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Increasing the particle-field interaction length scale permits the use of larger time steps and coarser grids. This promotes the use of multiple time step strategies over the quasi-instantaneous approximation, which is found to not conserve energy and momenta equally well. Finally, our investigations of the structural and dynamic properties of simple monoatomic systems show a consistent behavior between the present formulation and Gaussian core models.Advances in nanophotonics, quantum optics, and low-dimensional materials have enable