β-Secondary deuterium equilibrium and kinetic isotope effects on nucleophilic attack by methanol at a carbonyl: Computational estimation of deviation from the rule of the geometric mean

An approximation using sets of rigid-rotors is developed that permits the computational estimation of observed isotope effects from non-rigid molecules. The approximation is applied to position-specific β-secondary deuterium isotope effects for the gas phase nucleophilic attack by methanol at a carbonyl where the reactant is considered capable of free methyl rotation while products are conformationally constrained. Computations utilized the B3LYP DFT level of theory with the 6-31+G(d,p) basis set. The kinetic isotope effects computed for the attack of methanol at formaldehyde in the presence of ammonia are 1.030, 1.032 and 1.052 for the three methyl CH bonds. Equilibrium isotope effects for hydrogen-bonding of methanol as the donor to ammonia are 0.978 for the anti CH position and 1.047 for the two gauche CH positions, while complete ionization of methanol yielded a calculated equilibrium isotope effect of 1.496. When nucleophilic attack occurs prior to deprotonation the anti CH bond exhibits an equilibrium isotope effect of approximately 0.95, while the gauche positions demonstrate effects between 0.918 and 0.950 depending on steric and electronic effects in the 1-methoxyethanol protonated cation product. These estimations provide a framework to evaluate isotope effects from stereospecifically monodeuterated hydroxymethylenes in enzymatic reactions that employ primary alcohols as nucleophiles where the substrate exists as a non-rigid species capable of rotameric interconversion that becomes rigidly constrained at the transition state in the enzyme active site. The approximation can also be used to evaluate deviations from the rule of the geometric mean and the non-additivity of isotope effects by non-rigid molecules, and methanol ionization is considered as an example.