Effects of thermostatting in molecular dynamics on anharmonic properties of crystals: Application to fcc Al at high pressure and temperature.

The precision and accuracy of the anharmonic energy calculated in the canonical (NVT) ensemble using three different thermostats (viz., Andersen, Langevin, and Nosé-Hoover) along with no thermostat (i.e., microcanonical, NVE) are compared via application to aluminum crystals at ≈100 GPa for temperatures up to melting (4000 K) using ab initio molecular dynamics (AIMD) simulation. In addition to the role of the thermostat, the effect of using either conventional or the recently introduced harmonically mapped averaging (HMA) method is considered. The effect of AIMD time-step size Δt on the ensemble averages gauges accuracy, while for a given Δt, the stochastic uncertainty (computed using block averaging) provides the metric for precision. We identify the rate of convergence of block averages (with respect to block size) as an important issue in this context, as it imposes a minimum simulation length required to achieve reliable statistics, and it differs considerably among the methods. We observe that HMA with a Langevin thermostat in an NVT simulation shows the best performance, from the point of view of accuracy, precision, and simulation length. In addition, we introduce a novel HMA-based ensemble average for the temperature. In application to NVE simulations, the new formulation exhibits much smaller fluctuations compared to the conventional kinetic-energy approach; however, it provides only marginal improvement in uncertainty due to strong negative correlations exhibited by the conventional form (which acts to reduce its uncertainty but also slows convergence of the block averages).