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Laser–Induced Control of Condensed Phase Electron Transfer

Laser–Induced Control of Condensed Phase Electron Transfer. Rob D. Coalson , Dept. of Chemistry, Univ. of Pittsburgh Yuri Dakhnovskii , Dept. of Physics, Univ. of Wyoming Deborah G. Evans , Dept. of Chemistry, Univ. of New Mexico Vassily Lubchenko , Dept. of Chemistry, M.I.T. NH 3. CN. NH 3.

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Laser–Induced Control of Condensed Phase Electron Transfer

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  1. Laser–Induced Control of Condensed Phase Electron Transfer Rob D. Coalson, Dept. of Chemistry, Univ. of Pittsburgh Yuri Dakhnovskii, Dept. of Physics, Univ. of Wyoming Deborah G. Evans, Dept. of Chemistry, Univ. of New Mexico Vassily Lubchenko, Dept. of Chemistry, M.I.T. NH3 CN NH3 CN +3 +2 H3N Ru N C Ru CN H3N NC NH3 CN [polar Solvent]

  2. Tunneling in A 2-State System q |L> |R> Proton Transfer V(x) tropolone q Multi (Double) Quantum Well Structure q e- Electron Transport In Solids |R> |L> V(x) AlGaAs GaAs GaAs q

  3. 1. . . . . N Ru+2 Ru+3 e- Atomic Orbitals |D> |A> Molecular Electron Transfer |D> |A> Acceptor Donor Equivalent 2-state model  For any of these systems: |(t)> = cD(t) |D> + cA(t) |A> 1 where HAA HAD cA cA d = iħ dt cD cD HDA HDD For a Symmetric Tunneling System: HAA= HDD= 0; HAD= HAD =  (< 0)

  4. Given initial preparation in |D>, for a symmetric system: PD(t) = 1 – PA(t) = cos2(t) = t  2

  5. e- Now, apply an electric field E |D> |A> R R 0 2 2 Q: How does this modify the Hamiltonian?? A: It modifies the site energies according to “ - • E ” Permanent dipole moment of A HAA  eoR/2 0 - E H Thus: =   HDD 0 -eoR/2

  6. Analysis in the case of time-dependent E(t) = Eocosot Consider first the symmetric case:  0 1 0 d cA - cA i Eocosot = dt cD cD 0 -1  0 Permanent dipole moment difference Letting: cA(t) = e ia sinot cAI(t);cD(t) = e ia sinot cDI(t) Eo Eo ] [ sinot t Where: a = N.B.:0Eocosot'dt' = o (ħ)o Thus, Interaction Picture S.E. reads: 0 cAI e-2ia sinot  cAI d i = dt cDI cDI e2ia sinot  0

  7. e ib sint =  Jm(b) e imt Now note: m=-   e2ia sinot =   Jm(2a) e imot So: m=-  ·Jo(2a) , for /o << 1 RWA Thus, the shuttle frequency is renormalized to |Jo(2a)|   ] [ <<1  0 NB: Trapping or localization occurs at certain Eo values! 0 2.5 5.5 a [Grossman - Hänggi, Dakhnovskii – Metiu]

  8. Add coupling to a condensed phase environment ˆ ˆ 1 0 1 0 + VD(x)  H = T - Eocosot 0 1  VA(x) 0 -1 Nuclear coordinate kinetic energy Nuclear coordinate Field couples only to 2-level system VA(x) VD(x) D(x,t) A(x,t) x

  9. T+VD(x)  - 1 0 D(x,t) Now: Eocosot  T+VA(x) 0 -1 A(x,t) D(x,t) d = i dt A(x,t)

  10. Construction of (Diabatic) Potential Energy functions for Polar ET Systems: A D VD(x) A D VA(x)

  11. A few features of classical Nonadiabatic ET Theory [Marcus, Levich-Doganadze…] ˆ T+V1(x)  ˆ Hamiltonian = H ˆ  T+V2(x) (diabatic) nuclear coord. potential for electronic state 2 non-adiabatic coupling matrix element kinetic E of nuclear coordinates 1(x,t) States |(t)> = 2(x,t)

  12. Given initial preparation in electronic state 1 (and assuming nuclear coordinates are equilibrated on V1(x)) 1 2 1(x,0) Then, P2(t) = fraction of molecules in electronic state 2 = < 2(x,t)| 2(x,t)>  k12t x where k12 = (Golden Rule) rate constant

