Solvation of the Menshutkin reaction: A rigorous test of the effective fragment method

The recently developed effective fragment potential (EFP) method is used to study the effect of two, four, six, and eight solvating water molecules on the Menshutkin reaction between ammonia and methyl bromide. The EFP method reproduces all ab initio geometries and energetics (including zero-point energy, thermal, and entropy effects) for the two-water case very accurately. Energetics from all nb initio single-point energies at the EFP geometries for the four, six, and eight water cases are in excellent agreement with corresponding EFP energetics. In the gas phase, the above Menshutkin reaction is kinetically highly unfavorable with a free energy of activation (at 298.15 K) of 40.6 kcal/mol at the RHF level with a double-xi basis set augmented with polarization and diffuse functions. An ion-pair product is found, in agreement with previous work, in which the bromide anion is hydrogen-bonded to an ammonium hydrogen, giving a free energy of reaction of 2.8 kcal/mol. The addition of solvating water molecules has the effect of lowering the barrier and lowering the energy of the ion-pair product relative to the molecule-pair reactant. For eight solvating EFP water molecules, the free energy of activation is 22.8 kcal/mol and the free energy of reaction is -21.9 kcal/mol. Timings indicate that the EFP method allows the inexpensive addition of water molecules to a chemical system, accurately modeling all ab initio calculations with low computational cost.