2. Computational Details¶
\(\newcommand{\va}{V\cdot\AA^{1}}\newcommand{\eh}{E_h}\newcommand{\dc}{^\circ C}\newcommand{\kcalmol}{Kcal\cdot mol^{1}}\newcommand{\kjmol}{KJ\cdot mol^{1}}\)For the majority of this work the chosen choice of theory was the M062X^{1} DFT functional with the double\(\zeta\), singlyaugmented, Pople basis set with added diffuse functions (631+G*).^{2}^{3} While the use of Pople basis sets is somewhat outdated, M062X was parameterised to work with small basis sets and has been shown to work effectively with this family of basis sets.^{1} Through rigorous benchmarking, the combination of M062X/631+G* has been identified as one of the best performing functional/basis set combinations for modelling the perturbative effects of electric fields with a mean absolute deviation of \(0.08\:\kjmol\)^{7} and has become the standard for modelling these systems.^{7} In other portions of this project M062X has been used in conjunction with the more modern and robust Dunning’s augmented, polarised, triple\(\zeta\) basis set (augccpVTZ),^{4}^{5} to afford better nonOEEF perturbed results, while still keeping the computational cost relatively low. Errors for this method have been benchmarked to \(0.077\:\AA\) for geometry optimisations and \(10.75\:\kjmol\) for barrier heights.^{6}
For accurate benchmarking of nonOEEF perturbed systems, ωB97MV^{8} was chosen as it has been shown to generally be the best performing DFT functional for geometry optimisations and barrier heights^{6}^{9} with RMSD errors of \(0.014\:\AA\) and \(7.0\:\kjmol\) respectively^{6}. In this research it was paired with Ahlrichs’ quadruple\(\zeta\), doubly polarised basis set (Def2QZVPP)^{10}, as this family of basis sets have been parameterised^{11} to work effectively with the RIJ approximations^{12} that allow for significant speedups in the calculation of the coulombic terms of the DFT functional. These approximations introduce minimal errors of \(\sim0.2\:\kjmol\) with hybrid DFT methods while affording decreases in computational cost of more than 8 times, making this method attainable for the systems studied in this research. All thermodynamic calculations throughout this research were calculated using M062X/631+G* with CPCM solvation for OEEF perturbed systems and ωB97MV/Def2QZVPP with SMD solvation for nonOEEF perturbed systems. For standard state conditions, a temperature of \(298.15\:K\) was used for all thermodynamic calculations (except where otherwise stated) and all subsequent calculations assume 1 M concentrations.
For nonOEEF perturbed, high level energetic calculations where high level thermodynamic calculations were not required, ωB97MV was used in conjunction with Ahlrichs’ triple\(\zeta\), singly polarised basis set with added diffuse functions (Def2TZVPD)^{10}, with a slightly smaller integration grid. These modifications came with an associated RMSD error of \(0.018\:\AA\) for geometry optimisations and \(7.4\:\kjmol\) for energetics, such as PES scans.^{6}
Throughout this research, errors have mostly been mitigated due to the use of relative energies and energetic differences, rather than using absolute energies alone. The DFT functionals chosen have all been shown to be robust and are often used as benchmarking points of reference in themselves.^{13}
For all calculations involving the use of OEEFs, a tradeoff had to be made between choosing an affordable level of theory that would best describe the perturbative effects of the OEEF and also accurately representing the barrier heights of the system. While it could be assumed that more robust methods, such as ωB97MV would accurately represent both, given that the field of electrostatic catalysis is relatively new, few benchmark studies have been performed to verify this. Those performed by Aragonès et al.^{7} and Gryn’ova et al.^{14} had to be assumed representative of the systems studied in this work, due to time and resource limitations.^{15} As such, any and all kinetic and thermodynamic calculations performed on systems perturbed by OEEFs can only be considered to represent the change in rate as a result of the OEEF and should not be considered qualitative for absolute kinetics. This is made even more prevalent by the recognition that in the EyringPolanyi equation, the rate constant is proportional to the exponent of the free energy, so very small changes in the energy result in very large changes in the rate, with \(5.7\:\kjmol\) equating to an order of magnitude difference in rate constant at room temperature. Throughout this work, all rate constants have been reported specifically as \(\log(k)\), for the sake of simplicity.
A full breakdown of all the calculation details for all the jobs performed can be found in Appendix F.
It should be noted that throughout this work, all OEEF directions will be presented using the Gaussian^{16} notation, which has the vector pointing from negative to positive, which has become standard in the field of electrostatic catalysis. This is contrary to conventional physics notation which describes the vector pointing from positive to negative as has been used throughout this work for molecular dipoles. This has the effect that when aligned, the molecular dipole points in the same direction as the OEEF.

Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06Class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120 (1–3), 215–241. https://doi.org/10.1007/s002140070310x. ↩↩

Hehre, W. J.; Ditchfield, R.; Pople, J. A. Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules. J. Chem. Phys. 1972, 56 (5), 2257–2261. https://doi.org/10.1063/1.1677527. ↩

Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. V. R. Efficient Diffuse FunctionAugmented Basis Sets for Anion Calculations. III. The 321+G Basis Set for FirstRow Elements, Li–F. J. Comput. Chem. 1983, 4 (3), 294–301. https://doi.org/10.1002/jcc.540040303. ↩

Dunning, T. H. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90 (2), 1007–1023. https://doi.org/10.1063/1.456153. ↩

Kendall, R. A.; Dunning, T. H.; Harrison, R. J. Electron Affinities of the First‐row Atoms Revisited. Systematic Basis Sets and Wave Functions. J. Chem. Phys. 1992, 96 (9), 6796–6806. https://doi.org/10.1063/1.462569. ↩

Mardirossian, N.; HeadGordon, M. Thirty Years of Density Functional Theory in Computational Chemistry: An Overview and Extensive Assessment of 200 Density Functionals. Mol. Phys. 2017, 115 (19), 2315–2372. ↩↩↩↩

Aragonès, A. C.; Haworth, N. L.; Darwish, N.; Ciampi, S.; Bloomfield, N. J.; Wallace, G. G.; DiezPerez, I.; Coote, M. L. Electrostatic Catalysis of a Diels–Alder Reaction. Nature 2016, 531 (7592), 88–91. https://doi.org/10.1038/nature16989. ↩↩↩

Mardirossian, N.; HeadGordon, M. ΩB97MV: A Combinatorially Optimized, RangeSeparated Hybrid, MetaGGA Density Functional with VV10 Nonlocal Correlation. J. Chem. Phys. 2016, 144 (21), 214110. https://doi.org/10.1063/1.4952647. ↩

Goerigk, L.; Hansen, A.; Bauer, C.; Ehrlich, S.; Najibi, A.; Grimme, S. A Look at the Density Functional Theory Zoo with the Advanced GMTKN55 Database for General Main Group Thermochemistry, Kinetics and Noncovalent Interactions. Phys. Chem. Chem. Phys. 2017, 19 (48), 32184–32215. ↩

Weigend, F.; Ahlrichs, R. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. Phys. Chem. Chem. Phys. 2005, 7 (18), 3297. https://doi.org/10.1039/b508541a. ↩↩

Weigend, F. Accurate CoulombFitting Basis Sets for H to Rn. Phys. Chem. Chem. Phys. 2006, 8 (9), 1057–1065. https://doi.org/10.1039/B515623H. ↩

Neese, F.; Wennmohs, F.; Hansen, A.; Becker, U. Efficient, Approximate and Parallel Hartree–Fock and Hybrid DFT Calculations. A ‘ChainofSpheres’ Algorithm for the Hartree–Fock Exchange. Chem. Phys. 2009, 356 (1–3), 98–109. https://doi.org/10.1016/j.chemphys.2008.10.036. ↩

Santra, G.; Martin, J. M. L. Some Observations on the Performance of the Most Recent ExchangeCorrelation Functionals for the Large and Chemically Diverse GMTKN55 Benchmark. In AIP Conference Proceedings; 2019; Vol. 2186, p 030004. https://doi.org/10.1063/1.5137915. ↩

Gryn’ova, G.; Marshall, D. L.; Blanksby, S. J.; Coote, M. L. Switching Radical Stability by PHInduced Orbital Conversion. Nat. Chem. 2013, 5 (6), 474–481. https://doi.org/10.1038/nchem.1625. ↩

Gryn’ova, G.; Coote, M. L. Origin and Scope of LongRange Stabilizing Interactions and Associated SOMOHOMO Conversion in Distonic Radical Anions. J. Am. Chem. Soc. 2013, 135 (41), 15392–15403. ↩

Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H.; Li, X.; Caricato, M.; Marenich, A. V; Bloino, J.; Janesko, B. G.; Gomperts, R.; Mennucci, B.; Hratchian, H. P.; Ortiz, J. V; Izmaylov, A. F.; Sonnenberg, J. L.; WilliamsYoung, D.; Ding, F.; Lipparini, F.; Egidi, F.; Goings, J.; Peng, B.; Petrone, A.; Henderson, T.; Ranasinghe, D.; Zakrzewski, V. G.; Gao, J.; Rega, N.; Zheng, G.; Liang, W.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Throssell, K.; Montgomery Jr., J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M. J.; Heyd, J. J.; Brothers, E. N.; Kudin, K. N.; Staroverov, V. N.; Keith, T. A.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A. P.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Millam, J. M.; Klene, M.; Adamo, C.; Cammi, R.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Farkas, O.; Foresman, J. B.; Fox, D. J. Gaussian 16 Revision C.01; Gaussian, Inc., Wallingford, Connecticut, 2016. ↩