Analytical energy gradient for the second-order Møller–Plesset perturbation theory coupled with the reference interaction site model self-consistent field explicitly including spatial electron density distribution

Solvatochromic shifts of the activation free energies are important aspects to consider for reaction control. To predict the energies, the stationary points in a solution must be accurately determined along the reaction pathway. In this study, the second-order Møller-Plesset perturbation (MP2) theory combined with the reference interaction site model was applied using our fitting approach, and the MP2 analytical energy gradient was determined. The coupled-cluster energy and thermal correction were calculated using the MP2 optimized geometry with solvent effect, and the activation free energies of the Diels-Alder reaction between cyclopentadiene and methyl vinyl ketone are within an error of 2 kcal/mol compared with the experimental data.