  Vanadium dioxide(VO$_2$) is a paradigmatic example of a strongly correlated
system that undergoes a metal-insulator transition at a structural phase
transition. To date, this transition has necessitated significant post-hoc
adjustments to theory in order to be described properly. Here we report
standard state-of-the-art first principles quantum Monte Carlo (QMC)
calculations of the structural dependence of the properties of VO$_2$. Using
this technique, we simulate the interactions between electrons explicitly,
which allows for the metal-insulator transition to naturally emerge,
importantly without ad-hoc adjustments. The QMC calculations show that the
structural transition directly causes the metal-insulator transition and a
change in the coupling of vanadium spins. This change in the spin coupling
results in a prediction of a momentum-independent magnetic excitation in the
insulating state. While two-body correlations are important to set the stage
for this transition, they do not change significantly when VO$_2$ becomes an
insulator. These results show that it is now possible to account for electron
correlations in a quantitatively accurate way that is also specific to
materials.
