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.