LasttimeExcitedstates1. Absorption and emission model2. Methods for excited states3. Excited state geometry4.Solvatochromism
Last time 2 Excited states 1. Absorption and emission model 2. Methods for excited states 3. Excited state geometry 4. Solvatochromism
Contents1. Electron Correlation2. Configuration Interaction3. Size extensivity4. Perturbation methods5. Coupled-cluster methods6. Ab initio solution of the Schrodinger equation7. DFT8. Model chemistriesCramer,Chp7Jensen, Chp 4ForesmanandFrisch,Chp63
Contents 3 1. Electron Correlation 2. Configuration Interaction 3. Size extensivity 4. Perturbation methods 5. Coupled-cluster methods 6. Ab initio solution of the Schrödinger equation 7. DFT 8. Model chemistries Cramer, Chp 7 Jensen, Chp 4 Foresman and Frisch, Chp 6
Electronicenergycomponents. Total electronic energy can be partitioned;E = Et + Ene +E, + Ex +EcEt= kinetic energy of the electrons;ENE=Coulomb attraction energy between electrons and nuclei;E,=CoulombrepulsionenergybetweenelectronsEx= Exchange energy, a correction for the self-repulsions ofelectrons;Ec= Correlation energy between the motions of electrons withdifferent spins;Er, EnE, & E, are largest contributors to E;: Ex> Ec;C
Electronic energy components • Total electronic energy can be partitioned; E = ET + ENE +EJ + EX +EC ET = kinetic energy of the electrons; ENE = Coulomb attraction energy between electrons and nuclei; EJ = Coulomb repulsion energy between electrons EX = Exchange energy, a correction for the self-repulsions of electrons; EC = Correlation energy between the motions of electrons with different spins; • ET , ENE, & EJ are largest contributors to E; • EX > EC ; 4
Electron correlationenergyIn the Hartree-Fock approximation, each electron sees theaverage density of all of the other electrons;Two electronscannot be in the same placeat the sametime;Electrons must move two avoid each other, i.e. theirmotion must be correlated;For a given basis set, the difference between the exactenergy and the Hartree-Fock energy is the correlationenergy; ca 2o kcal/mol correlation energy per electron pair;Types of electron correlation;- Dynamical- Non-dynamical5
Electron correlation energy • In the Hartree-Fock approximation, each electron sees the average density of all of the other electrons; • Two electrons cannot be in the same place at the same time; • Electrons must move two avoid each other, i.e. their motion must be correlated; • For a given basis set, the difference between the exact energy and the Hartree-Fock energy is the correlation energy; • ca 20 kcal/mol correlation energy per electron pair; • Types of electron correlation; – Dynamical – Non-dynamical 5
Static correlationW_=N_(1sA-1sg) (1,2)- (1)师 (2)1=(1s (1)-1s())*(1s (2)-sp(2))(αβ-βα)-ls(1)ls.(2)-1sg(1)ls(2)+Is()s(2)+ 1s.()s (215A1SB（1,2)-(1(2)不(1sA(l)+ls(1)*(Is (2)+Is(2))(αβ-βα)= Is (1)ls (2)+ Isg (1)Isa (2)+ Is (1)Is (2)+ Is (1)sg (2)8ONV+=N,(1SA+1Sp)Covalent configuration lonic configuration6
Static correlation 6 Covalent configuration Ionic configuration