材料模拟更进一步：能确保维持基态的模型构建

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第一原理密度泛函理论计算是计算材料学研究中最常用的一种工具，但在模拟含数千个原子的大型结构时，通常还用到集群扩展模型，并需要人为手动调整参数以保证基态准确，从而决定材料属性，不方便，也不准确。来自美国麻省理工学院、加州大学伯克利分校和劳伦斯伯克利国家实验室的Gerbrand Ceder教授（美国2017年新科工程院院士）领导的国际研究团队，提出了一个系统的、数学上可靠的方法，即：基于压缩感知途径来建立集群扩展模型，利用二次规划对模型参数加以约束，从而保持基态而无需人为调整参数。他们以锂离子电池阴极的两种锂过渡金属氧化物（Li2xFe2(1-x)O2和Li2xTi2(1-x)O2）为例，构建了极具挑战的、带有压缩感知能力的集群扩展模型，证实了该方法的强大实用性，不仅保证了为模型构建而使用的参考结构集的基态准确，而且通过快速收敛迭代保证了样本之外尺寸较大的超胞的基态可靠性。因此，他们的方法为构建实用的、压缩的、受约束的、有预测功能的物理模型，提供了一种通用工具。该文近期发表于npj Computational Materials 3:30 (2017); oi:10.1038/s41524-017-0032-0; 标题与摘要如下，论文PDF文末点击阅读原文可以获取。

Construction of ground-state preserving sparse lattice models for predictive materials simulations （构建能保持基态稀有晶格的模型以预测模拟材料）

Wenxuan Huang, Alexander Urban, Ziqin Rong, Zhiwei Ding, Chuan Luo & Gerbrand Ceder

First-principles based cluster expansion models are the dominant approach in ab initio thermodynamics of crystalline mixtures enabling the prediction of phase diagrams and novel ground states. However, despite recent advances, the construction of accurate models still requires a careful and time-consuming manual parameter tuning process for ground-state preservation, since this property is not guaranteed by default. In this paper, we present a systematic and mathematically sound method to obtain cluster expansion models that are guaranteed to preserve the ground states of their reference data. The method builds on the recently introduced compressive sensing paradigm for cluster expansion and employs quadratic programming to impose constraints on the model parameters. The robustness of our methodology is illustrated for two lithium transition metal oxides with relevance for Li-ion battery cathodes, i.e., Li2x Fe2(1−x)O2 and Li2xTi2(1−x)O2, for which the construction of cluster expansion models with compressive sensing alone has proven to be challenging. We demonstrate that our method not only guarantees ground-state preservation on the set of reference structures used for the model construction, but also show that out-of-sample ground-state preservation up to relatively large supercell size is achievable through a rapidly converging iterative refinement. This method provides a general tool for building robust, compressed and constrained physical models with predictive power.

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