Computing finite-temperature elastic constants with noise cancellation

Elastic constants are central material properties, frequently reported in experimental and theoretical studies. While their computation is straightforward in the absence of thermal fluctuations, finite-temperature methods often suffer from poor signal-to-noise ratios, the presence of strong anharmonic effects, or require second-order derivatives with respect to spatial coordinates. Here, we show how to compute elastic constants in thermally ordered and disordered systems by generalizing a noise-cancellation method originally developed for piezoelectric coupling coefficients. A slight strain is applied to an equilibrated solid. Simulations of both the strained and unstrained (or oppositely strained) reference systems are performed using identical thermostatting schemes. As demonstrated theoretically and with generic one-dimensional models, this allows stress differences to be evaluated and elastic constants to be determined with favorable thermal noise. We then apply this approach across a diverse set of systems, spanning crystalline argon, ordered silicon, as well as amorphous silicon, poly(methyl methacrylate), and cellulose derivatives.