Challenges for density functional theory in simulating metal-metal singlet bonding: A case study of dimerized VO₂

VO₂ is renowned for its electric transition from an insulating monoclinic (M₁) phase, characterized by V-V dimerized structures, to a metallic rutile (R) phase above 340 K. This transition is accompanied by a magnetic change: the M₁ phase exhibits a non-magnetic spin-singlet state, while the R phase exhibits a state with local magnetic moments. Simultaneous simulation of the structural, electric, and magnetic properties of this compound is of fundamental importance, but the M₁ phase alone has posed a significant challenge to the density functional theory (DFT). In this study, we show none of the commonly used DFT functionals, including those combined with on-site Hubbard U to treat 3d electrons better, can accurately predict the V-V dimer length. The spin-restricted method tends to overestimate the strength of the V-V bonds, resulting in a small V-V bond length. Conversely, the spin-symmetry-breaking method exhibits the opposite trends. Each of these two bond-calculation methods underscores one of the two contentious mechanisms, i.e., Peierls lattice distortion or Mott localization due to electron-electron repulsion, involved in the metal-insulator transition in VO₂. To elucidate the challenges encountered in DFT, we also employ an effective Hamiltonian that integrates one-dimensional magnetic sites, thereby revealing the inherent difficulties linked with the DFT computations.