We propose an incremental construction of multi-timestep integrators to accelerate polarizable point dipole molecular dynamics while preserving sampling efficiency. We start by building integrators using frequency-driven splittings of energy terms and a Velocity-Verlet evaluation of the most rapidly varying forces, and compare a standard bonded/non-bonded split to a three-groups split dividing non-bonded forces (including polarization) into short-and long-range contributions. We then introduce new
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