《量子化学》教学课件_苏州大学第八章 密度泛函理论简介课件.ppt

《量子化学》; 从20世纪60年代密度泛函理论（DFT）提出以来，并在局域密度近似下导出著名的Kohn-Sham方程以来，DFT已逐渐成为量子化学计算领域的强有力的工具。 ; 最近几年，密度泛函方法得到了广泛的应用，通常可以得到比HF方法更好的计算结果，但只需中等程度的价格，对于中型或大型分子体系，其计算成本远低于MP2法。;电子动能算符;两种状态的波函数不同，能量也有所差异。 ; 但是它在描述化学键时有些不足，而且没有相关能校正时不宜处理热化学问题。; Density functional theory (DFT) attempts to calculate and other ground-state molecular properties from the ground-state electron density ; In DFT, is called the external potential acting on electron i, since it is produced by charges external to the system of electrons.;(1) the external potential (except for an arbitrary additive constant) ; ; “For systems with a nondegenerate ground state, the ground-state electron probability density determines the ground-state wave function and energy, and other properties”。;Here,;is also written as;8.2 The Hohenberg-kohn variational theorem; Let satisfy that and . By the Hohenberg-Kohn theorem, determines the external potential and this in turn determines the wave function that corresponds to the density . ; Let us use the wave function as a trial variation function for the molecule with Hamiltonian . According to the variation theorem;Since the left hand side of this inequality can be rewritten as;8.3 The Kohn-Sham method; ;. ; Since the electrons do not interact with one another in the reference system, the Hamiltonian of the reference system is; The KS operator is the same as the HF operator except that the exchange operators in the HF operator are replaced by , which handles the effects of both exchange and electron correlation. ; Various approximate functionals are used in molecular DFT calculations. The functional is written as the sum of an exchange-energy functional and a correlation-energy functional