*3.1. Isotherms and Isobars*

Although the main topic of the present study is calculation of the elastic coefficients, we also obtain predictions of *β*-HMX unit-cell volume as functions of pressure and temperature. Figure 1 shows unit-cell volume *V* as a function of pressure *P* at 300 K obtained in this work, along with MD results due to Sewell et al. [14] and experimental data of Yoo and Cynn [29], Gump and Peiris [30], and Olinger et al. [31]. The inset in Figure 1 shows the lower pressure part of the same data. The red curve in Figure 1 shows the third-order Birch–Murnaghan isotherm [32] fitted to our isotherm data. Fitting compression data to isotherms is subtle [10]. Here, we applied simple, unweighted fits of the Birch–Murnaghan fitting form to the experimental and simulated *V* = *V*(*P*) data. Our results are close to those of Sewell et al. This is not surprising as they used practically the same force field but with all covalent bonds fixed at constant values. The experimental results of Yoo and Cynn [29] are in overall qualitative agreement with our data but show slightly higher compressibility of the material. In addition, our simulations do not predict the subtle phase transition reported in [29] at approximately 27 GPa. Although we have limited results below 10 GPa, the changes in volume that we predict in this region are also similar to the volume changes observed experimentally in [30,31]. We provide in the Supplementary Materials the full set of lattice parameters and unit-cell volumes for all pressures and temperatures studied. The bulk moduli extracted from the experimental isotherm data are compared to our MD results in the next subsection.

**Figure 1.** Comparison of the 300 K isotherm from the present simulations to previous MD [14] and experimental results [29–31] at standard ambient temperature. *V* is the unit-cell volume. The red curve is the third-order Birch–Murnaghan isotherm [32] fitted to our data. The two fitting parameters of the Birch–Murnaghan equation are *K*<sup>0</sup> = 16.3 GPa and *K* <sup>0</sup> = 9.1. The inset shows the lower pressure part of the same data.

Figure 2 shows the five isotherms calculated in the present study. The higher temperature isotherms lie above the lower temperature ones. This behavior is physically reasonable: unit-cell volume increases as the temperature increases due to thermal expansion. The relative volume increase with increasing temperature becomes less pronounced for higher pressures. Otherwise, the isotherms are all quite similar.

**Figure 2.** Isotherms for 300, 500, 700 , 900, and 1100 K. *V* is the unit-cell volume. Lines are added to guide the eye.

Figure 3a shows isobars for the five pressures considered. As expected, the unit-cell volume increases as the temperature increases. The volume increase becomes less pronounced for higher pressure isobars. While the increase in unit-cell volume with increasing temperature is not surprising, the changes in the unit-cell geometry exhibit some interesting features. Figure 3b–d show the lengths of the unit-cell vectors **a**, **b**, and **c**, respectively. Surprisingly, at 5 and 10 GPa, the length of vector **a** *decreases* as the temperature increases. Somewhat similarly, at 20 and 30 GPa, vector **c** shows almost no change in length as the temperature changes. Similar counterintuitive behavior of some unit-cell lattice vectors was observed experimentally but not emphasized by Gump and Peiris [30]. Figure 3e shows how angle *β* (the angle between vectors **a** and **c**) changes with temperature and pressure. For a given temperature, *β* decreases with increasing pressure (the crystal becomes "more orthorhombic"). For a given pressure, the angle increases slightly as the temperature increases.

**Figure 3.** (**a**) Unit-cell volume as a function of temperature for five different pressures. (**b**) The length of unit-cell vector **a** as a function of temperature for five different pressures. (**c**) The same as (**b**) but for vector **b**. (**d**) The same as (**b**) but for vector **c**. (**e**) The same as (**b**) but for monoclinic lattice angle *β*. Lines are added to guide the eye.
