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 a diverse range of 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.