幻灯片2LasttimeCourse overviewModelA1.What is a model?2.Nature?3.Attitudeto use4.Howto evaluate?2Electronicstructurecalculation1.Whatiselectronicstructure calculation?2.Challenges3.Askrelevantquestions4.Advantages vs.disadvantages5.Status quo6.Environment7.ResourcesGaussian16andGaussview63.我们先来回顾一下上次课程的主要内容。1、模型与模拟信息简化和损失-》模型：模型是能够自动将输入转换为输出的“黑匣子”模型的关键是确定描述因子，建立描述因子与所关心性质间的关系，即机理、算法；模型好坏的评价；模型不能滥用；2、计算化学的根本问题预测化学反应要求的化学精度（1kcal/mol）：基团的性质无法迁移，因为性质的叠加会带来巨大的误差，远超化学精度；【还是有人在这条路上尝试，divideandconquer;QM/MM;FragmentMolecularOrbital Method 总能量（Etotal）计算准确（万分之一或者更高），但是反应看能量变化（△E），其精度就很难达到化学精度；计算资源消耗随所计算体系的大小的增加呈指数增加，对于HF或者DFT至少N^3。3、介绍了高斯和GV。安装是否有问题？
幻灯片 2 Course overview 1. Model 1. What is a model? 2. Nature? 3. Attitude to use 4. How to evaluate? 2. Electronic structure calculation 1. What is electronic structure calculation? 2. Challenges 3. Ask relevant questions 4. Advantages vs. disadvantages 5. Status quo 6. Environment 7. Resources 3. Gaussian 16 and Gaussview 6 Last time 2 我们先来回顾一下上次课程的主要内容。 1、模型与模拟 信息简化和损失-》模型； 模型是能够自动将输入转换为输出的“黑匣子” ； 模型的关键是确定描述因子，建立描述因子与所关心性质间的关系，即机理、 算法； 模型好坏的评价； 模型不能滥用； 2、计算化学的根本问题 预测化学反应要求的化学精度（1kcal/mol）； 基团的性质无法迁移，因为性质的叠加会带来巨大的误差，远超化学精度；【还 是有人在这条路上尝试，divide and conquer; QM/MM; Fragment Molecular Orbital Method 】 总能量（Etotal）计算准确（万分之一或者更高），但是反应看能量变化（ΔE）， 其精度就很难达到化学精度； 计算资源消耗随所计算体系的大小的增加呈指数增加，对于HF或者DFT至少 N^3。 3、介绍了高斯和GV。安装是否有问题？
幻灯片3Computational chemistrytryTheoryQuantummechanicClassicalmechanicsAccuracyHighLowStationaryQuantummecics(QM)Molecularmecchanics (MM)stateElectronicstructurecalculationNewtonianahinitiomoleculardvnamicMolecular dynamics (MD)mechanics(AIMD)/first-principlesMDSystemsizeSmallLargeMolecular (intramolecular)Macroscopic (intermolecular)PropertiesHybridsQM/MMReaxFF (QM-basedforcefield+ MD)Semi-empiricalmethodsCoarse-grained methods (e.g-SimplificationDensityfunctional-basedtightDPD)bindinemethodElectronicstructurecalculationInabiggerpicture.上节课更重要的是给出了计算化学的大体分类，如表。名称：电子结构计算、量子化学；分子模拟对于【稳态stationarystate/staticstate】可以采用QM或者MM方法处理。基于解不含时的薛定方程的QM的方法，即【电子结构计算】，主要是处理稳态（包括过渡态），也叫【量子化学QC】，这是本课程主要讲述的范围。【分子力学】也可以处理稳态，但不能处理过渡态。分子力学后面是力场(forcefield)如果对原子核的运动，采用牛顿力学描述，包含时间，QM方法变为AIMDQM/MM还是静力学，处理稳态；ReactiveFF反应力场，处理反应。DPDdissipativeparticledynamics耗散粒子动力学
幻灯片 3 Computational chemistry 3 Molecular simulation/ molecular modelling Electronic structure calculation/quantum chemistry Name Theory Quantummechanics Classical mechanics Accuracy High Low Quantum mechanics (QM)/ Molecular mechanics (MM) Electronic structure calculation Stationary state ab initio molecular dynamics Molecular dynamics (MD) (AIMD)/ first-principles MD Newtonian mechanics System size Small Large Properties Molecular (intramolecular) Macroscopic (intermolecular) ReaxFF (QM-based force field + MD) Hybrids QM/MM Coarse-grained methods (e.g. DPD) Semi-empirical methods; Density functional-based tight binding methods Simplification Electronic structure calculation In a bigger picture. 上节课更重要的是给出了计算 化学的大体分类，如表。 名称：电子结构计算、量子化学；分子模拟 对于【稳态stationary state/static state】可以采用QM或者MM方法处理。 基于解不含时的薛定谔方程的QM的方法，即【电子结构计算】，主要是处理稳 态（包括过渡态），也叫【量子化学QC】，这是本课程主要讲述的范围。 【分子力学】也可以处理稳态，但不能处理过渡态。分子力学后面是力场 （force field） 如果对原子核的运动，采用牛顿力学描述，包含时间，QM方法变为AIMD QM/MM还是静力学，处理稳态；Reactive FF反应力场，处理反应。 DPD dissipative particle dynamics耗散粒子动力学
幻灯片4ContentsBrief review of quantummechanics1.1.Describe wave properties of anelectron;2.Quantum free particle model and its various derivatives;本课内容1、电子的波动性，粒子在势阱中的模型和其变种2、继续学习高斯，计算单点能
幻灯片 4 Contents 4 1. Brief review of quantum mechanics 1. Describe wave properties of an electron; 2. Quantum free particle model and its various derivatives; 本课内容 1、电子的波动性，粒子在势阱中的模型和其变种 2、继续学习高斯，计算单点能
