Cope rearrangement CASSCF

Subsequent calculations have confirmed the allowed, aromatic nature of the transition state using various DFT methods.The breaking bond in the eneyne is on an average 1.83 A and the making bond is 1.88 A. Unfortunately, like the Cope rearrangement CASSCF calculations on this system indicate favorable formation of a diyl intermediate (bond distances of 1.87 and 1.67 A, respectively which reveals the need for inclusion of Dynamic Correlation. This and the related reactions have been reviewed by Hopf. ... 

CASSCF calculations.7 Treatment of substituted 5-triethylsilyloxyhexa-l,2,5-triene derivatives with catalytic amounts of W(CO)6 was found to give the products of formal Cope rearrangement 2-triethylsilyloxyhex-l-en-5-ynes. The mechanism is believed to involve 6-endo attack by the silyl enol ether on the tungsten-activated allene, followed by ring opening with simultaneous loss of W(CO)s.8... 

Why are the CASSCF computations not only quantitatively but also qualitatively incorrect Inclusion of dynamic correlation decreases the diradical connibution to the wavefunction, which is overestimated by CASSCF. This was a very surprising result at that time. The simple valence bond model described above would imply that the CASSCF approach should be satisfactory. The failure of CASSCF meant that much greater computational resources than anyone had expected would be needed to adequately describe even simple organic reactions, such as the Cope rearrangement. 

This problem was intensively studied both experimentally and theoretically. The quantum chemical calculations were carried out using various methods at different levels. The earlier calculations for the Cope reanangement based on a CASSCF wave function for six electrons in the bonds rearranged were found to overestimate the diradical character of the wave funclion- --. More recently, MP2 methods for the multireference wave function have been developed whose application to an estimate of the energy of the chair transition state has been described. AMI calculations of altemative transition states for the Cope rearrangement of 1,5-hexadiene derivatives have been discussed by Dewar and colleagues i -217... 

Although both of these diradical extremes have the same dominant electronic configuration as the aromatic TS [4], a proper wave function for each of these diradical extremes requires a different second configuration. Therefore, at least a three-configuration wave function is demanded for an unbiased study of the Cope rearrangement. Even better is a (6/6)CASSCF wave function in which three virtual orbitals are used to correlate the six electrons in the three bonding orbitals (two pi and one sigma) that are active in this reaction. 

It now seems hard to believe that, 20 years ago, (6/6)CASSCF/3-21G calculations were beyond the capabilities of the computers available to most computational chemists. Nevertheless, in the first ab initio study of the Cope rearrangement, published in 1984, (6/6)CASSCF/3-21G calculations could not actually be performed they could only be simulated [14]. Smaller MCSCF calculations were employed to obtain a partially optimized set of orbitals. Then those orbitals were used to carry out full Cl calculations for the 52 configurations that comprise the complete (6/6) active space at the C h stationary point for the chair Cope rearrangement of 1,5-hexadiene. 

The simulated (6/6)CASSCF calculations were performed at several partially optimized Ciu geometries. The calculations found that the Cope TS has an interallylic separation of / = 2.062 A, which is close to that of / = 2.023 A for the fully optimized RHF/3-21G TS. Thus, the simulated (6/6)CASSCF/3-21G calculations found that bond making and bond breaking occur synchronously in the Cope rearrangement via an aromatic TS (B). 

However, there still remained some hope that ab initio calculations on the Cope rearrangement might provide a different PES than AMI. The (6,6)CASSCF/6-31G value... 

Subsequently, Kozlowski et al. [24] also revisited the Cope rearrangement with inclusion of dynamic correlation between the active and inactive electrons. However, they used Davidson s own version of multi-reference, second-order perturbation theory [25], which allows the coefficients of the configurations in the CASSCE wave function to be recalculated after inclusion of dynamic electron correlation. Kozlowski et al. found that the addition of dynamic correlation to the (6/6)CASSCE wave function for the Cope TS causes the weight of the RHE configuration to increase at the expense of the pair conhgurations that are necessary to describe the two diradical extremes in Eig. 30.1. Thus, without the inclusion of dynamic electron correlation in the wave function, (6/6) CASSCF overestimates the diradical character of the C2 wave function [24]. 

The results of this study again call attention to the chameleonic nature of the C2 wave function for the Cope rearrangement. At small values of R the CASSCF wave function is essentially that for cyclohexane-1,4-diyl (structure A in Fig. 30.1) whereas, at large values of R the CASSCF wave function approaches that for two allyl radicals (structure... 

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). 

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