  Appropriate consideration of the electron correlation is essential to
reproduce the intriguing metal-insulator transition accompanying the
Peierls-type structural transition in VO$_2$. In the density functional
theory-based approach, this depends on the choice of the exchange-correlation
functional. Here, using a newly developed strongly constrained and
appropriately norm (SCAN) functional, we investigate the lattice and electronic
properties of the metallic rutile phase of VO$_2$ ($R$-VO$_2$) from the
first-principles calculations. We also explored the role of the Coulomb
correlation $U$. By adding $U$, we found that the phonon instability properly
describes the Peierls-type distortions. The orbital-decomposed density of
states presents the orbital selective behavior with the SCAN+$U$, which is
susceptible to the one-dimensional Peierls distortion. Our results suggest that
even with the SCAN functional, the explicit inclusion of the Coulomb
interaction is necessary to describe the structural transition of VO$_2$.
