A. Nitzan, Tel Aviv University IAS HU Tutorial: Electron transfer Jerusalem, July 2012

1. A. Nitzan, Tel Aviv University IAS HU Tutorial: Electron transfer Jerusalem, July 2012 • Relaxation, reactions and timescales • Electron transfer in condensed molecular systems • Fundamentals of molecular conduction

2. IAS Workshop 2012 • (1) Relaxation and reactions in condensed molecular systems • Timescales • Relaxation • Solvation • Activated rate processes • Low, high and intermediate friction regimes • Transition state theory • Diffusion controlled reactions

3. The importance of timescales

5. Molecular processes in condensed phases and interfaces Molecular timescales Electronic 10-16-10-15s Vibraional period 10-14s Vibrational xxxxrelaxation 1-10-12s Diffusion D~10-5cm2/s 10nm 10-7 - 10-8 s Chemical reactions xxxxxxxxx1012-10-12s Rotational period 10-12s Collision times 10-12s • Diffusion • Relaxation • Solvation • Nuclear rerrangement • Charge transfer (electron and xxxxxxxxxxxxxxxxproton) • Solvent: an active spectator – energy, friction, solvation

6. Frequency dependent friction MARKOVIAN LIMIT WIDE BAND APPROXIMATION

7. Molecular vibrational relaxation Relaxation in the X2Σ+ (ground electronic state) and A2Π (excite electronic state) vibrational manifolds of the CN radical in Ne host matrix at T=4K, following excitation into the third vibrational level of the Π state. (From V.E. Bondybey and A. Nitzan, Phys. Rev. Lett. 38, 889 (1977))

8. Dielectric solvation Born solvation energy Emission spectra of Coumarin 153 in formamide at different times. The times shown here are (in order of increasing peak-wavelength) 0, 0.05, 0.1, 0.2, 0.5, 1, 2, 5, and 50 ps (Horng et al, J.Phys.Chem. 99, 17311 (1995))

9. “real” solvation “Newton” The experimental solvation function for water using sodium salt of coumarin-343 as a probe. The line marked ‘expt’ is the experimental solvation function S(t) obtained from the shift in the fluorescence spectrum. The other lines are obtained from simulations [the line marked ‘Δq’ –simulation in water. The line marked S0 –in a neutral atomic solute with Lennard Jones parameters of the oxygen atom]. (From R. Jimenez et al, Nature 369, 471 (1994)). dielectric

10. Electron solvation The first observation of hydration dynamics of electron. Absorption profiles of the electron during its hydration are shown at 0, 0.08, 0.2, 0.4, 0.7, 1 and 2 ps. The absorption changes its character in a way that suggests that two species are involved, the one that absorbs in the infrared is generated immediately and converted in time to the fully solvated electron. (From: A. Migus, Y. Gauduel, J.L. Martin and A. Antonetti, Phys. Rev Letters 58, 1559 (1987) Quantum solvation (1) Increase in the kinetic energy (localization) – seems NOT to affect dynamics (2) Non-adiabatic solvation (several electronic states involved)

11. Activated rate processes wB w0 KRAMERS THEORY: Low friction limit High friction limit Transition State theory (action)

12. Effect of solvent friction TST A compilation of gas and liquid phase data showing the turnover of the photoisomerization rate of trans stilbene as a function of the “friction” expressed as the inverse self diffusion coefficient of the solvent (From G.R. Fleming and P.G. Wolynes, Physics Today, 1990). The solid line is a theoretical fit based on J. Schroeder and J. Troe, Ann. Rev. Phys. Chem. 38, 163 (1987)).

13. The physics of transition state rates Assume: (1) Equilibrium in the well (2) Every trajectory on the barrier that goes out makes it

14. The (classical) transition state rate is an upper bound • Assumed equilibrium in the well – in reality population will be depleted near the barrier • Assumed transmission coefficient unity above barrier top – in reality it may be less

15. Quantum considerations 1 in the classical case

16. IAS Tutorial 2012 • (1) Relaxation and reactions in condensed molecular systems • Timescales • Relaxation • Solvation • Activated rate processes • Low, high and intermediate friction regimes • Transition state theory • Diffusion controlled reactions

17. IAS Tutorial 2012 • (2) Electron transfer processes • Simple models • Marcus theory • The reorganization energy • Adiabatic and non-adiabatic limits • Solvent controlled reactions • Bridge assisted electron transfer • Coherent and incoherent transfer • Electrode processes

18. Theory of Electron Transfer • Rate – Transition state theory • Boltzmann • Activation energy • Transition probability

