Anharmonic Vibrational Raman Spectra in Polymorphic Molecular Crystals: Density-Functional-Perturbation Theory and Machine Learning

Anharmonic contributions to vibrational Raman spectra of molecular crystals can be decisive to identify the structure of different polymorphs. In this work we characterise the low-frequency Raman spectral region of different polymorphs of the flexible aspirin and paracetamol crystals. We include anharmonicities through the time-correlation formalism, combining ab initio molecular dynamics and density-functional perturbation theory (DFPT) implemented in a full-potential, all-electron framework [1]. Lattice expansion and anharmonic thermal nuclear motion strongly affect the collective vibrations of the low-frequency region. This effect is much less pronounced at higher frequencies. We obtain excellent agreement with experimental lineshapes, highlighting the necessity of going beyond the harmonic approximation. In order to bypass the cost of DFPT evaluations of the polarizability tensor, we employ different forms of Kernel Ridge Regression (KRR) and discuss their efficiency. Training our models on several hundreds of points, we reproduce Raman spectra that would otherwise require the calculation of tens of thousands of points. This technique is extended to surface-sensitive vibrational sum-frequency generation.
[1] H. Shang, N. Raimbault et al., New J. Phys. 20, 073040 (2018)