A critical comparison of approximation methods and models for equilibrium properties of low-barrier hydrogen bonds

Recent experimental evidence has led to the conclusion that short, strong hydrogen bonds can stabilize transition states of enzyme catalyzed biochemical reactions. Evidence for such hydrogen bonds is the low value of the isotopic fractionation factor, phi, which is defined as the equilibrium constant for the generic reaction, R-H + DOH <--> R-D + HOH, where H is the hydrogen atom participating in the low-barrier hydrogen bond in a molecule R-H. In this work we assess two approximation methods for computing the isotopic fractionation factors for single and multidimensional systems containing a low-barrier hydrogen bond. These methods are WKB and an approach that corrects the classical partition function via a quantum correction factor. We find that the latter approach is universally accurate and applicable in both single and multidimensional systems containing a low-barrier hydrogen bond. We also assess two different models for the coupling of a molecule's low-barrier hydrogen bond to other degrees of freedom, both internal and external to the molecule, and show that each leads to a lowering of the fractionation factor.