Machine learning predicted anharmonic frequencies and their effect in thermochemistry

Anharmonic effects play a crucial role in determining thermodynamic properties of liquids and gases. However, such data is computationally expensive and difficult to obtain. Machine learning (ML) methods are proving to be effective in making inexpensive computational approximations within theoretical chemistry and spectroscopy. In this work density functional theory (DFT) and vibrational self-consistent field (VSCF) are applied to obtain a vibrational dataset for HX, CH3X and C2H5X (X = F, Cl, Br) clusters of various sizes to train the gradient boosting ensemble model. It is shown that harmonic frequencies and reduced masses as descriptors are sufficient to train a ML model that significantly improves on harmonic frequencies and estimates anharmonic frequencies with negligible computational time. Anharmonic frequencies of the larger clusters (>10 atoms) of hydrogen fluoride were predicted using our ML model as a test case application. Quantum-mechanically calculated and ML-predicted harmonic/anharmonic frequencies were used as an input for quantum cluster equilibrium (QCE) method to generate thermodynamic data for the liquid and gas phases. QCE calculations show that anharmonic frequencies significantly affect and improve the final results, especially the populations of the clusters of liquid hydrogen fluoride. ML estimates provide an efficient way to include anharmonic contributions in the calculation of more accurate thermodynamic properties of condensed phases.

Keywords: machine learning, density functional theory, harmonic and anharmonic vibrational analysis, statistical thermodynamics, quantum cluster equilibrium, liquid hydrogen fluoride