Analytical harmonic vibrational frequencies with VV10-containing density functionals: Theory, efficient implementation, and benchmark assessments

TL;DR

This paper develops and implements the analytical second derivatives of VV10 for density functionals, assesses their impact on harmonic frequency calculations, and provides practical recommendations and scaling factors for improved vibrational analysis.

Contribution

It introduces the first derivation and efficient implementation of VV10's analytical second derivatives and evaluates their effect on vibrational frequency predictions.

Findings

VV10 contributions slightly increase computational cost for frequencies.

VV10 is crucial for systems with weak interactions like water clusters.

Scaling factors improve agreement between calculated and experimental frequencies.

Abstract

VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, {\omega}B97X-V and the hybrid mGGA, {\omega}B97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and efficient implementation of the analytical second derivatives of the VV10 energy. The additional compute cost of the VV10 contributions to analytical frequencies is shown to be small in all but the smallest basis sets for recommended grid sizes. This study also reports the assessment of VV10-containing functionals for predicting harmonic frequencies using the analytical second derivative code. The contribution of VV10 to simulating harmonic frequencies is shown to be small for small molecules but important for systems where weak interactions are important, such as water clusters. In the latter cases, B97M-V, {\omega}B97M-V, and {\omega}B97X-V perform very well. The convergence of frequencies with respect to grid size and atomic orbital basis set size is studied and recommendations reported. Finally, scaling factors to allow comparison of scaled harmonic frequencies with experimental fundamental frequencies and to predict zero-point vibrational energy are presented for some recently developed functionals (including r2SCAN, B97M-V, {\omega}B97X-V, M06-SX, and {\omega}B97M-V).