幻灯片5Matterwave:wave-particle dualityE=hyhe-For a photon:E=mc2p=mcPlanck's constalde Broglie Wavelength (1924)h=6.626×10-34ls77278The pilot-wave modelCarFoat10009.1×10-31m (kg)100km/hr0.0102.7 × 10-24p (kg m/s)2.8 ×1042.4 × 10-382.4 × 10-10[入 (m)Too small to detect.Comparableto sizeof atomRemarkClassical object!Must accountforwavepropertiesof an electron!eneDiffraction Nature1999,401,680FlPhthalocvalaninederivatives (CaaH2sF2aNgOg)shNanotechnology2012,Z.29Z.物质波，波粒二象性Louis-VictordeBroglie德布罗意公爵，Langevin的学生，其工作直接引发薛定调方程。还提出了几个重要的思想（wavepacket），有兴趣的同学可以看看他的传记。其对波动方程的解释不同于主流的哥本哈根解释即Born几率解释，他提出了thepilot-wave model, de Broglie-Bohm theory, and the causal interpretation of quantummechanics，(https://plato.stanford.edu/entries/gm-bohm/)。可能对现在研究热门的量子纠缠的理解有帮助。"It is the simplest exampleof what isoftencalleda hidden variables interpretation ofquantummechanics.InBohmianmechanicsasystemofparticlesisdescribedinpartby its wavefunction,evolving,as usual, according to Schrodinger's equation.However,thewavefunctionprovidesonlyapartial descriptionofthesystem.Thisdescriptioniscompletedbythespecificationoftheactualpositionsoftheparticles.Thelatterevolveaccordingtothe“guidingequation",whichexpressesthevelocitiesof the particles in terms of the wavefunction.Thus, in Bohmian mechanics theconfigurationofa system of particles evolves via a deterministicmotionchoreographed by thewave function. In particular, when a particle is sent intoa two-slit apparatus, the slit through which it passes and its location upon arrival on thephotographicplatearecompletelydeterminedbyitsinitial positionandwavefunction."1、其工作受到Planck和Einstein的影响【创新来自新思想的组合！】v=nu。2、宏观物体和微观粒子的主要差异是质量，大概10^34，速度差异宏观物体慢10^5，差异最终由质量主导，约为10^283，最大显示衍射和干涉性质（diffractionandinterfere）的分子weshowhowa
幻灯片 5 Matter wave: wave-particle duality de Broglie Wavelength (1924) Planck's constant For a photon: Car Electron 9.1 ×10−31 m (kg) 1000 v 100 km/hr 0.01 C 2.7 ×10−24 2.8 ×104 p (kg m/s) 2.4 ×10−10 2.4 ×10−38 λ (m) Comparable to size of atom. Must account for wave properties of an electron! Too small to detect. Classical object! Remark 5 The pilot-wave model Phthalocyanine derivatives (C48H26F24N8O8 ) show quantum interference, Nature Nanotechnology 2012, 7, 297. Fullerene Diffraction Nature 1999, 401, 680. 物质波，波粒二象性 Louis-Victor de Broglie 德布罗意公爵，Langevin的学生，其工作直接引发薛定谔 方程。 还提出了几个重要的思想（wave packet），有兴趣的同学可以看看他的传记。其 对波动方程的解释不同于主流的哥本哈根解释即Born几率解释，他提出了 the pilot-wave model, de Broglie-Bohm theory, and the causal interpretation of quantum mechanics, (https://plato.stanford.edu/entries/qm-bohm/)。可能对现在研究热门 的量子纠缠的理解有帮助。 “It is the simplest example of what is often called a hidden variables interpretation of quantum mechanics. In Bohmian mechanics a system of particles is described in part by its wave function, evolving, as usual, according to Schrödinger’s equation. However, the wave function provides only a partial description of the system. This description is completed by the specification of the actual positions of the particles. The latter evolve according to the “guiding equation”, which expresses the velocities of the particles in terms of the wave function. Thus, in Bohmian mechanics the configuration of a system of particles evolves via a deterministic motion choreographed by the wave function. In particular, when a particle is sent into a twoslit apparatus, the slit through which it passes and its location upon arrival on the photographic plate are completely determined by its initial position and wave function.” 1、其工作受到Planck和Einstein的影响【创新来自新思想的组合！】ν = nu。 2、宏观物体和微观粒子的主要差异是质量，大概10^34，速度差异宏观物体慢 10^5，差异最终由质量主导，约为10^28 3，最大显示衍射和干涉性质（diffraction and interfere）的分子 we show how a
combination of nanofabrication and nano-imaging allows us to record the full two-dimensional build-up of quantum interference patterns in real time forphthalocyanine（酞菁https://pubchem.ncbi.nlm.nih.gov/compound/phthalocyanine#section=3D-Conformer))moleculesandforderivativesofphthalocyaninemolecules,whichhave masses of514AMUand1,298AMUrespectively.4，思考问题：时间与空间是否是连续的还是有最小单位？
combination of nanofabrication and nano-imaging allows us to record the full twodimensional build-up of quantum interference patterns in real time for phthalocyanine （酞菁 https://pubchem.ncbi.nlm.nih.gov/compound/phthalocyanine#section=3DConformer） molecules and for derivatives of phthalocyanine molecules, which have masses of 514 AMU and 1,298 AMUrespectively. 4，思考问题：时间与空间是否是连续的还是有最小单位？