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In light of the recently published complete set of statistically correctGronbech-Jensen (GJ) methods for discrete-time thermodynamics, we revise adifferential operator splitting method for the Langevin equation in order tocomply with the basic GJ thermodynamic sampling features, namely the Boltzmanndistribution and Einstein diffusion, in linear systems. This revision, which isbased on the introduction of time scaling along with flexibility of adiscrete-time velocity attenuation parameter, provides a direct link betweenthe ABO splitting formalism and the GJ methods. This link brings about theconclusion that any GJ method has at least weak second order accuracy in theapplied time step. It further helps identify a novel half-step velocity, whichsimultaneously produces both correct kinetic statistics and correct transportmeasures for any of the statistically sound GJ methods. Explicit algorithmicexpressions are given for the integration of the new half-step velocity intothe GJ set of methods. Numerical simulations, including quantum-based moleculardynamics (QMD) using the QMD suite LATTE, highlight the discussed properties ofthe algorithms as well as exhibit the direct application of robust, time stepindependent stochastic integrators to quantum-based molecular dynamics.

Bringing discrete-time Langevin splitting methods into agreement with thermodynamics