适用于分子与固体的非局部机器学习交换泛函
Nonlocal Machine-Learned Exchange Functional for Molecules and Solids
AI总结：
本研究结合机器学习与物理约束，设计出兼具轨道依赖性和非局部性的低成本交换泛函，兼顾分子与固体体系的计算精度与效率，突破传统DFT的成本-精度权衡限制。
摘要：
为密度泛函理论（DFT）设计更优的交换关联泛函是现代电子结构理论的核心挑战。然而，当前的发展受限于泛函的数学形式：高效的半局部泛函对许多具有重要技术价值的体系精度不足，而更精确的杂化泛函因使用精确交换算符，对大型固态体系而言计算成本过高。在本研究中，我们将机器学习与精确物理约束相结合，设计出一种既依赖轨道又具有非局部性的交换泛函，其计算成本与半局部泛函大致相当，在平面波程序中计算速度远快于杂化DFT。通过训练具有多种不同特征集的泛函，我们阐明了轨道依赖特征和非局部特征在学习交换能中的作用，并确定这两类特征都为模型提供了至关重要且各自独立的重要信息。在使用具有表达力的非局部特征集训练出我们的新型交换泛函后，我们将其代入现有杂化泛函中，在热化学基准测试集上达到了杂化DFT的精度，并且相较于半局部DFT提升了带隙预测的准确性。为了证明我们方法的可扩展性以及带隙预测改进的实际效益，我们使用大型超胞计算了硅中的带电缺陷跃迁能级。由于该模型在分子体系和扩展体系中都具有良好的可迁移性和计算效率，它克服了半局部DFT与杂化DFT之间的成本-精度权衡问题，我们的通用方法为开发具有后杂化DFT精度、半局部DFT成本的通用交换关联泛函提供了可行路径。
英文摘要：
The design of better exchange-correlation functionals for Density Functional Theory (DFT) is a central challenge of modern electronic structure theory. However, current developments are limited by the mathematical form of the functional, with efficient semilocal functionals being inaccurate for many technologically important systems and the more accurate hybrid functionals being too expensive for large solid-state systems due to the use of the exact exchange operator. In this work, we use machine learning combined with exact physical constraints to design an exchange functional that is both orbital-dependent and nonlocal, but which can be evaluated at roughly the cost of semilocal functionals and is significantly faster than hybrid DFT in plane-wave codes. By training functionals with several different feature sets, we elucidate the roles of orbital-dependent and nonlocal features in learning the exchange energy and determine that both types of features provide vital and independently important information to the model. Having trained our new exchange functional with an expressive, nonlocal feature set, we substitute it into existing hybrid functionals to achieve hybrid-DFT accuracy on thermochemical benchmark sets and improve the accuracy of band gap predictions over semilocal DFT. To demonstrate the scalability of our approach as well as the practical benefits of improved band gap prediction, we compute charged defect transition levels in silicon using large supercells. Due to its transferability and computational efficiency for both molecular and extended systems, our model overcomes the cost-accuracy trade-off between semilocal and hybrid DFT, and our general approach provides a feasible path toward a universal exchange-correlation functional with post-hybrid DFT accuracy and semilocal DFT cost.
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