Box length search algorithm for molecular simulation of systems containing periodic structures

We have developed a box length search algorithm to efficiently find the appropriate box dimensions for constant-volume molecular simulation of periodic structures. The algorithm works by finding the box lengths that equalize the pressure in each direction while maintaining constant total volume. Maintaining the volume at a fixed value ensures that quantitative comparisons can be made between simulation and experimental, theoretical or other simulation results for systems that are incompressible or nearly incompressible. We test the algorithm on a system of phase-separated block copolymers that has a preferred box length in one dimension. We also describe and test a Monte Carlo algorithm that allows the box lengths to change while maintaining constant volume. We find that the box length search algorithm converges at least two orders of magnitude more quickly than the variable box length Monte Carlo method. Although the box length search algorithm is not ergodic, it successfully finds the box length that minimizes the free energy of the system. We verify this by examining the free energy as determined by the Monte Carlo simulation.