A modified Müller-Plathe method capable of quickly establishing an expected temperature difference in classical and <i>ab initio</i> molecular dynamics simulations for thermal transport calculations

The Müller-Plathe method [F. Müller-Plathe, <i>J. Chem. Phys.</i>, 1997, <b>106</b>, 6082] has been widely used to calculate the thermal transport properties of materials, with the advantages of easy implementation and no external thermostat needed. However, the temperature differences of model systems are uncontrollable in the original Müller-Plathe method, which largely depends on the selected time intervals for velocity exchanges in the molecular dynamics simulations, largely affecting the computational efficiency of the Müller-Plathe-method-based molecular dynamics simulations, especially first-principles calculations. In this paper, we improved the Müller-Plathe method to be capable of establishing the expected temperature difference by introducing a feedback-and-response mechanism into the method. The modified Müller-Plathe method was achieved by dynamically adjusting the heat flux direction in real-time through the proposed feedback-and-response mechanism, which represents a significant departure from the conventional approach of modulating the time interval for velocity exchange in the original Müller-Plathe method, and the prediction efficiency was significantly improved. The modified Müller-Plathe method was further validated by performing a series of classical and <i>ab initio</i> molecular dynamics simulations.