DFT理论及石墨烯体系的第一性原理研究--宏剑培训.ppt

密度泛函理论新进展及应用 杨金龙 中国科学技术大学 内容 密度泛函理论新进展 石墨烯条带体系的第一性原理计算研究 密度泛函理论新进展 理论体系 交换相关泛函、含时密度泛函、动力学平均场、密度泛函微扰理论 数值方法 基组、格点、线性标度 应用 物理、化学、生物、材料、纳米科学、光谱学 Part I: 理论体系 LDA underestimates Ec but overestimates Ex, resulting in unexpectedly good values of Exc. The LDA has been applied in, calculations of band structures and total energies in solid-state physics. In quantum chemistry,it is much less popular, because it fails to provide results that are accurate enough to permit a quantitative discussion of the chemical bond in molecules. Any real system is spatially inhomogeneous, it has a spatially varying density n(r), it would clearly be useful to also include information on the rate of this variation in the functional. In this approximation ,one tries to systematically calculate gradient-corrections of general functions of n(r) and ?n(r) Different GGAs differ in the choice of the function f(n,?n). GGAs used in quantum chemistry typically proceed by fitting parameters to test sets of selected molecules. Nowadays the most popular GGAs are PBE in physics, and BLYP in chemistry. Current GGAs seem to give reliable results for all main types of chemical bonds (covalent, ionic, metallic and hydrogen bridge). In addition to the density and its derivatives, Meta-GGAs depend also on the Kohn-Sham kinetic-energy density: So that Exc can be written as Exc [n(r),?n(r), τ (r)]. The additional degree of freedom provided by τ is used to satisfy additional constraints on Exc. Meta-GGAs have given favorable results, even when compared to the best GGAs. The full potential of this type of approximation is only beginning to be explored systematically. Common hybrid functional mix a fraction of Hartree-Fock exchange into the DFT exchange functional. L(S)DA+U Mott绝缘体，Hubbard模型 Anisimov et al.： Stoner I --Hubbard U 轨道序： Dudarev et al.：惩罚泛函 Part II:数值方法 数值离散方法 基组展开 LCAO基组（Gaussian基组、数值基组） 实空间网格 平面波基组：从OPW到PP 平面波展开 正交化平面波（OPW） 赝势（PP）方法 经验赝势 模守恒赝势 超软赝势 Muffin-tin势场与分波方法 Muffin-tin势