The present algorithm iteratively alternates a block of NMD standard MD steps and a multi-try MC step in which NMC trial moves are processed in parallel, as detailed below. This is similar to our prior algorithm, where blocks of NMD steps alternated with blocks of NMC single-try MC steps. Each block of MD starts from the configuration present at the end of the prior MC step and vice versa. The velocities of all the atoms in the system at the start of each MD block are the same as those at the end of the prior MD block; that is, a moved water molecule carries its velocities. In addition, the orientation of a moved water is not modified, as the orientation of waters in the bulk is randomized by the MD blocks. Trajectory snapshots (atomic coordinates and velocities and system properties such as energy) are saved during the MD block, but not during MC. Steps within the blue frame constitute the parallel MC part (see text for details). MC preparation comprises generation of the steric grid and the grid with the neighbor list for coarse energy calculations. Full energies are computed with the particle-mesh Ewald treatment of long-ranged electrostatics exactly as done during an MD step. Coarse and full energies are computed on the GPU, as are the steric grid and the coarse energy neighbor list.