*Article* **Elastic Coefficients of** *β***-HMX as Functions of Pressure and Temperature from Molecular Dynamics**

**Andrey Pereverzev \* and Tommy Sewell \***

Department of Chemistry, University of Missouri, Columbia, MO 65211, USA **\*** Correspondence: pereverzeva@missouri.edu (A.P.); sewellt@missouri.edu (T.S.)

Received: 15 November 2020; Accepted: 5 December 2020; Published: 10 December 2020 -

**Abstract:** The isothermal second-order elastic stiffness tensor and isotropic moduli of *β*-1,3,5,7 tetranitro-1,3,5,7-tetrazoctane (*β*-HMX) were calculated, using the P21/n space group convention, from molecular dynamics for hydrostatic pressures ranging from 10−<sup>4</sup> to 30 GPa and temperatures ranging from 300 to 1100 K using a validated all-atom flexible-molecule force field. The elastic stiffness tensor components were calculated as derivatives of the Cauchy stress tensor components with respect to linear strain components. These derivatives were evaluated numerically by imposing small, prescribed finite strains on the equilibrated *β*-HMX crystal at a given pressure and temperature and using the equilibrium stress tensors of the strained cells to obtain the derivatives of stress with respect to strain. For a fixed temperature, the elastic coefficients increase substantially with increasing pressure, whereas, for a fixed pressure, the elastic coefficients decrease as temperature increases, in accordance with physical expectations. Comparisons to previous experimental and computational results are provided where possible.

**Keywords:** HMX; elastic properties; molecular dynamics
