Generalized Application of Periodic Symmetry in Molecular Simulations

Periodic symmetry is widely used in molecular simulations to mimic the presence of an infinite bulk surrounding an N-atom model system. However, the traditional methods of applying periodic symmetry end up enforcing over-restrictive kinematic constraints between the periodic boundaries. After a brief overview of the periodic symmetry, the nature of the constraint is discussed briefly in this paper. Thereafter, the objective is to provide a means to ensure that periodicity is upheld while avoiding unnecessary constraint of the repeating cell boundaries. This paper demonstrates the usual application of periodic symmetry into a molecular simulation algorithm through a typical example. Meanwhile, a novel method is introduced, which uses equivalent external forces applied to physical boundary atoms. Comparisons between the classic treatment and the new method using one-dimensional and two-dimensional models are made. Moreover, the potential application of the new method in regular Finite Element Analysis is discussed.