**1. Introduction**

The high explosive 1,3,5,7-tetranitro-1,3,5,7-tetrazoctane, also known as octahydro-1,3,5, 7-tetranitro-1,3,5,7-tetrazocine (HMX), is an important energetic material which is used in a number of high performance military explosive and propellant formulations [1]. Several polymorphs of HMX are known [2–5], among which *β*-HMX is the thermodynamically stable form at standard ambient conditions. The elastic properties of *β*-HMX are important for understanding processes such as shock propagation and the resulting hot-spot formation that ultimately lead to ignition and detonation initiation [6].

Accurate experimental determination of elastic coefficients in molecular high explosives is challenging due to the low crystal symmetries characteristic of many energetic substances. This is particularly evident in the case of *β*-HMX for which there exist substantial differences among measured values of the elastic tensor obtained using different experimental techniques [7–9]. This disparity in the experimental data has been ascribed to sample purity and processing variations and is further complicated with questions about how to interpret or process the results [6,10].

In part because of these complexities, there are virtually no experimental data for elastic properties of *β*-HMX under the high temperatures and pressures relevant to high-explosive initiation and detonation. In the absence of practical experimental alternatives, molecular dynamics (MD) provides a viable path to obtaining some of the needed information. In the present study, we use MD to obtain elastic coefficients of *β*-HMX for wide intervals of temperature and hydrostatic pressure. The results obtained herein can be used both as a general reference and as input data for mesoscale continuum models of shock propagation and detonation initiation in *β*-HMX [11,12].
