Combining quantum mechanics and machine-learning calculations for anharmonic corrections to vibrational frequencies

Several methods are available to compute the anharmonicity in semi-rigid molecules. However, such methods are not routinely employed yet because of their large computational cost, especially for large molecules. The potential energy surface is required and generally approximated by a quartic force field potential based on ab initio calculation, thus limiting this approach to medium-sized molecules. We developed a new, fast and accurate hybrid Quantum Mechanic/Machine learning (QM//ML) approach to reduce the computational time for large systems. With this novel approach, we evaluated anharmonic frequencies of 37 molecules thus covering a broad range of vibrational modes and chemical environments. The obtained fundamental frequencies reproduce results obtained using B2PLYP/def2tzvpp with a root-mean-square deviation (RMSD) of 21 cm-1 and experimental results with a RMSD of 23 cm-1. Along with this very good accuracy, the computational time with our hybrid QM//ML approach scales linearly with N while the traditional full ab initio method scales as N2, where N is the number of atoms.