Single-Point Hessian Calculations for Improved Vibrational Frequencies and Rigid-Rotor-Harmonic-Oscillator Thermodynamics

The calculation of harmonic vibrational frequencies (HVF) to interpret infrared (IR) spectra and to convert molecular energies to free energies is one of the essential steps in computational chemistry. A prerequisite for accurate thermostatistics so far was to optimize the molecular input structures in order to avoid imaginary frequencies, which inevitably leads to changes in the geometry if different theoretical levels are applied for geometry optimization and frequency calculations. In this work, we propose a new method termed single-point Hessian (SPH) for the computation of HVF and thermodynamic contributions to the free energy within the modified rigid-rotor-harmonic-oscillator approximation for general nonequilibrium molecular geometries. The key ingredient is the application of a biasing potential given as Gaussian functions expressed with the root-mean-square-deviation (RMSD) in Cartesian space in order to retain the initial geometry. The theory derived herein is generally applicable to quantum mechanical (QM), semiempirical QM, and force-field (FF) methods. Besides a detailed description of the underlying theory including the important back-correction of the biased HVF, the SPH approach is tested for reaction paths, molecular dynamics snapshots of crambin, and supramolecular association free energies in comparison to high-level density functional theory (DFT) values. Furthermore, the effect on IR spectra is investigated for organic dimers and transition-metal complexes revealing improved spectra at low theoretical levels. On average, DFT reference free energies are better reproduced by the newly developed SPH scheme than by conventional calculations on freely optimized geometries or without any relaxation.