Eliminating imaginary vibrational frequencies in quantum-chemical cluster models of enzymatic active sites

In constructing finite models of enzyme active sites for use in quantum-chemical calculations, atoms at the periphery of the model system are often constrained to prevent structural collapse during geometry relaxation. A simple fixed-atom or ``coordinate lock'' approach is commonly employed but leads to undesirable artifacts including the appearance of small imaginary frequencies. These preclude the evaluation of finite-temperature free energy corrections, limiting thermochemical calculations to enthalpies only. Full-dimensional vibrational frequency calculations are possible by replacing the fixed-atom constraints with harmonic confining potentials, and here we compare that approach to an alternative strategy in which fixed-atom contributions to the Hessian are simply omitted. While that approach does eliminate imaginary frequencies, it tends to underestimate both the zero-point energy and the vibrational entropy, in addition to the artificial rigidity already introduced by fixed-atom constraints. Harmonic confining potentials eliminate imaginary frequencies and provide a flexible means to construct models that can be used in unconstrained geometry relaxations.