19. Electron transfer in polar media • Electrons are much faster than nuclei •  Electronic transitions take place in fixed nuclear configurations •  Electronic energy needs to be conserved during the change in electronic charge density Electronic transition Nuclear relaxation

20. Electron transfer Nuclear motion Nuclear motion Electron transition takes place in unstable nuclear configurations obtained via thermal fluctuations

21. Electron transfer EA Solvent polarization coordinate

22. Transition state theory of electron transfer Adiabatic and non-adiabatic ET processes Landau-Zener problem (For harmonic diabatic surfaces (1/2)KR2)

23. Electron transfer – Marcus theory We are interested in changes in solvent configuration that take place at constant solute charge distribution  They have the following characteristics: (1) Pn fluctuates because of thermal motion of solvent nuclei. (2) Pe , as a fast variable, satisfies the equilibrium relationship (3) D= constant (depends on  only) Note that the relations E = D-4P; P=Pn + Pe are always satisfied per definition, however D sE. (the latter equality holds only at equilibrium).

24. Electron transfer – Marcus theory Free energy associated with a nonequilibrium fluctuation of Pn q “reaction coordinate” that characterizes the nuclear polarization

25. The Marcus parabolas Use q as a reaction coordinate. It defines the state of the medium that will be in equilibrium with the charge distribution rq. Marcus calculated the free energy (as function of q) of the solvent when it reaches this state in the systems q =0 and q=1. q=1 q q=0

26. Electron transfer: Activation energy Reorganization energy Activation energy

27. Electron transfer: Effect of Driving (=energy gap)

28. Experimental confirmation of the inverted regime Marcus papers 1955-6 Miller et al, JACS(1984) Marcus Nobel Prize: 1992

29. Electron transfer – the coupling • From Quantum Chemical Calculations • The Mulliken-Hush formula • Bridge mediated electron transfer

30. Bridge assisted electron transfer EB

31. Veff A D B VAD VDB DE A D

32. B1 B2 BN … VAD VDB V12 DE A D Veff A D Green’s Function

33. Donor-to-Bridge/ Acceptor-to-bridge Bridge Green’s Function Franck-Condon-weighted DOS Reorganization energy Marcus expresions for non-adiabatic ET rates

34. Bridge mediated ET rate b’ (Å-1)= 0.2-0.6 for highly conjugated chains 0.9-1.2 for saturated hydrocarbons ~ 2 for vacuum

35. Bridge mediated ET rate (J. M. Warman et al, Adv. Chem. Phys. Vol 106, 1999).

36. constant Incoherent hopping STEADY STATE SOLUTION

37. ET rate from steady state hopping

38. Dependence on temperature The integrated elastic (dotted line) and activated (dashed line) components of the transmission, and the total transmission probability (full line) displayed as function of inverse temperature. Parameters are as in Fig. 3.

39. The photosythetic reaction center Michel - Beyerle et al

40. Dependence on bridge length

41. DNA (Giese et al 2001)

42. IAS Tutorial 2012 • (2) Electron transfer processes • Simple models • Marcus theory • The reorganization energy • Adiabatic and non-adiabatic limits • Solvent controlled reactions • Bridge assisted electron transfer • Coherent and incoherent transfer • Electrode processes AN, Oxford University Press, 2006

43. IAS Tutorial 2012 • (3) Molecular conduction • Simple models for molecular conductions • Factors affecting electron transfer at interfaces • The Landauer formula • Molecular conduction by the Landauer formula • Relationship to electron-transfer rates. • Structure-function effects in molecular conduction • How does the potential drop on a molecule and why this is important • Probing molecules in STM junctions • Electron transfer by hopping

44. Molecular conduction

45. Molecular Rectifiers Arieh Aviram and Mark A. RatnerIBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USADepartment of Chemistry, New York New York University, New York 10003, USA Received 10 June 1974 Abstract The construction of a very simple electronic device, a rectifier, based on the use of a single organic molecule is discussed. The molecular rectifier consists of a donor pi system and an acceptor pi system, separated by a sigma-bonded (methylene) tunnelling bridge. The response of such a molecule to an applied field is calculated, and rectifier properties indeed appear.

46. Xe on Ni(110)

47. Fabrication • Characterization • Stability • Funcionality • Control

48. Fabrication • Stability • Characterization • Funcionality • Control THE MOLECULE Strong electric field System open to electrons and energy Nonequilibrium Relaxation Electron-vibration coupling Heat generation

49. Landauer formula For a single “channel”: (maximum=1) Maximum conductance per channel

50. eF fL(E) – fR(E) T(E) eF T(E) fL(E) – fR(E) I g Weber et al, Chem. Phys. 2002 F