A Benchmark Study of Quantum Mechanics and Quantum Mechanics-Molecular Mechanics Methods for Carbocation Chemistry

Carbocations play key roles in classical organic reactions and have also been implicated in several enzyme families. A hallmark of carbocation chemistry is multitudes of competing reaction pathways, and to be able to distinguish between pathways with quantum chemical calculations, it is necessary to approach chemical accuracy for relative energies between carbocations. Here, we present an extensive study of the performance of selected density functional theory (DFT) methods in describing the thermochemistry and kinetics of carbocations and their corresponding neutral alkenes both in the gas-phase and within a hybrid quantum mechanics-molecular mechanics (QM/MM) framework. The density functionals are benchmarked against accurate ab initio methods such as CBS-QB3 and DLPNO-CCSD(T). Based on the findings in the gas-phase calculations of carbocations and alkenes, the best functionals are chosen and tested further for non-covalent interactions in model systems using QM and QM/MM methods. We compute the interaction energies between a model carbocation/alkane and model π, dipole, and hydrophobic systems using DFT and QM(DFT)/MM and compare with DLPNO-CCSD(T). These latter model systems are representative of side chains of amino acids such as phenylalanine/tyrosine, tryptophan, asparagine/glutamine, serine/threonine, methionine, and other hydrophobic groups. The Lennard-Jones parameters of the QM atoms in QM(DFT)/MM calculations are modified to obtain an optimal fit with the QM energies. Finally, a selected carbocation reaction is studied in the gas phase and in implicit chloroform solvent using QM and in explicit chloroform solvent using QM/MM and umbrella sampling simulations. This study highlights the highest accuracy possible with selected density functionals and QM/MM methods but also some limitations in using QM/MM methods for carbocation systems.