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