重正化二阶微扰理论的发展和在凝聚态物理中的应用

Developing generally applicable, highly accurate first-principles electron-structure methods is an essential task in physics, chemistry, and materials science. During the past decades, density functional theory (DFT) within local and/or semi-local approximations (LDA/GGAs) has been the most popular first-principles electronic-structure methods, thanks to its excellent balance between accuracy and computational cost. However, due to the intrinsic deficiencies of LDA/GGAs, as well as the ever-increasing need for better accuracy and reliability, there has been continuing efforts to develop more accurate and generally applicable methods and/or computational schemes. By combining DFT and many-body perturbation theory, we developed and implemented the so-called renormalized second-order perturbation theory (rPT2). Benchmark tests for various molecular systems indicate this method is accurate for covalent interactions, van der Waals interactions, and chemical reaction barrier heights. In the current project, we plan to carry out the following researches: 1) developing more efficient algorithm and computer code so that rPT2 can be applied to bigger and more complex systems; 2) applying rPT2 to challenging problems in condensed matter systems; 3) identify and fix the remaining possible shortcomings of rPT2 that could be exposed in this study. Our long-term goal is to develop a highly accurate and efficient electronic structure method and the corresponding computer code that can be applied to both molecular and condensed-matter systems.

基于第一性原理的电子结构方法在现代物理学，化学，和材料科学中都具有重要意义。密度泛函理论在局域或半局域近似下可以达成良好的精度与计算量的性价比，因而在过去数十年的电子结构计算中获得了广泛应用。然而，由于局域和半局域近似固有的缺陷，也由于现代科学研究中对于更高精度和可靠性计算的需求，有必要发展更为精准可靠，适用性更为广泛的第一性原理方法。有鉴于此，我们通过对密度泛函理论和多体微扰理论的结合，发展和实现了重正化二阶微扰理论。在各类分子系统中的基准测试表明该理论可以同时较精确地地描述共价键，范德华力，和化学反应势垒。在本项目中，我们拟在如下几方面开展研究：1)改良算法和程序，提高理论的效率和可计算系统的尺寸；2）在此基础上，将该理论应用于凝聚态物理系统中的疑难问题；3）对目前的理论方案在实际计算中暴露出的不足进行修正。我们的目标是发展一套对于分子物理和凝聚态物理普遍适用的精确高效的电子结构方法。

在本项目中，我们在全电子从头计算软件包FHI-aims中实现了周期性重正化二阶微扰理论（rPT2)，这为克服传统密度泛函理论方法在特定凝聚态物理和材料体系中局限性提供了一个尝试性的解决方案。其中，该理论的无规相近似（RPA）部分经过充分的效率优化和稳定性测试，实现了高度并行化，单独使用时，可程序化应用于百原子量级体系的计算。目前FHI-aims中的RPA模块可用于描述块体材料、二维范德华异质结、分子表面吸附、固体中的点缺陷等多种计算物理、化学、以及材料科学中感兴趣的体系。我们目前正在对完整的rPT2程序进行优化和测试。我们预料，RPA及其拓展方案rPT2，在不远的将来，将在物理和材料科学中多种体系的计算中发挥重要作用，对这些学科领域发展产生积极的影响。