LasttimeA brief review of quantum mechanics1= h/=h.deBroglie Wavelength:/p-/mStationarystate/steady-stateY(r.t)=y(r)e-%-time-independent stateAllowed wavefunctions-single-valued, continuous, piecewise continuous firstderivatives, nowhere infinite, square-integrableParticle on a ring. e.g. benzene π orbitals, C ringsParticle in a box (infinite square well, 1D, 2D, 3D): 1D (metal chains); 3D (quantum dot)Particle in a potential: Connect all modelsPostulates of non-relativisticquantum mechanics2
A brief review of quantum mechanics • de Broglie Wavelength: • Stationary state/steady-state – time-independent state • Allowed wavefunctions – single-valued, continuous, piecewise continuous first derivatives, nowhere infinite, square-integrable • Particle on a ring • e.g. benzene π orbitals, C rings • Particle in a box (infinite square well, 1D, 2D, 3D) • 1D (metal chains) ; 3D (quantum dot) • Particle in a potential • Connect all models • Postulates of non-relativistic quantum mechanics Last time 2
Single point energySinglepoint(singleconfiguration):apointonthepotentialenergysurfacewithknownatomiccoordinatesSinglepoint energy calculation:Computing the energyofa particular molecularstructure(spatialarrangementofatoms ornucleiandelectrons).· Basic information about the electronic structure;·Under some circumstances, the only doable calculation;. Upon the optimized structure using a lower level theory, a higher level ofcalculations can be doneto compute some propertiesEE=H亚-> Wavefunction, represented by basis set, e.g.6-31G个Hamiltonian,implementationofwhichiscalledmethod,e.g. HF, DFT, PM6Modelchemistry:method/basis setForesman,chapter23
Single point energy 3 Single point (single configuration): a point on the potential energy surface with known atomic coordinates Single point energy calculation: Computing the energy of a particular molecular structure (spatial arrangement of atoms or nuclei and electrons). • Basic information about the electronic structure; • Under some circumstances, the only doable calculation; • Upon the optimized structure using a lower level theory, a higher level of calculations can be done to compute some properties Hamiltonian, implementation of which is called method, e.g. HF, DFT, PM6 Wavefunction, represented by basis set, e.g. 6-31G Model chemistry: method/basis set Foresman, chapter 2
Configuration and singlepointon PESE3anormalpositionE2on the sideThe degree of degeneracy equals twoInclinedEonthesupportEo
Configuration and single point on PES on the support Potential energy of the chair Inclined The degree of degeneracy equals two on the side normal position 4
Potentialenergycurves(1-DpotentialenergysurfacesPotentialEnergy74pmRepulsiveAttractiveforcesforces-436kJ/mol-104kcal/molMoststablestate5
Potential energy curves (1-D potential energy surfaces) 5
Multidimensionalpotentialenergysurfaces(PEs)PESforwatermoleculeusaddlepointglobalmaximumlocalmaximumlocalminimumglobalminimumlocal minimumq,=H-O-HBondAngle104.5°0.0958nmTeporwsigClacier2oMoeryiaCanval RideRrdbankheThuatrosMadp6
Multidimensional potential energy surfaces (PES) 6 PES for water molecule
Singlepoint calculation:inputfileRoute SectionFormaldehyde.gjf/comCapital orlowercasesbothOK#Ptooutputmoreinformationincaseof%chk=Example.chkerrors,method/basisset,calculationtype#P HF/6-31G(d)Modelchemistry:method/basissetBlanklineTitleSectionFormaldehydeSinglePoint. Captionof calculation,use!to startcomments!(onlyintitlesection)Blank lineMoleculeSpecificationSection010 charge, 1 spin multiplicity = 2 x Stotal spinC 0. 0. 0.of molecule+1 = # of unpaired e +1.0 0. 1.22 0.Cor6,coordinates(numberformatH .94 -.54 0.must matchthecorrespondingvariable type);H-.94 -.54 0.Blanklinemarkstheendoffile,leaveBlank lineat least one7
