  We present a systematic investigation of the crystal and electronic structure
and the magnetic properties above and below the metal-insulator transition of
ball-milled VO$_2$ nanoparticles and VO$_2$ microparticles. For this research,
we performed a Rietveld analysis of synchrotron radiation x-ray diffraction
data, O $K$ x-ray absorption spectroscopy, V $L_3$ resonant inelastic x-ray
scattering, and magnetic susceptibility measurements. This study reveals an
unusual low-temperature phase that involves the formation of an elongated and
less-tilted V-V pair, a narrowed energy gap, and an induced paramagnetic
contribution from the nanoparticles. We show that the change in the crystal
structure is consistent with the change in the electronic states around the
Fermi level, which leads us to suggest that the Peierls mechanism contributes
to the energy splitting of the $a_{1g}$ state. Furthermore, we find that the
high-temperature rutile structure of the nanoparticles is almost identical to
that of the microparticles.
