Net-event kinetic Monte Carlo for overcoming stiffness in spatially homogeneous and distributed systems

A technique, termed net-event kinetic Monte Carlo (NE-KMC), is presented for overcoming large disparities in time scale that may render conventional KMC inefficient or intractable when fast reversible processes exist. The success of this approach derives from the consolidation of fast reversible processes into single “net events”. The resulting self-regulating method appropriately samples rare events even when partial equilibrium (PE) exists between fast reversible microscopic processes. Moreover, we show that computational savings over conventional KMC are proportional to the separation in time scales between the fast reversible process and rare events. We illustrate the capabilities of this new technique for a homogeneous series reaction system, and extend the net-event concept to distributed systems where multiple microscopic processes occur simultaneously. In a culminating example, we combine the time and length scale capabilities of NE-KMC and adaptive coarse-grained MC, respectively, to stochastically model diffusion through a realistically thick membrane.