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1、计算化学基本原理,haidiUSTC,“Computational chemistry simulates chemical structures and reactions numerically, based in full or in part on the fundamental laws of physics.”In Exploring Chemistry with Electronic Structure Methods, 1996,一、 计算化学的发展,理论发展：,1998年10月13日下午3时正，瑞典皇家科学院正式公布了1998年度诺贝尔化学奖获得者名单，美国的奥地利裔科学家瓦
2、尔特科恩（Walter Kohn）教授和英国的约翰波普（John Pople）教授分享了总额为97万美元的奖金。,Gaussian,计算机硬件发展：,不同计算方法的时间标度 ： CI N6 HF N4 DFT N3 MD N2,相关硬件：CPU （部分GPU）内存容量 （高达256GB）磁盘转速 （7200 rpm , 15000 rpm）IB网络卡 （节点数据交换）,二、 计算化学方法,Hatree-Fock & 后 Hartree-Fock 方法 基于复杂的电子波函数，波函数有 3N 个变量（N 为电子数，每个电子包含三个空间分量） Gaussian , Nwchem, Psi4, Gam
3、ess DFT 方法： 基于电子密度， 电荷密度仅是3个变量的函数 VASP, Siesta, CASTEP, Abinit, Crystal, Quantum EspressoMD 方法 基于经验和试验参数等 Gromacs, CPMD , Lammps,底层,高层,CalypsoUSPEX,只需要指定成分，化学计量比,三、 密度泛函理论的应用以及意义,1.材料力学性质模拟,E : 实验观察值,https:/en.wikipedia.org/wiki/Carbon_nanotube,2.材料超导性质计算,http:/arxiv.org/abs/1412.0460v1 Conventional
4、 superconductivity at 190 K at high pressures,3. 光解水材料,Ref: Origin of High Photocatalytic Properties in the Mixed-Phase TiO2:A First-Principles Theoretical Study,金红石(rutile) 和锐钛矿 (anatase),4. 低维纳米材料（0D, 1D, 2D ）,J. Am. Chem. Soc.,2013,135(40), pp 1519115200,Graphene,ACS Nano,2014,8(4), pp 40334041,P
5、hosphorene,Nano Lett.,2014,14(8), pp 49014906,5. 缺陷和原子吸附,Ref: Density Functional Theory Study of Metal Adatoms at or Near a Stone-wales Defect in Graphene,四、 密度泛函基本理论,F = m a,1. Kohn-Sham 方程,微观原子尺度： 电子-原子核 （简单库伦排斥）,量子力学 ,可解系统： - 两粒子体系（分析结果） - 粒子数目较少的体系（数值结果） - 谐振子（分析结果） 实际体系： 电子和核数目 mol 级别，1023,Au 原
6、子质量: 196.966569 2001kg Au原子数目 ,黑盒处理,Use a set of “accepted” approximations to solve the corresponding equations on a computer,NO EMPIRICAL INPUT,Chemical compositionNumber of atomsTypePosition,PropertiesEquilibrium structureBand structureVibrational spectrumMagnetic propertiesTransport properties,ID
7、EAL AB-INITIO CALCULATION,Born-Oppenheimer 近似,Nuclei are much slower than electrons,Electron/nuclei decoupling,Classical =,密度泛函理论,2. 非相互作用电子处于有效势场中,粒子密度,1.,定理1：所有可观测量都是密度的唯一泛函定理2：总能量对密度变分的极小就是总能量对波函数的变分极小，是体系的基态,关于DFT的两个定理 (Hohenbergand Kohn theorems ),自洽迭代,交换关联泛函,LDA,GGA,GGA,杂化泛函,Expand in terms of
8、 a finite set of known wave-functions,HCn=nSCn,基组,Treatment of the boundary conditions,3D periodic objects (crystals)periodic boundary conditions(might be considered as the repetition of a building block, the unit cell),Isolated objects (atoms, molecules, clusters)open boundary conditions(defined at
9、 infinity),Mixed boundary conditions 1D periodic (chains)2D periodic (slabs and interfaces),PBC,PBC,In a periodic solid: Number of atoms Number and electrons Number of wave functions ?,Bloch theorem will rescue us!,2. Wave function will be extended over the entire solid (),Reciprocal lattice,Real sp
10、ace Reciprocal space,A*B,VASP正格矢和倒格矢,A periodic potential commensurate with the lattice. The Bloch theorem,Bloch Theorem: The eigenstates of the one-electron Hamiltonian in a periodic potential can be chosen to have the form of a plane wave times a function with the periodicity of the Bravais lattice.,Brillouin Zone,It is possible to represent electronic wave functions over a region of k-space by the wave function at a single k-point.,Compute sets of spetial k-points,Monkhorst-Pack (1976),Kohn-Sham Equation,H,Thank your for you attention !,
