Comparison of DFT, MP2/CBS, and CCSD(T)/CBS methods for a dual-level QM/MM Monte Carlo simulation approach calculating the free energy of activation of reactions in solution and on water: a case study

It is important to develop an accurate dual-level approach for the prediction of the activation free energy barriers of reactions in solution phase, particularly in binary mixed solvent and under on water condition, in which the result obtained by the semiempirical method-based quantum mechanics/molecular mechanics/Monte Carlo (QM/MM/MC) simulation is improved by using a high level of theory to the QM section in the gas phase. In this work, several density functional theory methods MP2/CBS and CCSD(T)/CBS with extrapolation to the complete basis set limit have been selected to calculate the free energies of activation in gas phase for the 1,3-dipolar cycloadditions of the phthalazinium dicyanomethanide 1 with three dipolarophiles, methyl vinyl ketone, methyl acrylate, and styrene as case systems. The suitability of those methods to reproduce the accurate free energy of activation barriers has been evaluated by comparing the computed Delta G(solution)(not equal) values with the experimental ones in pure solvents (water and acetonitrile) as well as in binary water-acetonitrile mixed solvents with mol fractions of water of 0.619 and 0.9, respectively. In short, the best agreement is achieved with the TPSSKCIS and TPSSTPSS functionals with 6-311 +G(d, p) basis set, resulting in the root-mean-squared deviation (RMSD) of less than 1.5 kcal/mol. The Delta G(solution)(not equal) values under on water condition are also predicted. Our results indicate that the dual-level approach using appropriate functional is useful for the investigation of dynamical properties of reactions in solution.