  We investigate the equation of states of the $\beta$-polymorph of
cyclotetramethylene tetranitramine (HMX) energetic molecular crystal using
DFT-D2, a first-principles calculation based on density functional theory (DFT)
with van der Waals (vdW) corrections. The atomic structures and equation of
states under hydrostatic compressions are studied for pressures up to 100 GPa.
We found that the N-N bonds along the minor axis of the ring are more sensitive
to the variation of pressure, which indicates that they are potential "weak
spots" in atomic level within a single molecule of $\beta$-HMX. Our study
suggested that the van der Waals interactions are critically important in
modeling this molecular crystal.
