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

Abstract

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.

A comprehensive benchmark investigation of quantum chemical methods for carbocations

“…We initially assessed only quadruple- and triple-ζ AO basis sets under the CCSD(T) framework but ended up taking double-ζ aug-cc-pVDZ as it was considered as a reference method in a recent carbocation benchmark study. 48 Despite that smaller, finite AO basis sets (double- and triple-ζ) have been implicated in the basis set superposition error (BSSE), including intramolecular BSSE, 168,169 we were also interested in identifying AO basis sets responsible for significant errors in the case of carbocations. From Ahlrichs 57 def2 basis set family, we tested TZVPP, ma-TZVPP and QZVPP; Dunning 61–63,79 basis sets evaluated were as follows: aug-cc-pVDZ, cc-pVTZ, aug-cc-pVTZ, aug-cc-pwCVTZ and cc-pVQZ (Table 3).…”

“…We give special attention to double hybrids (rung 5) compared to previous carbocation benchmark studies, which undermined the potential of the class. 36,48 We completed a diverse selection of DFAs encompassing 40 years of developments in the area contemplating not only all rungs but also major sub-classes of DFAs, for instance: empirical and non-empirical double hybrids; among hybrids (rung 4) – global hybrids and range-separated hybrids (GGAs and meta-GGAs) were included.…”

“…The extension of the current study and particularly the methods selected to afford target energies starkly contrast with previous benchmark studies dedicated to carbocations. 36,48 Poor selection of reference methods can have broad implications for the quality of benchmark studies and ultimately result in inaccurate recommendations towards certain DFAs, which should be avoided at all costs for its domino effect. A recent benchmark study on carbocations employed CCSD(T)/aug-cc-pVDZ and CBS-QB3 as reference methods.…”

“…While working on this project, we encountered new benchmark results from the same group. 48 Once again, only a limited number of DFAs were evaluated for an extended series of carbocations with all except one DFA from the hybrid family (B3LYP, 31,32 M06, 35 M06-2X, 35 MN15, 49 PBE0, 50 PW6B95, 51 revPBE0, 52 SCAN0 53 and ωB97M-V 54 ). The double-hybrid B2PLYP, 55 which was applied in a recent mechanistic study to verify the involvement of methyl cations, 56 was also considered (Fig.…”

“…Due attention was given to double hybrids as their potential has been underappreciated. 36,48 We also analyzed London dispersion correction schemes on selected DFAs and inexpensive composite DFT methods ( e.g. , PBEh-3c 68 ).…”