Predicting Spin-Dependent Phonon Band Structures of HKUST-1 Using Density Functional Theory and Machine-Learned Interatomic Potentials

The present study focuses on the spin-dependent vibrational properties of HKUST-1, a metal-organic framework with potential applications in gas storage and separation. Employing density functional theory (DFT), we explore the consequences of spin couplings in the copper paddle wheels (as the secondary building units of HKUST-1) on the material's vibrational properties. By systematically screening the impact of the spin state on the phonon bands and densities of states in the various frequency regions, we identify asymmetric -COO- stretching vibrations as being most affected by different types of magnetic couplings. Notably, we also show that the DFT-derived insights can be quantitatively reproduced employing suitably parametrized, state-of-the-art machine-learned classical potentials with root-mean-square deviations from the DFT results between 3 cm-1 and 7 cm-1. This demonstrates the potential of machine-learned classical force fields for predicting the spin-dependent properties of complex materials, even when explicitly considering spins only for the generation of the reference data used in the force-field parametrization process.