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Electronic Tunneling through Dissipative Molecular BridgesUri Peskin Department of Chemistry,Technion-Israel Institute of TechnologyMusa Abu-Hilu(Technion)Alon Malka(Technion)Chen Ambor(Technion)Maytal Caspari(Technion)Roi Volkovich(Technion)Darya Brisker(Technion)Vika Koberinski(Technion)Prof.Shammai Speiser(Technion)Thanking:OutlineMotivation:Controlled electron transport in molecular devices and in biological systems.Background:ET in Donor-Acceptor complexes:The Golden Rule,the Condon approximaton and the spin-boson Hamiltonian.ET in Donor-Bridge-Acceptor complexes:McConnells formula for the tunneling matrix elements.The problem:Electronic-nuclear coupling at the molecular bridge and the breakdown of the Condon approximation.The model system:Generalized spin-boson Hamiltonians for dissipative through-bridge tunneling.Results:The weak coupling limit:Langevin-Schroedinger formulation,simulations and interpretation of ET through a dissipative bridgeBeyond the weak coupling limit:An analytic formula for the tunneling matrix element in the deep tunneling regime.Conclusions:Promotion of tunneling through molecular barriers by electronic-nuclear coupling.The effect of molecular rigidity.Motivation:Electron Transport Through MoleculesMolecular ElectronicsResonant tunneling through molecular junctions Tans,Devoret,Thess,Smally,Geerligs,Dekker,Nature(2019)Reichert,Ochs,Beckmann,Weber,Mayor,Lohneysen,Phys.Rev.Lett.(2019).Long-range Electron Transport In NatureThe Photosynthetic Reaction CenterDeep(off-resonant)tunneling through molecular barriers Electron transfer is controlled by molecular bridges Tunneling pathway between cytochrome b5 and methaemoglobinControlled tunneling through molecules?Minor changes to the molecular electronic density High sensitivity(exponential)to the molecular parameters A potential for a rational design based on chemical knowledgeResonant tunnelingDeep(off resonant)tunnelingWhy Off-Resonant(deep)Tunneling?Electron Transfer in Donor-Acceptor PairsDonor AcceptorElectronic tunneling matrix elementNuclear factor:Frank-Condon weighted density of statesThe role of electronic nuclear coupling?The case of through bridge tunneling:Theory:Electron Transfer in Donor-Acceptor PairsThe electronic Hamiltonian:Diabatic electronic basis functions:The Hamiltonian matrix:Theory:Electron Transfer in Donor-Acceptor PairsA Spin Boson Hamiltonian:The Harmonic approximation:Theory:Electron Transfer in Donor-Acceptor PairsThe Condon approximationDonor AcceptorThe golden rule expression for the rate An electronic tunneling matrix elementA nuclear factorMcConnell(1961):Introducing a set of bridge electronic states;The direct tunneling matrix element vanishesDonor AcceptorLong Range Electronic TunnelingThe donor and acceptor sites are connected via an effective tunneling matrix element through the bridgeMcConnells Formula:A tight binding modelThe deep tunneling regime:First order perturbation theoryA simple expression for the effective tunneling matrix element Tunneling oscillations at a frequency:Superexchange dynamics througha symmetric uniform bridgeH.M.McConnell,J.Chem.Phys.35,508(1961)Deep tunneling through a molecular bridgeThe role of bridge nuclear modes?Validity of the Condon approximation?Davis,Ratner and Wasielewski(J.A.C.S.2019).Molecules 1-5Charge transfer is gated by bridge vibrations Electronic nuclear coupling at the bridge:Rigid bridges enable highly efficient electron energy transfer Lokan,Paddon-Row,Smith,La Rosa,Ghiggino and Speiser(J.A.C.S.2019).Breakdown of the Condon approximation!Structural(promoting)bridge modes:Electronically active(accepting)bridge modes:A generalized“spin-boson”model:The nuclear potential energy surface changes at the bridge electronic sitesHarmonic nuclear modes Linear e-nuclear coupling in the bridge modes The e-nuclear coupling is restricted to the bridge sites A Dissipative Superexchange Model:A symmetric uniform bridge Introducing nuclear modes with an Ohmic()spectral density The nuclear frequencies:10-500(1/cm)are larger than the tunneling