Strongly Anharmonic Nuclear Dynamics in Solids: Accurate Computations and Rapid Estimates for Statistical Mechanics

Many material properties are determined by the anharmonicity of the potential-energy surface (PES), i.e., by features of the PES that are not captured by a harmonic second-order Taylor expansion. Typically, such effects are treated perturbatively in first-principles calculations by solely accounting for the third-order term in the expansion [1]. Little is yet known about the role of higher-order terms.
To shed light on this question, we chose representative materials with differing anharmonicity (e.g. Si, Ga₂O₃, CsCl, ZrO₂ ), for which we perform ab initio molecular dynamics (AIMD) simulations to obtain the thermal conductivity via the Green-Kubo formalism, which accounts for all anharmonic effects [2]. Finite-size and -time corrections are applied by mapping onto the harmonic picture. We critically discuss strategies to reduce the computational cost, e.g., by employing a temperature-dependent Taylor expansion [3]. These investigations reveal that higher-order terms are essential for a quantitative and qualitative description of highly anharmonic systems such as ZrO₂.
[1] D. A. Broido, et al., Appl. Phys. Lett. 91, 231922 (2007).
[2] C. Carbogno, R. Ramprasad, and M. Scheffler, Phys. Rev. Lett. 118, 175901 (2017).
[3] O. Hellman, et al., Phys. Rev. B 87, 104111 (2013).