Non-equilibrium hybrid insertion/extraction through the 4th dimension in grand-canonical simulation

The process of inserting/deleting a particle during grand-canonical Monte-Carlo (MC) simulations is investigated using a novel, original technique: the trial event is made of a short nonequilibrium molecular dynamics (MD) trajectory during which a coordinate w along a 4th dimension is added to the particle in the course of insertion/deletion and is forced to decrease from large values down to zero (for insertion) or increased from 0 up to large values (for extraction) at imposed v_w velocity. The probability of acceptation of the whole MC move is controlled by the chemical potential and the external work applied during the trajectory. Contrary to the standard procedures which create/delete suddenly a particle, the proposed technique gives time to the fluid environment to relax during the gradual insertion/extraction before the acceptation decision. The reward for this expensive trial move is a gain of many orders of magnitude in the success rate. The power and wide domain of interest of this hybrid "H4D" algorithm which marries stochastic MC and nonequilibrium deterministic MD flavors are briefly illustrated with hard sphere, water, and electrolyte systems. The same approach can be easily adapted in order to measure the chemical potential of a solute particle immersed in a fluid during canonical or isobaric simulations. It then becomes an efficient application of the Jarzynski theorem for the determination of solvation free energy.