ZPE corrections in Table , which are computed using only the real-valued frequencies, are consistently lower for the zeroed-out Hessian than they are for the unmodified Hessian with fixed-atom constraints, by 8 kcal/mol on average. This is a direct result of the larger value of n im for the zeroed-out Hessian and suggests that this approach likely underestimates the true ZPE. Using harmonic constraints, the ZPE is larger than it is for either fixed-atom calculation. The difference is greatest for the largest dipeptide considered, and in Fig. we demonstrate that the difference scales approximately linearly with the number of anchor atoms, using several of the model systems that are considered below.