Lecture 4

1. A. Nitzan, Tel Aviv University SELECTED TOPICS IN CHEMICAL DYNAMICS IN CONDENSED SYSTEMS Boulder, Aug 2007 Lecture 4

2. Boulder Aug 2007 • (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 Chapter 13-15

3. Boulder Aug 2007 • (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 Chapter 16

4. Boulder Aug 2007 • (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 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. Current from classical kinetics = 0 at steady state Quantum mechanical resalt:

16. A. Nitzan Boulder Aug 2007 PART D • 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 Issues in molecular conductions

17. A Inject and detect Light Control type and number of molecule Temperature measurement and control THE IDEAL EXPERIMENT (Original picture from Datta et al) Molecule(s) T2 T1 Current measurement vs. V and Vg REPRODUCIBLE!

18. G Source-Drain potential (V) Gate potential VG S D D S

19. 2-level bridge (local representation) • Dependence on: • Molecule-electrode coupling GL , GR • Molecular energetics E1, E2 • Intramolecular coupling V1,2

20. 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)

21. “Switching”

22. Tsai et. al. Appl.Phys.Lett 1992: Random telegraph signals in Me-SiO2-Si junctions Tip height Time (s) time Moore et al (P.S. Weiss) Conduction switching in Oligo(phenylene ethynylene) molecules (nitro functionalized) STM under waterS.Boussaad et. al. JCP (2003) Switching • Conformational changes • Transient charging • Polaron formation

23. Dynamics of current voltage switching response of single bipyridyl-dinitro oligophenylene ethynylene dithiol (BPDN-DT) molecules between gold contacts. In A and B the voltage is changed relatively slowly and bistability give rise to telegraphic switching noise. When voltage changes more rapidly (C) bistability is manifested by hysteretic behavior Lortscher et al (Riel), Small, 2, 973 (2006)

24. 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.

25. Switching with light Chem. Commun., 2006, 3597 - 3599, DOI: 10.1039/b609119a Uni- and bi-directional light-induced switching of diarylethenes on gold nanoparticles Tibor Kudernac, Sense Jan van der Molen, Bart J. van Wees and Ben L. Feringa “In conclusion, photochromic behavior of diarylethenes directly linked to gold nanoparticles via an aromatic spacer has been investigated. Depending on the spacer, uni- (3) or bidirectionality (1,2) has been observed.”

26. Nanotechnology 16 (2005) 695–702 Switching of a photochromic molecule on gold electrodes: single-molecule measurements J. He, F. Chen, P. Liddell, J. Andr´easson, S D Straight, D. Gust, T. A. Moore, A. L. Moore, J. Li, O. F Sankeyand S. M. Lindsay Current–voltage data (open circles) for (a) open molecules 1o and (b) closed molecules 1c

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

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

29. Electron transfer in DNA

30. DNA-news-1

31. DNA-news-4

32. DNS-news-3

33. DNA-news-2

34. Conjugated vs. Saturated Molecules: Importance of Contact Bonding Au// S/Au Au/S S/Au Kushmerick et al., PRL (2002) negative bias Positive bias 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

35. Lindsay & Ratner 2007

36. 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

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

38. Experiment Theoretical Model

39. Experimental i/V behavior

40. 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.

41. Potential distribution

42. NEGF - HF calculation

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

44. B A A B

45.  L Single molecule vs. molecular layer With Galperin, Ingold and Grabert J. Chem. Phys., 117, 10837-41 (2002)

46. Xu and Tao, Science, 301, 1221 (2003) (D) A conductance histogram obtained from 1000 measurements shows peaks near 1 , 2 , and 3 0.01 G0 that are ascribed to one, two, and three molecules, respectively. (F) In the absence of molecules, no such steps or peaks are observed within the same conductance range.

47. Cui et al (Science 2001): The sulfur atoms (red dots) of octanethiols bind to a sheet of gold atoms (yellow dots), and the octyl chains (black dots) form a monolayer. The second sulfur atom of a 1,8-octanedithiol molecule inserted into the monolayer binds to a gold nanoparticle, which in turn is contacted by the gold tip of the conducting AFM.

48. J. G. Kushmerick et al., Nano Lett. 3, 897 (2003). A. S. Blum, J. G. Kushmerick, et al., The J. Phys. Chem. B 108, 18124 (2004).

49. A. Salomon, D. Cahen, S. M. Lindsay, et al., Advanced Materials 15, 1881 (2003).

50. Red – single molecule; black – molecular layer. Dashed black is molecular layer per molecule 1-nitro-2,5-di(phenylethynyl- 4’-mercapto)benzene Red – single molecule; black – molecular layer per molecule Y. Selzer et al., Nano Letters 5, 61 (2005).