A. Constrained Dipeptides. To investigate how constraints impact vibrational frequencies and vibrational ZPE in proteins, a data set of ten tetrapeptides was prepared, each having the sequence ABAB for distinct amino acids A and B with charge-neutral side chains. Geometry optimizations were performed using vacuum boundary conditions (ε = 1), with dihedral ψ and φ angles constrained at 180 • , which maintains a virtually flat backbone structure. Next, the central BA dipep-tide was extracted from the optimized geometry as indicated in Fig. , for use in subsequent restrained-atom optimization and vibrational frequency calculations. For those calculations, we defined four anchor atoms: two C α atoms at the points of separation from the tetrapeptide, as well as two C β atoms on side chains R A and R B ; see Fig. . Restrained-atom optimizations and harmonic frequency calculations were performed on these ten dipeptide models using either harmonic confining potentials or, alternatively, fixed-atom constraints. In the latter case we will compare frequencies obtained from an unmodified Hessian versus those computed from the zeroed-out Hessian that is defined in eq. 3.