Coupling Continuum and Density Functional Theories for Materials Modeling

本研究涉及材料系统建模的改进方法。许多材料建模问题严重依赖于量子力学模型。然而，为了让量子力学真正有用，我们必须将它与连续统模型或分子力学模型结合起来。这种方法的成功已经在化学应用中得到了很好的证明。本项目探索基于量子力学（密度泛函理论）与分子力学或连续介质力学相结合的材料建模方法。尽管量子力学/分子力学耦合方法取得了相当大的成功，获得了2013年诺贝尔化学奖，但其在一般材料体系，特别是金属体系中的应用，长期以来一直存在争议。这个问题来自于分子力学和量子力学界面处误差的非局域效应。这个问题对金属系统来说尤其严重。该项目解决了材料系统建模中的这些重要挑战。有许多技术障碍需要克服。首先，人们需要提高密度泛函理论（DFT）算法的效率，以能够处理非齐次系统，例如具有点缺陷或一小部分扩展缺陷的系统。下一个障碍是基于分子力学或连续介质理论推导出与DFT一致的经典模型。这意味着DFT模型在一定限度内简化为经典模型。第三个问题是设计从DFT平滑地移动到经典模型的耦合方案。目前的项目将侧重于第二个和第三个问题，从一维模型问题开始。研究的起点是DFT的费米算符公式。通过对费米算符的形式进行连续逼近，PI的目标是达到一致的DFT/分子力学或DFT/连续体模型耦合方案。

This research concerns improved methods for the modeling of material systems. Many materials modeling problems rely heavily on quantum mechanical models. However, for quantum mechanics to be really useful, one has to couple it with either continuum models or molecular mechanics models. The success of such an approach has been well documented in chemistry applications. This project explores approaches based on quantum mechanics (density functional theory) coupled with molecular mechanics or continuum mechanics in modeling materials. Although the coupled quantum mechanics/molecular mechanics approach has enjoyed a considerable amount of success, winning the 2013 Nobel Prize in chemistry, its application to general material systems, particularly metallic systems, has been at issue for a long time. The problem comes from the non-local effect of the errors made at the interface between the molecular mechanics and quantum mechanics regions. This problem is particularly severe for metallic systems. This project tackles these important challenges in the modeling of material systems.There are many technical hurdles that one needs to overcome. First of all, one needs to improve the efficiency of density functional theory (DFT) algorithms to be able to handle inhomogeneous systems, such as systems with point defects or a small portion of extended defects. The next hurdle is to derive classical models, based on either molecular mechanics or continuum theory, that are consistent with DFT. This means that the DFT models reduce to classical models in some limit. A third problem is to design coupling schemes that move smoothly from DFT to classical models. The current project will focus on the second and third problems, beginning with one-dimensional model problems. The investigation's starting point is the Fermi operator formulation of DFT. By making successive approximations on the Fermi operator formalism, the PI aim to arrive at a consistent DFT/molecular mechanics or DFT/continuum model coupling scheme.