材料性质全量子第一性原理模拟方法的发展及其在凝聚态物理中的应用

Theoretical description of material properties, according to the Born-Oppenheimer approximation, can be categorized into two main tasks: an accurate ab-initio description of the electronic structures and a proper treatment of the nuclei's movement on the corresponding potential energy surfaces (PESs). As one of the most powerful methods on fulfilling such tasks, standard ab-initio molecular dynamics (MD) normally addresses the electronic states well enough. The treatment of the nuclei's propagation, however, stays on the level of the classical approximation where only the thermal effects are included. It is well-known that for light elements like hydrogen, when the distance between the two classical PES minima of one nucleus is short enough to be comparable to the nuclear de Broglie wavelength, the quantum nuclear effects (QNEs) can be really important. As a prominent example, replacing H by D in water, one of the most ubiquitous matters on earth, basic properties like the melting and boiling points can be significantly changed. Properly describing phenomena like these requires a fully quantum treatment of both the electrons and the nuclei. In this project, we aim to provide such a tool by combining the path-integral molecular dynamics (PIMD) method with one of the best all-electron ab-initio electronic structure calculation packages, FHI-aims. Our research can be categorized into two parts. First, we will use the well-established ab-initio PIMD method to study the thermostatic properties of some materials, where an ab-initio treatment of the electronic structures is essential. The phase diagram of hydrogen under mega-bar pressure is one of such examples. This phase diagram of the simplest element poses one of the biggest challenges in condensed matter physics calculations in the last more than half a century. Since the FHI-aims package allows different choices for the calculation of the electronic states and the PIMD method gives a proper description of the QNEs, our developed method will provide an accurate description for the thermostatic property of this material. Besides this, beyond the standard ab-initio PIMD method, we also plan to implement the adiabatic centroid molecular dynamics (adiabatic CMD) and the ring-polymer molecular dynamics (RPMD) methods in the same code. These two methods allow the real-time propagation of the nuclei to be accurately addressed with QNEs included. When combined with ab-initio electronic structures, such an extension allows dynamic quantities of many real systems to be calculated. Other fundamental problems in condensed matter physics to be studied include, i.e. the calculation of the nuclear zero-point energy and the impact of QNEs on liquid water structures. In summary, this project will i) provide a powerful tool on a fully quantum description of both the thermostatic and dynamic properties of real materials, and ii) answer some fundamental questions in condensed matter physics.

材料性质的模拟，依据玻恩-奥本海默近似，可归结为电子结构的计算和原子核运动的描述两个层面的内容，其目的是准确重复实际系统在所有自由度的进动。目前国际上非常盛行的一个方法是基于第一性原理电子结构计算的分子动力学。该方法中，电子系统的第一性原理计算保证了电子结构的质量，而对原子核的经典近似，却令其在对与核量子效应相关的性质描述中（如氢键的同位素依赖性、生物分子中的质子输运等），完全丧失了功能。材料性质的全量子模拟（含核量子效应），也因此成为近年来计算物理方法发展的一个前沿。本研究项目计划使用路径积分方法发展一个基于第一性原理电子结构计算的全量子模拟程序，实现对实际材料核量子效应的准确模拟。与方法的发展相结合，我们也将对高压下氢相图、真实系统零点能计算、质子传输、核量子效应对水及其溶液结构的影响等物理问题进行准确、系统的描述。在发展一个强大的材料性质全量子模拟工具的同时，解决一些基本的物理问题。

材料性质的模拟，依据玻恩-奥本海默近似，可基本归结为电子结构的计算和原子核运动的描述两个层面的内容。它的目标是准确重复实际系统在所有自由度的进动。就这个目标而言，基于第一性原理电子结构计算的分子动力学是目前最为通行的一个方法。在该方法中，电子系统的第一性原理计算保证了电子结构的质量，但对原子核的经典近似却令其在对与核量子效应相关的性质描述中完全丧失了功能。材料性质的全量子模拟（含核量子效应）也因此成为近年来计算物理方法发展的一个前沿。..在该项目中，我们针对这个前沿问题，基于第一性原理路径积分分子动力学，发展了一系列用于分子与凝聚态体系性质全量子模拟的程序与方法。这些方法包括：第一性原理路径积分分子动力学，第一性原理的路径积分分子动力学模拟与中心固定增强取样方法的结合，以及第一性原理的路径积分分子动力学模拟与热力学积分方法的结合。它们的实现主要依赖于FHI-aims与VASP两个软件包。在过去的四年中，基于这些我们自主开发的计算方法，我们系统的研究了凝聚态物理、表面科学、高压物理中的多个问题。其中，对氢相图与锂相图的研究系统揭示了轻元素核量子效应对其高压下相图的影响。对固体表面水的成像、成核、协同量子隧穿效应、氢键中核量子效应的研究系统揭示了氢的核量子效应对类似体系结构、动力学性质的影响。..基于这些工作，本项目发表学术论文十一篇，含Science、Nature Physics、Nature Materials各一篇，Nature Communications两篇。我们认为这个项目在发展一个强大的材料性质全量子模拟工具的同时，解决了一些凝聚态物理与表面物理中的问题，较为完满地完成了既定目标。