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

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

6. Landauer formula (maximum=1) Maximum conductance per channel For a single “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. “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”. Cui et al (Lindsay), Science 294, 571 (2001)

10. ET vs Conduction

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

12. A relation between g and k  eV

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. PART D Issues in molecular conductions A. Nitzan Boulder Aug 2007 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. (Original picture from Datta et al) THE IDEAL EXPERIMENT T1T1 T2T2 Inject and detect Light Temperature measurement and control Control type and number of molecule Molecule(s) REPRODUCIBLE! A Current measurement vs. V and Vg

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

19. 2-level bridge (local representation) Dependence on: Molecule-electrode coupling  L,  R Molecular energetics E 1, E 2 Intramolecular coupling V 1,2

20. 0 1 2 3 4 5 6 -0.500.51 I / arb. units 0.0 - 0.5 0.5 I V (V) Ratner and Troisi, 2004

21. “Switching”

22. Switching Conformational changes Conformational changes Tsai et. al. Appl.Phys.Lett 1992: Random telegraph signals in Me-SiO 2 - Si junctions Transient charging Transient charging STM under water S.Boussaad et. al. JCP (2003) time Polaron formation Polaron formation Time (s) Tip height Moore et al (P.S. Weiss) Conduction switching in Oligo(phenylene ethynylene) molecules (nitro functionalized)

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. 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. [Ca +2 ]=1x10 -6 M I. Inoue et al, Journal of Physiology 541.3, pp. 769-778(2002)

25. 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.” Switching with light

26. Current–voltage data (open circles) for (a) open molecules 1o and (b) closed molecules 1c 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 Sankey and S. M. Lindsay

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

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 Kushmerick et al., PRL (2002) 2- vs. 1-side Au-S bonded conjugated system gives at most 1 order of magnitude current increase compared to 3 orders for C 10 alkanes! S/AuAu/S S/AuAu// Au//CH 3 (CH 2 ) 7 S/Au Au/S(CH 2 ) 8 SAu Positive bias negative bias

35. Lindsay & Ratner 2007

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

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

38. Experiment Theoretical Model

39. Experimental i/V behavior

40. Experimental (Sek&Majda) a Current 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 - CH 2 CH 2 CH 2 CH 2 CH 2 CH 3... CH 3 CH 2 - SH MO Segment Orbital

44. A B A B

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

46. (D) A conductance histogram obtained from 1000 measurements shows peaks near 1, 2, and 3 0.01 G 0 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. Xu and Tao, Science, 301, 1221 (2003)

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

51. 3,4,9,10-perylenetetracarboxylicacid- Dianhydride (PTCDA) on silver(111) Analysis yields: effective mass m eff =0.43m ee Temirov et al, Nature Vol 444 (2006)

52. [1]Yaliraki S N and Ratner M A, Molecule-interface coupling effects on electronic transport in molecular wires J. Chem. Phys. 109 5036-43 (1998) [2]Magoga M and Joachim C, Conductance of molecular wires connected or bonded in parallel Phys. Rev. B-Condens Matter 59 16011-21( 1999) [3]Lang N D and Avouris P, Electrical conductance of parallel atomic wires Phys. Rev. B-Condens Matter 62 7325 (2000) [4]Kim Y-H, Tahir-Kheli J, Schultz P A, Goddard W A and Iii 2006 First-principles approach to the charge-transport characteristics of monolayer molecular-electronics devices: Application to hexanedithiolate devices Phys. Rev. B (Condensed Matter and Materials Physics) 73 235419 * Weak effect * strong effect

53. Probes of different sizes see different numbers of molecule Molecular layers and islands Observations of single molecule behavior does not necessarily imply single molecules

54. Slopes: 1.15, 1.48, and 1.55 are found for the “small”, “medium”, and “large” clusters, respectively. The larger than unity slope indicates a dipole enhancement, with the effect increasing with increasing cluster size.” D. Deutsch, A. Natan, Y. Shapira and L. Kronik, JACS, 2/2007 Natan, A.; Zidon, Y.; Shapira, Y.; Kronik, L. Phys. ReV. B 2006, 73, 193310. The smaller than unity slope indicates a dipole reduction, with the effect increasing with increasing coverage

55. 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

56. Overbarrier electron transmission through water (D 2 O on Pt(1,1,1)

57. A look from above on a water film

58. 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.

59. The numerical problem (1)Get a potential (2)Electrostatics (3)Generate Water configurations (4)Tunneling calculations (5)Integrate to get current

60. 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

61. 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 S 1 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).

62. 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.

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

64. CALCULATION OF TRANSMISSION FACTORS

65. 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

66. Tunneling current in water Current against bias voltage in a biased tip-planar electrode junction under water. Upper and lower lines are results for single water configurations characterized by tip-substrate separation of 5.85Å (2 water monolayers) and 12.15Å (4 water monolayers), respectively. The intermediate group of lines are results for 5 different water configurations at tip-substrate separation 9Å (3 water monolayers).

67. V 1r V 1l Resonant tunneling?

68. Resonance transmission through water

69. Tunneling supporting structures in water

70. Transmission through several water configurations (equilibrium, 300K) A compilation of numerical results for the transmission probability as a function of incident electron energy, obtained for 20 water configurations sampled from an equilibrium trajectory (300K) of water between two planar parallel Pt(100) planes separated by 10Å. The vacuum is 5eV and the resonance structure seen in the range of 1eV below it varies strongly between any two configurations. Image potential effects are disregarded in this calculation.