Introducing Open Boundary Conditions in Modeling Nonperiodic Materials and Interfaces: The Impact of the Periodicity Assumption

Abstract

Simulations are essential to accelerate the discovery of new materials and to gain full understanding of known ones. In this work, we introduce the first method allowing open boundary conditions in material and interface modeling. The new method, which we named ROBIN (recursive open boundary and interfaces) allows for discretizing millions of atoms in real space, thereby not requiring any symmetry or order of the atom distribution. The computational costs are limited to solving quantum properties in a focus area. It is verified in detail that the impact of the infinite environment on that area is included exactly. Calculations of graphene with the same amount of 1) periodic (currently available methods) and 2) randomly distributed silicon atoms shows that assuming periodicity elevates a small perturbation into a strong impact on the material property prediction. Graphene was confirmed to produce a band gap with periodic substitution of 3% carbon with silicon in agreement with published periodic boundary condition calculations. Instead, 3% randomly distributed silicon in graphene only shifts the energy spectrum. The predicted shift agrees quantitatively with published experimental data. Periodic boundary conditions can be applied on truly periodic systems only. Other systems should apply an open boundary method.Computer aided material predictions represent the firststep of many new material discoveries 1-3 . Material simulations can power machine learning searches for new materials with specific properties 4-6 . However, modeling experimental reality with wide-spread idealized, periodic boundary conditions 7,8 is prone to artifacts: Irregular interfaces, impurities, cracks and dislocations are not compatible with idealized conditions. A common approach to limit artificial periodicity effects is to make the repeating unit cell as large as numerically feasible and apply various correction algorithms 9-12 .Instead, we introduce the Recursive Open Boundary and INterfaces (ROBIN) method that can handle arbitrary geometries and atom distributions and does not need any periodicity assumption. It is based on the nonequilibrium Green's function method (NEGF). The NEGF method had been applied on charge 13,14 , spin 15,16 and heat 17,18 transport in open nanodevices. The ROBIN extension of NEGF models materials in infinitely extended real space and supports regular and irregular systems. We verify the ROBIN method in 2D and 3D crystalline systems. Calculations of graphene confirm recent work 19 that periodically distributed silicon impurities can open bandgaps. In stark contrast and presumably closer to any experiment, random distributions of the

Molecular dynamics simulation for chlorinated butyl rubber composite reinforced by dendritic amino‐terminated aromatic polyamide

“…Thus, we need to use periodic boundary conditions. To get rid of the boundary effect caused by the size limitation of the simulated system 3,4 . We also need to introduce the nearest neighbor image convention.…”

“…To get rid of the boundary effect caused by the size limitation of the simulated system. 3,4 We also need to introduce the nearest neighbor image convention. Any particle can interact with only one "nearest" particle or image particle.…”