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We show a unified second-order scheme for constructing simple, robust andaccurate algorithms for typical thermostats for configurational sampling forthe canonical ensemble. When Langevin dynamics is used, the scheme leads to theBAOAB algorithm that has been recently investigated. We show that the scheme isalso useful for other types of thermostat, such as the Andersen thermostat andNos\'e-Hoover chain. Two 1-dimensional models and three typical realisticmolecular systems that range from the gas phase, clusters, to the condensedphase are used in numerical examples for demonstration. Accuracy may beincreased by an order of magnitude for estimating coordinate-dependentproperties in molecular dynamics (when the same time interval is used),irrespective of which type of thermostat is applied. The scheme is especiallyuseful for path integral molecular dynamics, because it consistently improvesthe efficiency for evaluating all thermodynamic properties for any type ofthermostat.

A unified thermostat scheme for efficient configurational sampling for classical/quantum canonical ensembles via molecular dynamics