Systematic comparisons between broken symmetry and symmetry-adapted approaches to transition states by chemical indices: A case study of the Diels-Alder reactions

Systematic comparisons between broken symmetry (BS) and symmetry-adapted (SA) approaches to transition states were carried out using chemical indices, which are defined using the occupation numbers of natural orbitals (NOs) by both BS and SA methods. For the former, unrestricted Hartree-Fock, UMP2, UQCISD(T), and UCCSD(T), together with hybrid density functional theory (DFT) methods such as UB2LYP and UB3LYP, were employed, while CASSCF, UNO CASCI, UNO CASCI MP2 (≡ CASMP2(CI)). and MRMP2 were used for the latter approach. To begin with, we examined the functional behaviors of chemical indices during the C-C bond dissociation process of ethylene or the least motion association reaction of triplet methylenes. The bonding characteristics revealed by the chemical indices are largely dependent on the computational methods. Next, the energy difference between concerted and nonconcerted transition structures of the Diels- Alder reaction of butadiene and ethylene was calculated by both BS and SA methods. The origin of excellent energetics by the hybrid DFT methods for this reaction was revealed in terms of the chemical indices. These indices are also useful to understand the nature of the chemical bonds at TSs and the role of unstable intermediates in stepwise mechanisms. Furthermore, the ability of phenyl groups to stabilize nonsynchronous TS for the Diels-Alder and the Cope rearrangement reactions was examined by the NO analyses of the BS hybrid DFT solutions. The difference of the chemical indices for substituted systems provides useful information for the theoretical consideration of the reaction mechanism and stereospecificity of pericyclic reactions. Finally, implications of the computational results are discussed in relation to appropriate selection of effective hybrid DFT methods for large systems with moderate radical characters, for which the SA computations are difficult.