What Are the Best Affordable Multi-Coefficient Strategies for Calculating Transition State Geometries and Barrier Heights?

We compare hybrid density functional theory and multi-coefficient correlation methods for locating saddle point geometries and calculating barrier heights on a Born−Oppenhiemer potential energy surface. We located reactant, product, and saddle point stationary points by the multi-coefficient Gaussian-3 (MCG3) method for 15 reactions, and by the multi-coefficient quadratic configuration interaction with single and double excitations (MC-QCISD) method for 22 reactions; and the resulting structures and energies are compared to those obtained by the Møller−Plesset second order perturbation theory (MP2), QCISD, and modified Perdew−Wang 1-parameter-for-kinetics (MPW1K) methods. We examined three single-level methods with two basis sets, 6-31+G(d,p) and MG3. By comparison to calculations on five systems where the saddle point has been optimized at a high level of theory, we conclude that the best saddle point geometries for the methods tested are those found at the MC-QCISD, MCG3, and MPW1K levels. MP2 was shown to have systematic deficiencies in predicting saddle point geometries. Our recommended most affordable methods are the MPW1K/6-31+G(d,p) and MC-QCISD methods for fully optimized calculations and the MCG3//MPW1K/6-31+G(d,p) method for single-point calculations with mean unsigned errors in calculating reaction energies and barrier heights of 1.6, 1.6, and 1.1 kcal/mol respectively.