Single point calculation: input file 7 %chk=Example.chk #P HF/6-31G(d) Blank line Formaldehyde Single Point Blank line 0 1 C 0. 0. 0. O 0. 1.22 0. H .94 -.54 0. H -.94 -.54 0. Blank line Route Section • Capital or lower cases both OK • #P to output more information in case of errors, method/basis set, calculation type • Model chemistry: method/basis set Molecule Specification Section • 0 charge, 1 spin multiplicity = 2 x Stotal spin of molecule+1 = # of unpaired e +1. • C or 6, coordinates (number format must match the corresponding variable type); • Blank line marks the end of file, leave at least one Title Section • Caption of calculation, use ! to start comments！(only in title section) Formaldehyde.gjf/com
Singlepointcalculation:outputfileGaussView 5.0.8OXFile Edit View Calculate Results Windows HelpFormaldehyde.out/log,chkSunmary..OECharge Distribution..·智A昌胎AR0Surfaces/Contours.电电用包创Gl:m3:Vi-Gaussian Calculatien SonnaryVibrationsi口File HameE2_01HMR.LOXGl:3:V1-E2_01.out(G:/xjtu/aeetings/简File Type.1ogUV-VIS,SPCalculation TypeE201.out(G:/xjtu/meetings/简明计算化学实验/res/egs/EXPLORE/EXAMPGi:m3:Vi-DisplayChargeBistribuRHFCalculation MethodAtomic ChargesBasis Set6-31G(d)MullikenType:0ChargeSingletSpin-0.440to0.440Color Range:E(RHP)-113.86370368au(-0.440)RMS Gradient ormau Show HumbersInaginary FreqColor Atomsby Charge2.8449DebyeDipole MonentSymmetriceColor RangeC2VPoint Group(0.129)Fixed Color Range (from Preferences)(0.156)|(0.156)Job cpu time:odays0hours0minut1.0 seconds.Dipole Moment Mebye)2.8449Magnitude:OkViewFileSave Data0.00000.0000Vector:ShowVectorScale:MDefaultOrigin:CloseCancelHelp4 atoms,16 electrons, neutral, singletInquireSelect Atom1
Single point calculation: output file 8 Formaldehyde.out/log, chk
Single point calculation:output fileFormaldehyde.out/log,chkUnit: a.u.;Distance: A (some software use Bohr, 1B = 0.529 A)Charge: e;Energy: Hartree; 1 Hartree = 27.2 eV = 2625.5 kJ/mol;O energyreferencepoint:thenucleusand electrons areinfinitelyapartGaussian 16, Revision A.03 (release 2016);Whenaskquestions,betterprovidetheversionyouuse;Standard orientation:toimproveefficiency;centerofnuclearcharge is the origin of the coordinate;SCF Done: E;Mulliken Charge;Dipole;NormalterminationofGaussian9
Single point calculation: output file 9 • Gaussian 16, Revision A.03 (release 2016); • When ask questions, better provide the version you use; • Standard orientation: to improve efficiency; center of nuclear charge is the origin of the coordinate; • SCF Done: E; • Mulliken Charge; • Dipole; • Normal termination of Gaussian Formaldehyde.out/log, chk • Unit: a.u.; • Distance: Å (some software use Bohr, 1B = 0.529 Å ); • Charge: e; • Energy: Hartree; 1 Hartree = 27.2 eV = 2625.5 kJ/mol; • 0 energy reference point: the nucleus and electrons are infinitely apart
Singlepointcalculation:molecularorbitals.口XAG2:1MOsCurrentSurface130.73665G2:1-MOSE口XLUMO120.37335Current Surface:130.73665110.33337HOMO120.37335100.248380.13577110.333370.44043100.248380.522900.13577国11-0.63916化-0.440430.69706AEEEE-0.52290C0.872570.639161.39235D11.339270.6970620.58203MO(MO=9):Isovalue=0.02)-0.87257-1.39235SinzletG:/xjtu/meetings/简明Chsrge:SpinGaussian Mosfrom:VisualireNexMOsCalculationDiagran11.33927Cube Grid:CoarseIsovalue:0.0220.58203MO((MO=8):Isovalue=0.02)VAddTypeHighlightedAddList:Ba-9a6a~9UpdateCurrentListOkHelpCancel10
Single point calculation: molecular orbitals 10 LUMO HOMO
Formaldehyde'sMOsFormaldehyde-MO.chk#P HF/6-31G(d)#9 LUMO(C-0 元*)#7 HOMO-2#7 HOMO-1#8 HOMOC-O 元O LP or C-O g?O LP"...the more accuratethe calculations became, the more the conceptstendedtovanishintothinair."J.Chem.Phys.43,S2(1965)11Robert Mulliken and the Molecular Orbitals - SciHi Blog
Formaldehyde’s MOs 11 #P HF/6-31G(d) Formaldehyde-MO.chk #7 HOMO-1 C-O π #8 HOMO O LP #9 LUMO (C-O π*) #7 HOMO-2 O LP or C-O σ? Robert Mulliken and the Molecular Orbitals - SciHi Blog “.the more accurate the calculations became, the more the concepts tended to vanish into thin air.” J. Chem. Phys. 43, S2 (1965)