Universal Scaling between On-Site Coulomb Repulsion and Numbers of Core and Valence Electrons in Transition Metal Trichalcogenides

Electron correlations that determine a broad spectrum of the physical properties of transition metal compounds are largely manifested by the on-site Coulomb repulsion U, which so far has been mainly evaluated on a case-by-case basis. Here we employ a linear response method based on constrained local density approximation to systematically investigate U in representative classes of transition metal trichalcogenides, with the transition metals covering all the unfilled 3d, 4d, and 5d orbitals. We uncover a characteristic scaling dependence of U on two elemental physical parameters, namely, the numbers of the core and valence electrons. Such a universal scaling law reflects the intuition that more unfilled d electrons residing on a smaller spherical core will feel stronger Coulomb repulsion. Next, by using the artificial intelligence-based SISSO (Sure Independence Screening and Sparsifying Operator) approach, we identify a more sophisticated descriptor that not only further refines the scaling law, but also captures the crystal-field splitting effect as pictorially reflected by invoking an elliptical core instead of a spherical core. The approach developed in this study should find transferability in other classes of transition metal compounds.