Synergism of Catalysis and Reaction Center Rehybridization in Nucleophilic Additions to Cumulenes: The One-, Two- and Three-Water Hydrolyses of Carbodiimide and Methyleneimine

The results of a theoretical study of the one-, two- and three-water hydrolyses of carbodiimide and the one- and two-water hydrolyses of methyleneimine are presented. All structures were optimized and characterized at the MP2(full)/6-31G* level of theory. Energies for the one-water hydrolysis of carbodiimide were determined at numerous higher levels of theory, up to the QCISD(T)(fc)/6-311+G(3df, 2p)//MP2- (full)/6-31G* level. The ΔE ₀ (ΔG ₂₉₈ ) activation barriers for the rate-determining steps of the one-, two- and three-water hydrolyses of carbodiimide, respectively, are 44.8 (46.3), 29.3 (32.3) and 22.9 (26.2) kcal mol ^-1 at the MP2(full)/6-31G* level. The consideration of a second water molecule catalyzes the hydrolysis by 15.5 kcal mol ^-1 on the E ₀ surface and by 14.0 kcal mol ^-1 on the G ₂₉₈ surface with respect to the one-water hydrolysis. Placement of a third water molecule opposite the site of proton transfer catalyzes the reaction by an additional 6.4 kcal mol ^-1 on the E ₀ surface and by 6.1 kcal mol ^-1 on the G ₂₉₈ surface. The catalytic effect of the third water molecule results from the synergistic effects of rehybridization and charge relaxation in the transition state. The charge relaxation in the transition state is illustrated through natural population analysis calculations on the pre-coordination complexes and the transition state structures. We also consider the placement of the third water molecule in the proton transfer chain and we show this to be of little catalytic relevance. The activation barriers determined for the one- and two-water hydrolyses of methyleneimine are ΔG ₂₉₈ = 51.9 and ΔG ₂₉₈ = 35.5 kcal mol ^-1 , respectively, and they are larger than for carbodiimide. The results are compared with the hydrolyses of carbon dioxide and formaldehyde.