Combining Quantum Mechanics and Machine-Learning Calculations for Anharmonic Corrections to Vibrational Frequencies

Several methods are available to compute the anharmonicity in semirigid molecules. However, such methods are not yet routinely employed because of their high 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 mechanics/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.