计算学简介重点分析.ppt

一、多体情况下的Shr?dinger方程 物理模型： 材料中电子和原子核均在运动中 粒子间存在着相互作用 二、多体物理模型的三个基本近似 ⒈ 非相对论近似： 外层电子的运动速度较低， 可以忽略相对论效应，? i = ? 0 变分原理 三、化学键与 LCAO – MO 近似 颁奖公告称：The development did not really started until the beginning of the 1960s, when two events became decisive: Walter Kohn’s Contributions Walter Kohn’s theoretical work has formed the basis for simp-lifying the mathematics in descriptions of the bonding of atoms, the density-functional theory (DFT). The simplicity of the method makes it possible to study very large molecules. John Pople’s Contributions John Pople has developed quantum chemistry into a tool that can be used by the general chemist and has thereby brought chemistry into a new era where experiment and theory can work together in the exploration of the properties of molecular systems. Chemistry is no longer a purely experimental science. 计算软件 GAUSSIAN CRYSTAL CASTEP SIESTA VASP … … Walter Kohn showed that it is not necessary to consider the motion of each individual electron: it suffices to know the average number of electrons located at any one point in space. 1964年，理论证明多电子体系的基态能量是电子密度的单变量函数 1965年，运用变分原理导出 Kohn-Sham 自洽场方程 ( DFT的基础方程 ) DFT法用于分子的成功是众多科学家多年不懈努力的结果，但首先归功于理论奠基人Kohn “It has taken more than thirty years for a large number of researchers to render these calculations practicable, and the method (DFT) is now one of the most widely used in quantum chemistry.” 为寻找复杂体系波函数{??}的合理形式，将分子轨道表示为原子轨道{?i}的线性组合 优点：利于建立化学键理论的电子结构基础 Molecular Obital expressed as a Linear Combination of Atomic Orbitals 量子力学在原子分子层次上揭示材料问题的本质。材料制备过程是伴随着反应体系原子的重排而发生的电子运动状态的改变，这些微观运动均服从薛定谔方程。 量子力学理论使化学与物理学在原子分子水平上会师，两学科的界限趋于模糊，都是材料科学的基础。 量子力学奠基人之一 Dirac 在 1929说: The fundamental laws necessary for the mathematical treatment of large parts of physics and the whole of chemistry are thus fully known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved. 1952年H. Schull等三人用手摇计算机花两年才完成一个N2分子的从头算 (ab