Introduction to Theories of Chemical...

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Introduction to Theories of Chemical Reactions Graduate Course Seminar Beate Flemmig FHI
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  • Introduction to Theories ofChemical Reactions

    Graduate Course SeminarBeate Flemmig


  • I. Overview

    What kind of reactions?

    • gas phase / surface• unimolecular / bimolecular• thermal / photochemical

  • What kind of information?

    • structure of reactants, products• ΔEreact• mechanism• TS, Ea• k• τ, lifetime of intermediates

  • What kind of theoretical approach?

    • MO and VB theoryalmost without calculation, based on symmetryarguments

    • Quantum ChemistryBorn-Oppenheimer approximationsolution of electronic Schrödinger equationoptimization of stationary points of PESfollow IRCTD data → TS theory

  • • Molecular Dynamicssemiempirical potentialor calculation of forces ‘on the fly’ (CPMD)T ≥ 0

    • beyond BO (wave-packet dynamics)more than one PES (photochemistry!)solution of nuclear SEreal-time evolution of a chemical reactionrelated to “pump-probe“ spectroscopy or ”femtosecondchemistry”

    • statistical mechanicsmany particles

  • An attempt to summarize the approaches …

    R. Daudel, Quantum Chemistry, John Wiley, p. 299

    a: number of particles

    x: electronic coordinates

    X: nuclear coordinates

    t: time

  • II.ExampleReaction:Chelate RingInversion

    Organometallics, 22 (2003) 1196.

  • k(TC ) =RTCNAh


    k(TC ) =π


    experimentally ΔEa 62 kJ/mol from 1H NMR

    H. Köpf, Angew. Chem. 83, 146-147, (1971)

    M. Hesse, H. Meier, B. ZeehSpektroskopische Methoden in derorganischen Chemie Thieme Verlag 1991

    approximate formulaΔν between signalsof H at the twoC5H5-rings

    coalescence temp.TC (~ 20 ºC)

  • Stabilizing and destabilizing effects of folding

    Lewis structure

  • III. Application of MO TheoryRing opening and closing of ozone - A forbidden reaction

  • molecular plane σ preserved in the reactionlevels of MOs with different symmetry w. r. t. σ are crossing

  • computed* kinetic persistence of the cyclic isomer* K. Ruedenberg et al. J. Chem. Phys. (1991) 94 8054.

  • life time of the intermediate

    k = Ae−EaRT

    τ ~ 1k


  • half-life time

    d xd t

    = k c0−x[ ]

    ln c0c0−x

    = kt

    x := 12c0

    t :=τ

    τ = ln2k−1

    unimolecular reaction

    first-order rate law

  • Fill in numbersassume preexponential factor of 1015s-1 (unimolecular reaction)

    calculated barrier 23 kcal/mol = 95.7 kJ/mol (the lower one)

    room temperature 25ºC

    k = Ae−EaRT

    k =1015s−1e−95.7kJmol-1


    k =0.64 ⋅10−2s-1

    τ = ln2k−1

    τ = 44 s

  • Use cyclic ozone as a ligand

    6 π electron donor

  • applied an ‘18-electron strategy’

    Some Predicted Complexes

    Transition Metal Complexes of Cyclic and Open Ozone and Thiozone Flemmig, B.;Wolczanski, P. T.; Hoffmann, R. J. Am. Chem. Soc. 2005 ASAP Article

  • Woodward - Hoffmann Rules

    to explain stereoselectivity of cycloadditions

  • different symmetry elements remain,depending on the mechanism

  • correlation diagram: level-crossing for disrotatory path

    see also: R. Hoffmann, Angew. Chem. Int. Ed. (2004) 43, 6586 - 6590

  • coefficients ofHückel

    solutions(π systems)

    correspond toparticle-in-a-box solutions

  • VB-Theory

    S. Shaik, A. Shurki, Angew. Chem.Int. Ed. (1999) 38, 586 - 625.

  • IV. Application of QuantumChemistry

    use Born-Oppenheimer approximation

    and solve the electronic Schrödinger equation (for fixed R)

  • ideally: determine electronic properties as functions ofnuclear coordinates - i. e. determine the PES

    Potential Energy Surface, PES:

    • governs nuclear motion, forces on the nuclei Fx = -∂E/∂x

    • stationary points correspond to (meta)stable species (local orglobal minima) and to transition states (saddle points)

    • shape of PES around stationary points determinesvibrational spectra

    • electronic transitions correspond to transitions from onePES to another

    • minimum energy path corresponds to reaction coordinate

  • in reality: Calculated PES only available for very small systems,for example H+H2 in colinear arrangement

    without Coulomb interactions with Coulomb interactions

    H. Eyring, M. Polanyi, 1931 M. Karplus et al. 1968

  • in practice: stationary points of PES, their characterization(frequency calculations), and maybe the reaction path (IRCcalculation)

  • Transition State Theory

    k = kbTh


    QRe−Eak bTEyring equation

    H. Eyring, J. Chem. Phys. (1935) 3, 107

    partition function

    Q = g jlevels∑ e

    −ε jk bT

    εvib = n +12

  • Example: Study of a Radical ClockRearrangement on a Surface

    FTIR: ring modes at1393 cm-1and 1434 cm-1 vanish andC=C stretch mode emerges at 1645 cm-1

    C. M. Friend, I. Kretzschmar, JACS (2000) 122 12395.

  • Cyclopropylmethoxide and 3-butenyloxide on Mo(110)

    Flemmig, B.; Kretzschmar, I.; Friend, C. M.; Hoffmann, R. J. Phys. Chem. A. 2004; 108(15) 2972-2981

    ΔEtotal = 31 kJ/mol

  • Alternative mechanisms already for the isolated molecule

  • Which is the rate-determining step ?

    … the one with the highest activation energy (not the onewith the highest barrier)

    see also: H. Eyring et al. The Theory of Rate Processes, McGraw Hill, New York 1941.

  • V. Molecular Dynamics

    classical equations of motion€

    H = TK +U

    TK =12



    nuclei have kinetic energy TK > 0

    U :Te (r) + VeK (r,R) + Vee (r) + VKK(R)PI : classical momentum




    = −∂H∂RI

    solutions RI(t) and PI(t) are the trajectories of the nuclei

  • VI. Wave-Packet Dynamicstreat also the nuclei quantum-mechanically

    HΦ(R,t) = ih ∂∂tΦ(R,t)

    H = TK +U+ [Hextern ]

    TK =h2



    simulations only for intervals of a few picoseconds

    very fast reactions: e.g. laser-induced isomerizations

  • R



  • References/Acknowledgement

    • C. Engler (Uni Leipzig) Überblick über dieNäherungshierarchie und Lösungsansätze in derQuantentheorie, Graduate Course

    • H.-J. Werner (Uni Stuttgart) Computational Chemistry inCatalysis, Graduate Course

    • R. Hoffmann (Cornell) Bonding in Molecules, CHEM798

    • W. J. Moore, D. O. Hummel, Physikalische Chemie, deGruyter Berlin 1986.