  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 Kelvin. 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 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 better treat 3d electrons, 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
bond-calculation method underscores one of the two contentious mechanisms,
i.e., Peierls or Mott, 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.
