Simulations are essential to accelerate the discovery of new materials and to gain full understanding of known ones. Although hard to realize experimentally, periodic boundary conditions are omnipresent in material simulations. In this work, we introduce ROBIN (recursive open boundary and interfaces), the first method allowing open boundary conditions in material and interface modeling. The computational costs are limited to solving quantum properties in a focus area that allows explicitly discretizing millions of atoms in real space and to consider virtually any type of environment (be it periodic, regular, or random). The impact of the periodicity assumption is assessed in detail with silicon dopants in graphene. 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. Key insight of this assessment is, assuming periodicity elevates a small perturbation of a periodic cell into a strong impact on the material property prediction. Periodic boundary conditions can be applied on truly periodic systems only. More general systems should apply an open boundary method for reliable predictions.

中文翻译：

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在非周期性材料和界面建模中引入开放边界条件：周期性假设的影响

模拟对于加快发现新材料并充分了解已知材料至关重要。尽管很难通过实验实现，但是周期性边界条件在材料模拟中无处不在。在这项工作中，我们介绍了ROBIN（递归开放边界和界面），这是在材料和接口建模中允许开放边界条件的第一种方法。计算成本仅限于解决焦点区域中的量子性质，该焦点区域允许在现实空间中明确离散数百万个原子，并考虑几乎任何类型的环境（周期性，规则或随机环境）。用石墨烯中的硅掺杂剂详细评估了周期性假设的影响。证实石墨烯会产生带隙，该带隙可周期性地用硅取代3％的碳，这与已公布的周期性边界条件计算相符。相反，石墨烯中3％随机分布的硅只会移动能谱。预测的位移与公开的实验数据在数量上一致。该评估的关键见解是，假设周期性会增加周期性单元的小扰动，从而对材料性能预测产生强烈影响。周期性边界条件只能应用于真正的周期性系统。更一般的系统应采用开放边界方法进行可靠的预测。该评估的关键见解是，假设周期性会增加周期性单元的小扰动，从而对材料性能预测产生强烈影响。周期性边界条件只能应用于真正的周期性系统。更一般的系统应采用开放边界方法进行可靠的预测。该评估的关键见解是，假设周期性会增加周期性单元的小扰动，从而对材料性能预测产生强烈影响。周期性边界条件只能应用于真正的周期性系统。更一般的系统应采用开放边界方法进行可靠的预测。