The application of multireference quantum chemical methods in mechanistic studies of [4π + 2π] cycloadditions

Abstract

[4π + 2π]cycloadditions are an important synthetic process for the formation of six-membered ring systems. Though there have been many computational studies that model [4π + 2π]cycloadditions using ab initio or DFT, there are relatively few reports on the use of multireference methods. To date there has been no benchmarking study that examines the performance of multireference methods in models of [4π + 2π] cycloadditions and no agreement in regards to active space or basis set selection. This thesis seeks to determine an active space and basis set combination that yields accurate and reliable results, and applies this to the polymerisation of methanal azine and a set of eight cycloadditions. The performance of multireference, single reference and DFT methods is also discussed. Chapter 2 benchmarks CASSCF and CASPT2 reaction barriers against experimental results for the stepwise biradical, asynchronous biradical and concerted mechanisms of the butadiene-ethene reaction and the butadiene dimerization to determine active space and basis set effects. The effect of lone pairs on the active space and basis set selection is also considered via the reactions of butadiene with methanal azine and itself. The large errors of CASSCF with respect to experimental results and the unrealistically high barriers can be attributed to the neglect of dynamic electron correlation effects, therefore CASPT2 was used for the remainder of the study. It was found that a (6,6) active space yielded results closer to the experimental benchmark than (4,4) for the butadiene-ethene reaction and that increasing the active space beyond (6,6) had little effect on the reaction barriers of the butadiene dimerization, butadiene-methanal azine reaction and the methanal azine dimerization when B3LYP/6-31G(d) geometries were employed for the concerted reaction mechanism. The differences in barriers across active spaces observed for the hetero-cycloadditions were attributed to CASSCF geometry effects and the selective inclusion of nitrogen lone pairs in the active space, suggesting that the active space must contain either all or no electron lone pairs. cc-pVTZ was found to provide the most reliable barriers with cc-pVDZ only 4.3±3.2 kJ/mol¯¹ behind, on average, across all hetero-reactions and active spaces studied. The use of CASPT2 in conjunction with a (6,6) active space and the cc-pVDZ and cc pVTZ basis sets was examined in Chapter 3. The polymerisation of methanal azine was modelled using CASPT2, CCSD(T), MP2 and six DFT methods to determine whether [4π + 2π] cycloadditions were a viable polymerisation pathway. CCSD(T) and CASPT2(6,6)/cc-pVTZ could not model the polymerisation past the trimerization step and therefore other methods were sought. CASPT2(6,6)/cc-pVDZ gave results that were 11.6 kJ/mol¯¹, on average, within the CCSD(T) barriers and enthalpies, and was therefore used to model the dimerization to pentamerization reactions. The polymerisation was found to proceed mainly via bridging ring structures, however the high barriers and entropic effects suggest that further work is required to fully characterise the polymer. SCS-MP2 and DFT methods were able to predict the same reaction progression as CASPT2, however M06 and M06-2X could not differentiate between bridging or fused ring pathways. The performance of CASPT2(6,6), MP2 based methods, CCSD(T) and GGA, meta-GGA, hybrid and double hybrid DFT functionals for reaction barriers, energies and Gibbs free energies was also studied via models of eight [4π + 2π] cycloadditions, benchmarking against experimental results, where available, and CCSD(T)/CBS. CASPT2(6,6) with either a double-ζ or triple-ζ basis set yielded the most accurate Gibbs free energies of activation compared to experimental results, however was outperformed by CCSD(T)/cc-pVTZ and SCS-MP2 for reaction barriers and energies. B2PLYPD, mPW2PLYPD and M06-2X were the highest performing DFT methods, with errors and deviations from CCSD(T)/CBS comparable to those of SCS-MP2.