在原子尺度凝聚态体系的计算模拟中，薛定谔方程处理的是电子和原子核形成的多体系统。相对于电子结构量子层面算法的发展，人们对原子核的描述还经常停留在经典的层面。近年来，随着第一性原理路径积分分子动力学方法的发展，在对于这些体系的热力学性质的描述上人们已经可以严格地描述核量子效应。但对于与动力学相关的诸多性质的描述，绝大部分研究还停留在经典实际系统、量子简单模型、或半经典的力场体系。第一性原理分子动力学发展的历史告诉我们动力学方法只有与第一性原理电子结构计算结合（进而可描述化学键断裂）才能最大程度地发挥功效。这里我们计划将核量子效应的描述拓展至动力学行为研究的层面，侧重第一性原理电子结构与现有半经典动力学方法的结合，并应用到凝聚态体系中的诸如热导、质子传输、表面上的有机反应等模拟中，为真实体系第一性原理量子动力学的发展进行必要的铺垫。

In computer simulations of molecules and condensed matters, the many-body Schrodinger equation to be solved is composed by interacting electrons and nuclei. Compared with the state-of-the-art electronic structure methods which address the quantum mechanical nature of the interacting electrons rather well, in most theoretical simulations, the nuclei are still treated as classical point-like particles. Recent development of the first-principles path-integral molecular dynamics method allows the thermostat properties of molecules and condensedmatters to be rather accurately simulated at the quantum mechanical level. Concerning dynamical properties, however, the situation is far from being satisfactory: 1) some simulations stay at the purely classical level, 2) some uses quantum mechanics but the system is restricted to very few atoms or simple model, or 3) in some semi-classical simulations the system is large (to condensed matters) but force fields are used to describe the inter-atomic interactions. The.development of first-principles molecular dynamics in the last ~30 years tells us that the dynamics method needs first-principles electronic structures (so that the bond breaking processes can be described) to maximally exert its power. Here, we aim to investigate the influence of nuclear quantum effects on the dynamical properties of condensed matter, using a combination of first-principles electronic structure and semiclassical quantum dynamics methods. The phenomena to be studied include the thermal conductivity of 2D and 3D crystals, the proton diffusion in superionic ice, and surface reactions etc.. We hope this project can help to pave the way for fully quantum dynamics in condensed matter systems.