frequency!and a uniform electronic-nuclear coupling:M.A-Hilu and U.Peskin,Chem.Phys.296,231(2019).Coupled Electronic-Nuclear DynamicsA mean-field approximation:The coupled SCF equations:Mean-fields:The Langevin-Schroedinger equationA non-linear,non Markovian dissipation termFluctuationsAt zero temperature,R(t)vanishesInitial nuclear position and momentum Electronic bridge populationU.Peskin and M.Steinberg,J.Chem.Phys.109,704(2019).Numerical Simulations:Weak e-n couplingThe tunneling frequency increases!The tunneling is suppressed!Simulations:Strong e-n CouplingInterpretation:a time-dependent Hamiltonian The Instantaneous electronic energy:Weak coupling:Energy dissipation into nuclear vibrations lowers the barrier for electronic tunnelingA time-dependentMcConnell formulaInterpretation:a time-dependent Hamiltonian The Instantaneous electronic energy:Weak coupling:Energy dissipation into nuclear vibrations lowers the barrier for electronic tunnelingStrong coupling:“Irreversible”electronic energy dissipation Resonant TunnelingNumerically exact simulations for a single bridge mode Tunneling suppression at strong couplingTunneling acceleration at weak coupling A dissipative-acceptor model:The acceptor population:Dissipation leads to a unidirectional ETThe tunneling rate Increases with e-n coupling at the bridge!Introducing a bridge modeA.Malka and U.Peskin,Isr.J.Chem.(2019).A dimensionless measure for the effective electronic-nuclear coupling:Interpretation:Nuclear potential energy surfacesDeep tunneling=weak electronic inter-site couplingEntangled electronic-nuclear dynamics beyond the weak coupling limitA small parameter:The symmetric uniform bridge model:M.A.-Hilu and U.Peskin,submitted for publication(2019).A Rigorous Formulation The Donor/Acceptor HamiltonianThe Bridge HamiltonianThe coupling Hamiltonian(purely electronic!)Introducing vibrational eigenstates:Diagonalizing the tight-binding operator:Regarding the electronic coupling as a(second order)perturbation In the absence of electronic coupling the ground state is degenerate:The energy splitting temperature reads:Frank-Condon overlap factorsThe energy splitting:Expanding the denominators in powers ofand keeping the leading non vanishing terms givesInterpretation:Effective electronic couplingEffective barrier for tunnelingMcConnells expression:Summation over vibronic tunneling pathways:Lower barrier for tunnelingMultiple“Dissipative”pathwaysThe effective tunneling barrier decreasesAn example(N=8)The tunneling frequency increases by orders of magnitudewith increasing electronic nuclear coupling1/cm The“slow electron”adiabatic limit Considering only the ground nuclear vibrational state:A condition for increasing the tunneling frequency by increasing electronic-nuclear coupling:An example(N=8)The slow electron approximationSpectral densitiesMolecular rigidity=small deviations from equilibriumconfigurationFlexible vs.Rigid molecular bridgesIncreasing rigidity A consistency constraint:Langevin-Schroedinger simulations:The tunneling frequency increases with bridge rigidity A rigorous treatment:The“slow electron”limitRigidity=larger Frank Condon factor!Summary and ConclusionsA rigorous calculation of electronic tunneling frequencies beyond the weak electronic-nuclear coupling limit,predicts acceleration by orders of magnitudes for some molecular parametersAn analytical approach was introduced and a formula was derived for calculations of tunneling matrix elements in a dissipative McConnell model.A comparison with approximate methods for studying open quantum systems is suggested.The way for rationally designed,controlled electron transport in“molecular devices”is still long The effect of electronic-nuclear coupling in electronically active molecular bridges was studied using generalized McConnell models including bridge vibrations.Mean-field Langevin-Schroedinger simulations of the coupled electronic-nuclear dynamics suggest that weak electronicnuclear coupling promotes off-resonant(deep)through bridge tunneling谢谢你的阅读v知识就是财富v丰富你的人生
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