  We present a combined density-functional theory and single-site dynamical
mean-field theory (DMFT) study of vanadium dioxide (VO$_2$) using an
unconventional set of bond-centered orbitals as the basis of the correlated
subspace. VO$_2$ is a prototypical material undergoing a metal-insulator
transition (MIT), hosting both intriguing physical phenomena and the potential
for industrial applications. With our choice of correlated subspace basis, we
investigate the interplay of structural dimerization and electronic
correlations in VO$_2$ in a computationally cheaper way compared to other
state-of-the-art methods such as cluster DMFT. Our approach allows us to treat
the rutile and M1 monoclinic VO$_2$ phases on an equal footing and to vary the
dimerizing distortion continuously, exploring the energetics of the transition
between the two phases. The choice of basis presented in this work hence offers
a complementary view on the long-standing discussion of the MIT in VO$_2$ and
suggests possible future extensions to other similar materials hosting
molecular-orbital-like states.