  13. In classical Marcus (Levich-Doganadze) theory, k12 is determined by 3 molecular parameters: , Er,  ( ) ½  -(Er- )2/4Er kBT k12 =2 e ErkT w/ Er = “Reorganization Energy” ;  = “Reaction Heat” 1 2  Er x ( ) ½  -(Er+ )2/4Er kBT k21 = 2 For the “backwards” Reaction: e ErkT

  14. To obtain electronic state populations at arbitrary times, solve kinetic [“Master”] Eqns.: dP1(t)/dt = - k12P1(t) + k21P2(t) dP2(t)/dt = k12P1(t) - k21P2(t) Note that long-time asymptotic [“Equilibrium”] distributions are then given by: P2() k12 /kBT Keq = = = e P1() k21 for Marcus formula rate constants N.B. Marcus theory for nonadiabatic ET reactions works experimentally. See:Closs & Miller, Science 240, 440 (1988)

  15. Control of Rate Constants in Polar Electronic Transfer Reactions Via an Applied cw Electric Field The Hamiltonian is: VD VA x ˆ hD 0  1 0 0 + 12Eocosot ˆ + H = ˆ  0 hA 0 0 -1 The forward rate constant is: [Y. Dakhnovskii, J. Chem. Phys. 100, 6492 (1994)   Re ˆ ˆ  Jm(a) ·  kDA = 2 2 ˆ -i hAt i hDt dt e imot tr { }  D e e m=- 0  a = 2 12 Eo/ ħo

  16. ( ) ½  2   Jm(212Eo/ħo) • kDA = 2 4 ErkT AD m=- + -(Er – + ħmo)2/4Er kBT e Rate constants in presence of cw E-field

  17. 300 D 200 J1 2 Schematically: 100 A J0 2 Energy 0 J-1 2 -100 ħo -200 0 5 x In polar electron transfer reactions, for Reorganization Energy Er ħo (the quantum of applied laser field)

  18. Jo(a) 2 J1(a) 2 J2(a) 2 a

  19. Dramatic perturbations of the “one-way” rate constants may be obtained by varying the laser field intensity: Forward rate constant [Activationless reaction, Er=1eV]

  20. Dakhnovskii and RDC showed how this property can be used to control Equilibrium Constants with an applied cw field: D A “bias” 

  21. Results for activationless reaction: PA(00) PD(00) eq = Y. Dakhnovskii and RDC, J. Chem. Phys. 103, 2908 (1995)

  22. Activationless ET  = 100 cm -1 Evans, RDC, Dakhnovskii & Kim, PRL 75, 3649 (95) Er =  = ħo = 1eV

  23. REALITY CHECK on coherent control of mixed valence ET reactions in polar media  “·E” (1)  E  • Orientational averaging will reduce magnitude of desired effects [Lock ET system in place w/ thin polymer films]

  24. (2) Dielectric breakdown of medium? • To achieve resonance effects for  = 34D • Er = ħo = 1eV • Electric field  107 V/cm Giant dipole ET complex, solvent w/ reduced Er, pulsed laser reduce likelihood of catastrophe] (3) Direct coupling of E(t) to polar solvent   [Dipole moment of solvent molecules << Dipole moment of giant ET complex]

  25. ħ0 1eV ; intense fields  (multiphoton) excitation to higher • energy states in the ET molecule, which are not considered in • the present 2-state model. ħ 1eV ħ 1eV ħ 1eV ħ 1eV

  26. Absolute Negative Conductance in Semiconductor Superlattice - + -Keay et al., Phys. Rev. Lett. 75, 4102 (1995)

  27. Absolute Negative Conductance in Semiconductor Superlattice -Keay et al., Phys. Rev. Lett. 75, 4102 (1995)

  28. Immobilized long-range Intramolecular Electron Transfer Complex: D Tethered Alkane Chain molecule  E (ħ) A  k (Inert) Substrate

  29. Light Absorption by Mixed Valence ET Complexes in Polar Solvents: ħ ħ Transmitted Photons Ru+3 Incident Photons Ru+2 Solvent ħ ħ ħ ħ

  30. Absorption Cross Section Formula:

  31. Δ Marcus Gaussian permanent dipole moment difference

  32. Barrierless Hush Absorption = PRL 77, 2917 (1996) J. Chem. Phys. 105, 9441 (1996)

  33. emission absorption Stimulated Emission using two incoherent lasers J. Chem. Phys. 109, 691 (1998)

  34. J. Chem. Phys. 109, 691 (1998)

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