This work investigates the modification of the Nóse–Hoover thermostat, a well-known tool for controlling system temperature in nanoscale dynamical simulations. Nóse–Hoover response is characterized by a mean temperature converging to a target temperature. However, oscillations in the actual system temperature consistently appear over time. To reduce these oscillations, the Nóse–Hoover control law is modified to resemble a proportional–derivative controller. The modified thermostat is compared to the standard and shown to significantly reduce deviations. Gains are varied and compared to show effects on response and simulation time. Work–energy calculations show the modified dynamics drive the system to a low-energy state significantly faster than the standard. The behavior of the modified thermostat is illustrated using a simulation of a molten salt solution.

Molecular dynamics simulations require significant computational resources to generate modest time evolutions. Large active forces lead to large accelerations, requiring subfemtosecond integration time steps to capture the resultant high-frequency vibrations. It is often necessary to combine these fast dynamics with larger scale phenomena, creating a multiscale problem. A multiscale method has been previously shown to greatly reduce the time required to simulate systems in the continuum regime. A new multiscale formulation is proposed to extend the continuum formulation to the atomistic scale. A canonical ensemble model is defined using a modified Nóse–Hoover thermostat to maintain the constant temperature constraint. Results show a significant reduction in computation time mediated by larger allowable integration time steps.

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