/mol for cyclization of 2,6-difluoro-phenylnitrene (10b) is 4.1 kcal/mol higher than the barrier computed for lb -+ 2b. In contrast, the calculated barriers to rearrangement of 3,5-difluoro-phenylnitrene (lOe) and 4-fluorophenylnitrene (10c) are very similar to that computed for unsubstituted phenylnitrene (lb). These computational results are consistent with the observed reluctance of pentafluorophenylnitrene (10a) and 2,6-difluorophenylnitrene (10b) to rearrange,48 1 81 83 and with the relative ease... 

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. 

By furnishing both explanations and predictions, calculations have not only led to an understanding of experiments that have already been performed on la and lb, but also have motivated new ones. The study of the chemistry of phenylcarbene (la) and phenylnitrene (lb), particularly the ring expansion reaction that each undergoes, thus provides an excellent example of the synergy between calculations and experiments. 

Pople-Parr-Pariser (PPP) calculations in 1986 indicated that the visible band of triplet phenylnitrene at 500 nm is the result of promotion of an electron from the... 

According to calculations, there is essentially no barrier to cyclization of singlet vinylnitrene, but at the same level of theory, the corresponding barrier in singlet phenylnitrene is predicted to be 9 kcal/mol. Thus, the latter species should be more easily detected in solution. Taking into account that this level of theory overestimates the barrier to cyclization of singlet vinylnitrene by 3.4 kcal/mol, one can extrapolate that the best prediction of the barrier to cyclization of singlet phenylnitrene is close to 6 kcal/mol. 

Singlet phenylnitrene undergoes ISC three orders of magnitude more slowly than arylcarbenes. " There are at least three reasons why arylcarbenes do ISC much faster than singlet phenylnitrene. The rate of a radiationless transition increases as the energy separation between the two states goes to zero. The calculated... 

Applications of Electronic Structure Calculations to Explaining and Predicting the Chemistry of Three Reactive Intermediates—Phenylnitrene, Cubyl Cation,... 

APPLICATIONS OF ELECTRONIC STRUCTURE CALCULATIONS TO EXPLAINING AND PREDICTING THE CHEMISTRY OF THREE REACTIVE INTERMEDIATES—PHENYLNITRENE, CUBYL CATION, AND PROPANE-1,3-DIYL... 

Calculations of PN are more challenging than that of PN because it is, of course, an excited state of phenylnitrene. The first two electronically excited singlet states of PN are both of Ai symmetry and are calculated to be at 1610 and 765 nm. Neither of these transitions have been detected, since both of these states have zero oscillator strength due to symmetry considerations, and they lie outside the wavelength range accessible to our spectrometer. ... 

Cyclic ketenimine K is the major, trappable, reactive intermediate in solution when phenyl azide (at moderate concentrations) is decomposed photo-lytically at 298 K. The rate of decay of singlet phenylnitrene is equal to the rate of formation of the cyclic ketenimine. Nevertheless, the calculations of Karney and Borden" reveal that this is a two-step process (Scheme 2). The first step, cyclization to benzazirine BZ is rate determining, followed by fast electrocyclic ring opening to cyclic ketenimine K. The predicted potential energy surface is shown in Fig. 8. 

Of particular interest are the results in Table 7 for cyclization of singlet or/Ao-cyanophenylnitrene (8c). The barrier to cyclization of 8c away from the cyano substituent to give 9c is calculated to be about the same as that for cyclization of PN, and the barrier to cyclization of 8c toward the cyano substituent to give 10c is predicted to be either about the same as (CASSCF) or slightly lower than (CASPT2) the barrier to cyclization of 8c away from the cyano group. This prediction is very different from the computational and experimental results for cyclization of ortho-methy -phenylnitrene where cyclization away from the ortho substituent is strongly preferred over cyclization toward the substituent. 

Fig. 13 Arrhenius treatment of A r(= qbs isc) for singlet pora-fluoro- 16b (1), meto,meto-difluorophenylnitrene 16c (2) in pentane and ortho,onho-Ai uoro-phenylnitrene 16d (4) in CCI4 and for singlet 2-fluorophenylnitrene 16a (3) calculated as described in the text. (5) Arrhenius treatment of the rate constant of ring opening reaction (k ) for benzazirine 17a.

Many of the same considerations affecting these vinylidene examples arise in comparing the relative energies of the electronic states of phenylnitrene (Figure 14.3). In this system, there are many different theoretical data available to compare to experiment, which itself is available for the lowest two singlet states. Results from ASCF calculations at the HF and DFT levels of theory are listed in Table 14.1, as are results from many additional levels that will be discussed at appropriate points later in the chapter. 

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