Kinetic isotope effects from QM/MM subset hessians: "Cut-off" analysis for S_N2 methyl transfer in solution

Isotopic partition-function ratios and kinetic isotope effects for reaction of S-adenosylmethionine with catecholate in water are evaluated using a subset of 324 atoms within its surrounding aqueous environment at the AM1/TIP3P level. Two alternative methods for treating motion in the six librational degrees of freedom of the subset atoms relative to their environment are compared. A series of successively smaller subset Hessians are generated by cumulative deletion of rows and columns from the initial 972 X 972 Hessian. We find that it is better to treat these librations as vibrations than as translations and rotations and that there is no need to invoke the Teller-Redlich product rule. The validity of "cut-off" procedures for computation of isotope effects with truncated atomic subsets is assessed: to ensure errors in ln(KIE) < 1% (or 2% for the quantum-corrected KIE) for all isotopic substitutions considered, it is necessary to use a less-restrictive procedure than is suggested by the familiar two-bond cutoff rule.