Polarizability Models for Simulations of Finite Temperature Raman Spectra from Machine Learning Molecular Dynamics

Raman spectroscopy is a powerful and nondestructive method that is widely used to study the vibrational properties of solids or molecules. Simulations of finite-temperature Raman spectra rely on obtaining polarizabilities along molecular dynamics trajectories, which is computationally highly demanding if calculated from first principles. Machine learning force fields (MLFF) are becoming widely used for accelerating molecular dynamics simulations, but machine-learning models for polarizability are still rare. In this work, we present and compare three polarizability models for obtaining Raman spectra in conjunction with MLFF molecular dynamics trajectories: (i) model based on projection to primitive cell eigenmodes, (ii) bond polarizability model, and (iii) symmetry-adapted Gaussian process regression (SA-GPR) using smooth overlap of atomic positions. In particular, we investigate the accuracy of these models for different systems and how much training data is required. Models are first applied to boron arsenide, where the first- and second-order Raman spectra are studied as well as the effect of boron isotopes. With MoS$_2$ we study the applicability of the models for highly anisotropic systems and for simulating resonant Raman spectra. Finally, inorganic halide perovskites CsPbBr$_3$ and CsSnBr$_3$ are studied with a particular interest in simulating the spectra across phase transitions and the evolution of the central peak. All models can be used to efficiently predict polarizabilities and are applicable to large systems and long simulation times, and while all three models were found to perform similarly for BAs and MoS$_2$, only SA-GPR offers sufficient flexibility to accurately describe complex anharmonic materials like the perovskites.