《分子电子结构》研究生课程教学资源（Electronic Structure of Molecules）7-PES

LasttimeBasis set1. Gaussian type orbitals2. Pople basis sets3.Dunning basis sets4.Basis set effect5.Pseudopotentials or EffectiveCorePotentials6. Population analysis2

Last time 2 Basis set 1. Gaussian type orbitals 2. Pople basis sets 3. Dunning basis sets 4. Basis set effect 5. Pseudopotentials or Effective Core Potentials 6. Population analysis

Contents1. Potential energy curves/surfaces2.Born-Oppenheimer Approximation3. Properties from energy derivatives4. Exploring PESs1. Rigid scan2. Relaxed scan3

Contents 3 1. Potential energy curves/surfaces 2. Born-Oppenheimer Approximation 3. Properties from energy derivatives 4. Exploring PESs 1. Rigid scan 2. Relaxed scan

Configurations,energylevels,andstablestatesofachairEseanormalpositionE2onthesideInclinedE,onthesupportEo1

Configurations, energy levels, and stable states of a chair on the support Potential energy of the chair Inclined on the side normal position 4

Potentialenergycurves(1-DpotentialenergysurfacesPotentialEnergy74pm0000RepulsiveAttractiveforcesforcesDissociationEnergyHarmonic-436kJ/molMorse-104kcal/molMoststablestatev-V(r) = De(1-exp[-a(r-r)2V=5DV=4D.V=3V=2V=1V=0InternuclearSeparation(r)5

Potential energy curves (1-D potential energy surfaces) 5 V(r) = De {1-exp[-a(r-re ) 2

Examples:potentialenergycurvesoftheX,moleculeexcitedstatesNattNa3703020H++H(1S)400006233200.6738+5s18H38+4p30266.9938+3d1629172.8952.2m2Zg13s+4s1425739.994'2H(1S)+H(n=2)S300002'z.122150103'ztbllT=10.5ns3s+3p16973.37EAE=4.5-12.5eV8A'Z200006132ub'll4H(IS)+H(IS)111/R210000a'z00.20.30.10.43s+3s6022.02r (nm)XzH2OLn1214161820222446108IntemuclearDistance (A)6Na2J.Chem.Phys.143,104304(2015)

Examples: potential energy curves of the X2 molecule excited states 6 H2 J. Chem. Phys. 143, 104304 (2015) Na2

TypicalpotentialenergycurvesMolecularinversioninammoniapianartransitiorstate20001466cm1500ReactinnCoordinat1365cmEnergyprofileor1000reactioncoordinatediagram507.cm500503cm90120150180210240270Ammoniaimproopertorsion angle (degrees)HaCH-CH3+BrBrS2 reaction of chloroethane with bromide ionReactionCo-ordinate

Typical potential energy curves 7 Molecular inversion in ammonia Energy profile or reaction coordinate diagram SN2 reaction of chloroethane with bromide ion

Multidimensionalpotentialenergysurfaces(PEs)PESforwatermoleculeusaddlepointglobalmaximumlocalmaximumlocalminimumglobalminimumlocal minimumq,=H-O-HBondAngle104.5°0.0958nmTeporwsigClacier2oMoeryiaCanval RideRrdbankheThuatrosMadp8

Multidimensional potential energy surfaces (PES) 8 PES for water molecule

ModelpotentialenergysurfaceSecondOrderSaddlePointTransitionStructureATransitionStructureBMinimumforProductAMinimumforProductB0-0.5Second Order。0.5SaddlePoint0Valley-Ridge0.5-0.5InflectionPointMinimumforReactant-1Abstract axis, Hypersurface (3N-6 dimensions); multiplestates (So,S...); multiple pathways linking minima9J.Comp.Chem.2003,24,1514

Model potential energy surface 9 Abstract axis, Hypersurface (3N-6 dimensions); multiple states (S0 ,S1.); multiple pathways linking minima J. Comp. Chem. 2003, 24, 1514

Born-OppenheimerapproximationThe PES arises as a natural consequence of the BOA (adiabatic approx.);This assumes that theelectronic distribution ofthe molecule adjustsquickly to any movement of the nuclei;Theelectronicwavefunction depends uponthenuclearpositions butnot upontheirvelocities;Wavefunctionofamoleculetobebrokenintoitselectronicandnuclear (vibrational, rotational)components;Itotal = Pelectronic X nuclearH(r,R)x(r,R) = Eex(r,R)The nuclear motion (e.g., rotation, vibration) sees a smeared outpotential fromthe speedyelectrons;[T +E(R)](R) =E(R)Allcomputations ofmolecularwavefunctionsforlargemoleculesmakeuseofit,andwithout itonlythelightestmolecule,H,,canbehandled;Exceptwhenpotentialenergysurfacesfordifferentstatesgettooclosetoeachotherorcross,theBOAisusuallyquitegood10

• The PES arises as a natural consequence of the BOA (adiabatic approx.); • This assumes that the electronic distribution of the molecule adjusts quickly to any movement of the nuclei; • The electronic wavefunction depends upon the nuclear positions but not upon their velocities; • Wavefunction of a molecule to be broken into its electronic and nuclear (vibrational, rotational) components; Born-Oppenheimer approximation 10 • All computations of molecular wavefunctions for large molecules make use of it, and without it only the lightest molecule, H2 , can be handled; • Except when potential energy surfaces for different states get too close to each other or cross, the BOA is usually quite good • The nuclear motion (e.g., rotation, vibration) sees a smeared out potential from the speedy electrons;

Nuclei can“travel"onthisPESNuclearmotioncouldbedescribedquantummechanically,e.g.smallamplitudemotionscorrespondtomolecularvibrationsor“tunneling"Expensiveandspecialized.ExtremelyShort-LivedReactionResonancesinCl+HD(V=1)->DCl+HduetoChemicalBondSoftening,Science,2015,347,60;Unimoleculardissociation dynamics of vibrationally activatedcH,CHooCriegeeintermediatesto0Hradicalproducts,NatureChemistry,2016,8,509;Large amplitude motions can lead to reactions can be described as classicalparticles rolling along thePES. Essence of classical ab initio moleculardynamics.EachpointonthePESisStatistical mechanicsconnectsthedynamicsasolutiontoelectronicSchrodingerequationof anindividualmoleculewiththebehaviorofmacroscopicsamplesSEECan focus on locating“critical points"alongPES,like stableminima("molecules")and(R)saddlepoints("transitionstates").Leastexpensiveandmostcommonincomputationalchemistry.11

• Nuclear motion could be described quantum mechanically, e.g. small amplitude motions correspond to molecular vibrations or “tunneling”. Expensive and specialized. • Extremely Short-Lived Reaction Resonances in Cl + HD (V = 1)→DCl + H due to Chemical Bond Softening, Science, 2015, 347, 60; • Unimolecular dissociation dynamics of vibrationally activated CH3CHOO Criegee intermediates to OH radical products, Nature Chemistry, 2016, 8, 509; • Large amplitude motions can lead to reactions can be described as classical particles rolling along the PES. Essence of classical ab initio molecular dynamics. Nuclei can “travel” on this PES 11 • Statistical mechanics connects the dynamics of an individual molecule with the behavior of macroscopic samples • Can focus on locating “critical points” along PES, like stable minima (“molecules”) and saddle points (“transition states”). Least expensive and most common in computational chemistry. Each point on the PES is a solution to electronic Schrodinger equation