Eliminating Imaginary Vibrational Frequencies in Quantum-Chemical Cluster Models of Enzymatic Active Sites.

In constructing finite models of enzyme active sites for quantum-chemical calculations, atoms at the periphery of the model must be constrained to prevent unphysical rearrangements during geometry relaxation. A simple fixed-atom or "coordinate-lock" approach is commonly employed but leads to undesirable artifacts in the form of small imaginary frequencies. These preclude 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. Here, we compare that approach to an alternative strategy in which fixed-atom contributions to the Hessian are simply omitted. While the latter strategy does eliminate imaginary frequencies, it tends to underestimate both the zero-point energy and the vibrational entropy while introducing artificial rigidity. Harmonic confining potentials eliminate imaginary frequencies and provide a flexible means to construct active-site models that can be used in unconstrained geometry relaxations, affording better convergence of reaction energies and barrier heights with respect to the model size, as compared to models with fixed-atom constraints.

Fragment-Based Calculations of Enzymatic Thermochemistry Require Dielectric Boundary Conditions.

Electronic structure calculations on enzymes require hundreds of atoms to obtain converged results, but fragment-based approximations offer a cost-effective solution. We present calculations on enzyme models containing 500-600 atoms using the many-body expansion, comparing to benchmarks in which the entire enzyme-substrate complex is described at the same level of density functional theory. When the amino acid fragments contain ionic side chains, the many-body expansion oscillates under vacuum boundary conditions but rapid convergence is restored using low-dielectric boundary conditions. This implies that full-system calculations in the gas phase are inappropriate benchmarks for assessing errors in fragment-based approximations. A three-body protocol retains sub-kilocalorie per mole fidelity with respect to a supersystem calculation, as does a two-body calculation combined with a full-system correction at a low-cost level of theory. These protocols pave the way for application of high-level quantum chemistry to large systems via rigorous, ab initio treatment of many-body polarization.

Systematic Evaluation of Counterpoise Correction in Density Functional Theory.

A widespread belief persists that the Boys-Bernardi function counterpoise (CP) procedure "overcorrects" supramolecular interaction energies for the effects of basis-set superposition error. To the extent that this is true for correlated wave function methods, it is usually an artifact of low-quality basis sets. The question has not been considered systematically in the context of density functional theory, however, where basis-set convergence is generally less problematic. We present a systematic assessment of the CP procedure for a representative set of functionals and basis sets, considering both benchmark data sets of small dimers and larger supramolecular complexes. The latter include layered composite polymers with ∼150 atoms and ligand-protein models with ∼300 atoms. Provided that CP correction is used, we find that intermolecular interaction energies of nearly complete-basis quality can be obtained using only double-ζ basis sets. This is less expensive as compared to triple-ζ basis sets without CP correction. CP-corrected interaction energies are less sensitive to the presence of diffuse basis functions as compared to uncorrected energies, which is important because diffuse functions are expensive and often numerically problematic for large systems. Our results upend the conventional wisdom that CP "overcorrects" for basis-set incompleteness. In small basis sets, CP correction is mandatory in order to demonstrate that the results do not rest on error cancellation.