A machine learning model for nuclear Hessians based on GFN2-xTB-derived atomistic features

The determination of vibrational frequencies is by now indispensable in computational chemistry. They build a cornerstone in quantum chemistry for the computation of thermodynamic corrections and vibrational spectra. Determining the harmonic vibrational frequencies, however, requires computing the nuclear Hessian matrix, which is significantly more costly than evaluating the electronic energy or its first derivatives (forces). The Hessian is thus a valuable target for prediction by machine learning models, as this promises a significant reduction in the computational cost. In this work, a physically motivated machine learning model is presented for the prediction of Hessian matrices. Features from the semi-empirical method GFN2-xTB are used to predict block matrices of the corresponding Hessian matrix using a feedforward neural network. Only one single-point calculation with the efficient GFN2-xTB method is necessary for the generation of features, which reduces the cost for the Hessian significantly. The model is fitted to reproduce GFN2-xTB Hessian matrices on a data set that covers the complete periodic table up to radon. To verify its performance, a variety of benchmark sets are evaluated. This study shows that the model can reproduce harmonic oscillator free energies with an error within the chemical accuracy (1 kcal mol −1 ) when combined with standard partition function approximations. Additionally, single applications are chosen for the computation of broadened line spectra to show the accuracy of the model, e.g., when used for simulation of IR spectra. The model is implemented and published is an open source Python package which can be obtained from https://git.rwth-aachen.de/bannwarthlab/hessian_ml .