LasttimeCourse overview1. Model1.What is a model?2.Nature?3.Attitude to use4.How to evaluate?2.Electronic structurecalculation1.Whatiselectronic structurecalculation?2.Challenges3.Askrelevantquestions4.Advantagesvs.disadvantages5.Status quo6.Environment7.Resources3.Gaussian16andGaussview62
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
Computational chemistryNameElectronic structureMolecular simulationcalculation/quantum chemistrymolecularmodellingTheoryQuantummechanicsClassical mechanicsHighLowAccuracyStationaryQuantummechanics(QM)/Molecularmechanics (MM)stateElectronic structure calculationNewtonianab initiomoleculardynamicsMoleculardynamics (MD)mechanics(AIMD)/first-principlesMDSmallSystemsizeLargePropertiesMacroscopic(intermolecular)Molecular (intramolecular)HybridsQM/MMReaxFF(QM-basedforcefield+ MD)SimplificationCoarse-grained methods (e.g.Semi-empiricalmethodsDPD)Densityfunctional-basedtightbinding methods3
Computational chemistry 3 Name Electronic structure calculation/quantum chemistry Molecular simulation/ molecular modelling Theory Quantum mechanics Classical mechanics Accuracy High Low Stationary state Quantum mechanics (QM)/ Electronic structure calculation Molecular mechanics (MM) Newtonian mechanics ab initio molecular dynamics (AIMD)/ first-principles MD Molecular dynamics (MD) System size Small Large Properties Molecular (intramolecular) Macroscopic (intermolecular) Hybrids QM/MM ReaxFF (QM-based force field + MD) Simplification Semi-empirical methods; Density functional-based tight binding methods Coarse-grained methods (e.g. DPD)
Contents1.Brief review of quantum mechanics1. Describe wave properties ofanelectron;2. Quantum free particle model and its various derivatives;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;
Matterwave:wave-particledualityhcE=hvc = AvFor a photon:E:=pc-E=mc2p= mcPlanck's constanthhde Broglie Wavelength (1924)h = 6.626 × 10-34 Js1pmvThe pilot-wave modelCarElectron9.1 X 10-31m (kg)1000v100 km/hr0.01 C2.7 X 10-242.8 X 104p (kg m/s)2.4 X 10-102.4 X 10-38入 (m)RemarkToo small to detect.Comparabletosizeofatom.Classical object!Mustaccountforwaveproperties ofan electron!FullereneDiffractionNature1999,401,680Phthalocyanine derivatives (C4gH26F24NgOg) show quantum interference, NatureNanotechnology 2012,Z, 2975
Matter wave: wave-particle duality de Broglie Wavelength (1924) Planck's constant For a photon: Car Electron m (kg) 1000 9.1 × 10−31 v 100 km/hr 0.01 C p (kg m/s) 2.8 × 104 2.7 × 10−24 λ (m) 2.4 × 10−38 2.4 × 10−10 Remark Too small to detect. Classical object! Comparable to size of atom. Must account for wave properties of an electron! 5 𝐸 = ℎ𝜈 𝐸 = 𝑚𝑐 2 𝑐 = 𝜆𝜈 𝑝 = 𝑚𝑐 𝐸 = ℎ𝑐 𝜆 = 𝑝𝑐 λ = ℎ 𝑝 = ℎ 𝑚𝑣 ℎ = 6.626 × 10−34 Js The pilot-wave model Phthalocyanine derivatives (C48H26F24N8O8 ) show quantum interference, Nature Nanotechnology 2012, 7, 297. Fullerene Diffraction Nature 1999, 401, 680
DescribewavepropertiesofanelectronWhat Is Life?Schrodingerequation(1926)a=HUY not a physical observable!访Expressedasdifferentialeguation:at记-v?y(r,t)+V(r,t) Y(r,t)Single particle, non-relativistic:2matSteady-state,ortime-independentV(r)allowstheseparation-y(r)+V(r)y(r)= Ey(r)of variablesrandT2mKinetic energy+Potential energy=Total EnergyQuantumharmonicoscillatorotoAstationarystateisnotmathematicallyconstantY(r,t)=y(r)e"%pTheprobabilitythattheparticleisat locationxisindependentoftime(r,t)2 =e-at/h(r,0)2 = e-it/(r,0)2 =(a,0)vp6
= Describe wave properties of an electron Schrödinger equation (1926) Expressed as differential equation: Kinetic energy + Potential energy = Total Energy Steady-state, or time-independent: V(r) allows the separation of variables r and T Single particle, non-relativistic: A stationary state is not mathematically constant The probability that the particle is at location x is independent of time Quantum harmonic oscillator 6 What Is Life? Ψ not a physical observable!