B3LYP Cope rearrangements

Density functional theory has also been applied to the Cope rearrangement. Nonlocal methods, such as BLYP and B3LYP, find a single transition state with approximately 2 A. The barrier height is in excellent agreement with experiment. These first DFT results were extremely encouraging because DFT computations are considerably less resonrce-intensive than MRPT. Moreover, analytical first and second derivatives are available for DFT, allowing for efficient optimization of stmc-tures (particularly transition states) and the computation of vibrational frequencies needed to characterize the nature of the stationary points. Analytical derivatives are not available for MRPT calculations, which means that there is a more difficult optimization procedure and the inability to fully characterize structures. 

The calculated activation enthalpies for the Cope rearrangements of various cyano- and phenyl-substituted 1,5-hexadienes were calculated at B3LYP/6-31G and are listed in Table 4.8. 

A couple of initial observations are warranted. First, the agreement in the activation enthalpy between the calculated B3LYP and the experimental values is Only outstanding Second, radical-stabilizing substituents, such as cyauo aud phenyl, can dramatically decrease the activation barrier of the Cope rearrangement, suggesting a greater participation by the radical contributors to the wavefunction (see Scheme 4.7). 

Table 30.2 Dissection of the effects of phenyl substituents on lowering the energy of the TS for the chair Cope rearrangement of 1,5-hexadiene. Energies (kcal/mol) were obtained from B3LYP/6-31G calculations at different interallylic distances (R) in the maimer described in the text...

Fig. 10.39. Comparison of transition structure geometry for anionic oxy-Cope (right) rearrangement with Cope rearrangement (left) showing atom separation distances and Mulliken charges (B3LYP/6-31IG ). Reproduced from Helv. Chim. Acta, 84, 124 (2001), by permission of Wiley-VCH.

Finally, the activation energies (without zero point corrections) calculated for the 1,5-hydrogen shift in cycloheptatriene by MROPT2, CASSCF, and B3LYP are 38.7, 60.2, and 40.6 kcal/mol, respectively, and a zero point correction would lower these energies by about 4 kcal/mol. Clearly, the CASSCF method without dynamic correlation is suspect just as in the Cope rearrangement (see Chapter 7, Section 4.1). 

The (BLW)PBE/IGLOO-III level Vc2C8 couplings calculated by Jana et al for semibullvalenes have been found to correlate with the (BLW)-B3LYP/6-311 + G(d,p) level calculated reaction barrier heights for the Cope rearrangements of these compounds. 

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