Correlation between the rate order and the number of molecules in the reaction of trimethyl phosphite with water in acetonitrile solvent

Density functional theory calculations of the title reaction, P(OCH?)? + (H?O)(n) in CH?CN, were conducted, where n is the number of water molecules. Two routes, the routes suggested by (A) Aksnes and (B) Arbuzov, were traced with various n values. Both routes consist of two transition states (TSs) and one intermediate. Route B was found to be more likely than route A. In the former, the activation free energy (ΔG(?)) of n = 3 is slightly smaller than that of n = 2. The n = 3 TS geometry is composed of a nucleophile H?O, a proton donor H?O, and an auxiliary one. Indeed, the geometry appears to be plausible for ready proton relays along hydrogen bonds, but it is inconsistent with the observed third-order rate constant. Catalytic water molecules were added to the n = 2 and 3 bond-interchange circuits. Then route B with n = 2 + 2 was found to be best. By n = 2 + 10 and n = 3 + 12 models, the n = 2 based route B was confirmed to be likely.