Advances and Challenges of SCAN and r²SCAN Density Functionals in Transition-Metal Compounds

Transition-metal compounds (TMCs) with open-shell d-electrons are characterized by a complex interplay of lattice, charge, orbital, and spin degrees of freedom, giving rise to various fascinating applications. Often exhibiting exotic properties, these compounds are commonly classified as correlated systems due to strong inter-electronic interactions called Hubbard U. This inherent complexity presents significant challenges to Kohn-Sham density functional theory (KS-DFT), the most widely used electronic structure method in condensed matter physics and materials science. While KS-DFT is, in principle, exact for the ground-state total energy, its exchange-correlation energy must be approximated in practice. The mean-field nature of KS implementations, combined with the limitations of current exchange-correlation density functional approximations, has led to the perception that DFT is inadequate for correlated systems, particularly TMCs. Consequently, a common workaround involves augmenting DFT with an on-site Hubbard-like U correction. In recent years, the strongly constrained and appropriately normed (SCAN) density functional, along with its refined variant r²SCAN, has achieved remarkable progress in accurately describing the structural, energetic, electronic, magnetic, and vibrational properties of TMCs, challenging the traditional perception of DFT's limitations. This review explores the design principles of SCAN and r²SCAN, highlights their key advancements in studying TMCs, explains the mechanisms driving these improvements, and addresses the remaining challenges in this evolving field.