Mail:
Dept. of Chemistry
Ohio State University
100 W. 18th Ave.
Columbus, OH 43210
Office:
412 CBEC
Email:
herbert@
chemistry.ohio-state.edu
Analytical Hessians are often viewed as essential for the calculation of accurate harmonic frequencies, but the implementation of these analytic second derivatives is non-trivial and the coupled-perturbed equations that result engender a sizable memory footprint for large systems, relative to density functional theory energy and gradient calculations. Here, we benchmark the alternative approach to harmonic frequencies via finite differences of analytic first derivatives, a procedure that is amenable to large-scale parallelization. Not only for absolute harmonic frequencies but also for isotopic and conformer-dependent frequency shifts in flexible molecules, we find that the finite-difference approach exhibits mean errors < 0.1 cm–1 as compared to results based on an analytic Hessian. For very small harmonic frequencies corresponding to non-bonded vibrations in non-covalent complexes (for which the harmonic approximation is questionable anyway), the finite-difference errors can be larger, but even in these cases errors can be reduced below 0.1 cm–1 by judicious choice of the displacement step size and a higher-order finite-difference approach. The surprising accuracy and robustness of the finite-difference results suggests that having the analytic Hessian is not so important in today's era of commodity processors that are readily available in large numbers.