Hessian QM9: A quantum chemistry database of molecular Hessians in implicit solvents

A significant challenge in computational chemistry is developing approximations that accelerate \emph{ab initio} methods while preserving accuracy. Machine learning interatomic potentials (MLIPs) have emerged as a promising solution for constructing atomistic potentials that can be transferred across different molecular and crystalline systems. Most MLIPs are trained only on energies and forces in vacuum, while an improved description of the potential energy surface could be achieved by including the curvature of the potential energy surface. We present Hessian QM9, the first database of equilibrium configurations and numerical Hessian matrices, consisting of 41,645 molecules from the QM9 dataset at the $\omega$B97x/6-31G* level. Molecular Hessians were calculated in vacuum, as well as water, tetrahydrofuran, and toluene using an implicit solvation model. To demonstrate the utility of this dataset, we show that incorporating second derivatives of the potential energy surface into the loss function of a MLIP significantly improves the prediction of vibrational frequencies in all solvent environments, thus making this dataset extremely useful for studying organic molecules in realistic solvent environments for experimental characterization.