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Lecture 4

A. Nitzan, Tel Aviv University ELECTRON TRANSFER AND TRANSMISSION IN MOLECULES AND MOLECULAR JUNCTIONS AEC, Grenoble, Sept 2005. Lecture 4. Grenoble Sept 2005. (1) Relaxation and reactions in condensed molecular systems Kinetic models Transition state theory

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Lecture 4

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  1. A. Nitzan, Tel Aviv University ELECTRON TRANSFER AND TRANSMISSION IN MOLECULES AND MOLECULAR JUNCTIONS AEC, Grenoble, Sept 2005 Lecture 4

  2. Grenoble Sept 2005 • (1) Relaxation and reactions in condensed molecular systems • Kinetic models • Transition state theory • Kramers theory and its extensions • Low, high and intermediate friction regimes • Diffusion controlled reactions Coming March 2006 Chapter 13-15

  3. Grenoble Sept 2005 • (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 Coming March 2006 Chapter 16

  4. Grenoble Sept 2005 • (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 Coming March 2006 Chapter 17

  5. Donor gives an electron and goes from state “a” (reduced) to state “b” (oxidized). Eb,a=Eb-Ea is the energy of the electron given to the metal ELECTRODE PROCESSES Transition rate to a continuum (Golden Rule) D A EF Rate of electron transfer to metal in vacuum M Rate of electron transfer to metal in electrolyte solution Reorganization energy here – from donor only (~0.5 of “regular” value)

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

  7. General case Unit matrix in the bridge space Bridge Hamiltonian B(R) + B(L) -- Self energy Wide band approximation

  8. Molecular level structure between electrodes LUMO HOMO

  9. Cui et al (Lindsay), Science 294, 571 (2001) “The resistance of a single octanedithiol molecule was 900 50 megaohms, based on measurements on more than 1000 single molecules. In contrast, nonbonded contacts to octanethiol monolayers were at least four orders of magnitude more resistive, less reproducible, and had a different voltage dependence, demonstrating that the measurement of intrinsic molecular properties requires chemically bonded contacts”.

  10. ET vs Conduction

  11. A relation between g and k Electron charge conduction Electron transfer rate Decay into electrodes Marcus

  12. A relation between g and k l0.5eV

  13. ET rate from steady state hopping

  14. Incoherent hopping LARGE N: Or at T=300K.

  15. PART D Issues in molecular conductions

  16. Grenoble Sept 2005 • (3) Molecular conduction • Structure-function effects in molecular conduction • The role of contacts • How does the potential drop on a molecule and why this is important • Probing molecules in STM junctions • Electron transfer by hopping • Charging • Switching

  17. 2-level bridge (local representation) • Dependence on: • Molecule-electrode coupling GL , GR • Molecular energetics E1, E2 • Intramolecular coupling V1,2

  18. 6 5 4 I / arb. units 3 2 1 0 -1 -1 -0.5 0 0.5 1 I Ratner and Troisi, 2004 0.5 0.0 - 0.5 V (V)

  19. “Switching”

  20. Reasons for switching • Conformational changes • Transient charging • Polaron formation time Tsai et. al. PRL 1992: RTS in Me-SiO2-Si junctions STM under waterS.Boussaad et. al. JCP (2003)

  21. I. Inoue et al, Journal of Physiology 541.3, pp. 769-778(2002) [Ca+2]=1x10-6M Single (K+) channel currents from Schwann cells isolated enzymatically from the giant axons of the squids Loligo forbesi, Loligo vulgaris and Loligo bleekeri. The channel conductance was 43.6 pS when both internal and external solutions contained 150 mM K+. Activity was weakly dependent on membrane voltage but sensitive to the internal Ca2+ concentration.

  22. Giese et al, 2002 Michel-Beyerle et al Xue and Ratner 2003 Selzer et al 2004 Temperature and chain length dependence

  23. V. J. Langlais et al, PRL 83, 2809 (1999)

  24. Electron transfer in DNA

  25. DNA-news-1

  26. DNA-news-4

  27. DNS-news-3

  28. DNA-news-2

  29. “Prediction is very difficult, Especially of the future ” attributed to Niels Bohr

  30. Conjugated vs. Saturated Molecules: Importance of Contact Bonding Au// S/Au Au/S S/Au Kushmerick et al., PRL (2002) Au/S(CH2)8SAu 2- vs. 1-side Au-S bonded conjugated system gives at most 1 order of magnitude current increase compared to 3 orders for C10 alkanes! Au//CH3(CH2)7S/Au

  31. Excess electron density Xue, Ratner (2003) Potential profile Galperin et al JCP 2003 Where does the potential bias falls, and how? • Image effect • Electron-electron interaction (on the Hartree level) Vacuum Galperin et al 2003

  32. Tian et al JCP 1998 Why is it important? D. Segal, AN, JCP 2002 Heat Release on junction

  33. Experiment Theoretical Model

  34. Experimental i/V behavior

  35. Experimental (Sek&Majda) aCurrent at the negative bias refers to the measurement with the Hg side of the junction biased negative relative to the Au side.

  36. Potential distribution

  37. NEGF - HF calculation

  38. HS - CH2CH2CH2CH2CH2CH3 . . . CH3CH2 - SH Segment Orbital MO

  39. B A A B

  40. TIMESCALE CONSIDERATIONS Does the tunneling electron interact with other degrees of freedom and what are the possible consequences of this interaction? The case of electron tunneling in water

  41. Overbarrier electron transmission through water (D2O on Pt(1,1,1)

  42. A look from above on a water film

  43. Effective Barrier The effective one-dimensional barrier obtained by fitting the low energy tunneling probability to the analytical results for tunneling through a rectangular barrier. Solid, dotted, and dashed lines correspond to the polarizable, nonpolarizable, and bare barrier potentials, respectively.

  44. The numerical problem • Get a potential • Electrostatics • Generate Water configurations • Tunneling calculations • Integrate to get current

  45. Potentials for electron transmission through water Water-Water.....................RWKM, SPC/E Electron-Water..............Barnett et al +correction for many body polarizability Water-Wall........Henziker et al (W-Pt), Hautman et al (W-Au) Electron-Wall..............Square Barrier Earlier studies – Tunneling through static water configurations

  46. STM model Fig. 1. A model system used to compute electron transmission between two electrodes, L and R separated by a narrow spatial gap (M) containing a molecular species. The surface S1 of L is shaped to mimic a tip. The lines A'B', C'D' and AB and CD are projections of boundary surfaces normal to the transmission direction (see text for details). The numerical solution is carried on a grid (Shown).

  47. Potential distribution A cut of the external potential distribution between the tip and the flat substrate for a voltage drop of 0.5V between these electrodes The image potential along different lines normal to the flat electrode: (1) x=0 (a line going through the tip axis); (2) x=11.96au (distance from the tip axis); (3) x=23.92au.

  48. MOLECULAR DYNAMICS TO GENERATE WATER CONFIGURATIONS Figure - Ohmine et al

  49. CALCULATION OF TRANSMISSION FACTORS

  50. CALCULATION OF TRANSMISSION FACTORS Absorbing boundary conditions Green's function method: Replace  by i(r), smoothly rising towards edges of M system, provided LM and MR boundaries are set far enough

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