1. A. Nitzan, Tel Aviv University International workshop on molecular electronics Řež (near Prague), Czech Republic, June 2006 Lecture 1: Relaxation, reactions and electron transfer in condensed molecular systems (parts A and B) Lecture 2: Fundamentals of molecular conduction (Part C)

2. Molecular conduction

3. Molecular Rectifiers Arieh Aviram and Mark A. Ratner IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA Department 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.

4. Xe on Ni(110)

5. Moore’s “Law”

6. Cornell group

7. First Transport Measurements through Single Molecules Single-wall carbon nanotube on Pt Dekker et al. Nature 386(97) Nanopore Reed et al. APL 71 (97) Break junction: dithiols between gold Molecule lying on a surface Molecule between two electrodes Dorogi et al. PRB 52 (95) @ Purdue Au(111) Pt/Ir Tip SAM 1 nm ~1-2 nm Self-assembled monolayers Adsorbed molecule addressed by STM tip C 60 on gold Joachim et al. PRL 74 (95) STM tip Au Reed et al. Science 278 (97) @ Yale Nanotube on Au Lieber et al. Nature 391 (98)

8. AN, Oxford University Press, 2006 Řež, June 2006 (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 (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 (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 13-15Chapter 16 Chapter 17

9. PART A Relaxation and reactions in molecular systems

10. Molecular processes in condensed phases and interfaces Diffusion Relaxation Solvation Nuclear rerrangement Charge transfer (electron and xxxxxxxxxxxxxxxxproton) Solvent: an active spectator – energy, friction, solvation Molecular timescales Diffusion D~10 -5 cm 2 /s Electronic 10 -16 -10 -15 s Vibraional 10 -14 s Vibrational xxxxrelaxation 1-10 -12 s Chemical reactions xxxxxxxxx10 12 -10 -12 s Rotational 10 -12 s Collision times 10 -12 s

11. Molecular vibrational relaxation Relaxation in the X 2 Σ+ (ground electronic state) and A 2 Π (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)) Golden Rule  Fourier transform of bath correlation function

12. Molecular vibrational relaxation The relaxation of different vibrational levels of the ground electronic state of 16 O 2 in a solid Ar matrix. Analysis of these results indicates that the relaxation of the  < 9 levels is dominated by radiative decay and possible transfer to impurities. The relaxation of the upper levels probably takes place by the multiphonon mechanism. (From A. Salloum, H. Dubust, Chem. Phys.189, 179 (1994)).

13. Frequency dependent friction WIDE BAND APPROXIMATION MARKOVIAN LIMIT

14. Dielectric solvation 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)) Born solvation energy

15. Continuum dielectric theory of solvation How does solvent respond to a sudden change in the molecular charge distribution? Electric displacement Electric field Dielectric function Dielectric susceptibility polarization Debye dielectric relaxation model Electronic response Total (static) response Debye relaxation time

16. Continuum dielectric theory of solvation WATER:  D =10 ps  L =125 fs

17. “real” solvation 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 S 0 –in a neutral atomic solute with Lennard Jones parameters of the oxygen atom]. (From R. Jimenez et al, Nature 369, 471 (1994)). “Newton” dielectric

18. 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)

19. Electron tunneling through water 1 2 3 Polaronic state (solvated electron) Transient resonance through “structural defects”

20. Electron tunneling through water Time (ms) STM current in pure water S.Boussaad et. al. JCP (2003)

21. Chemical reactions in condensed phases  Bimolecular  Unimolecular diffusion Diffusion controlled rates R

22. excitation reaction Thermal interactions Unimolecular reactions (Lindemann)

23. Activated rate processes KRAMERS THEORY: Low friction limit High friction limit Transition State theory (action) Diffusion controlled rates

24. Effect of solvent friction 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)). TST

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

26. 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

27. Quantum considerations 1 in the classical case

28. (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 Quantum effects Chapter 13-15 AN, Oxford University Press, 2006 Řež, June 2006

29. PART B Electron transfer

30. (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 Řež, June 2006 AN, Oxford University Press, 2006

31. Theory of Electron Transfer Activation energy Activation energy Transition probability Transition probability Rate – Transition state theory Rate – Transition state theory  Rate – Solvent controlled NOTE: “solvent controlled” is the term used in this field for the Kramers low friction limit. Transition rate

32. 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

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

34. Electron transfer Solvent polarization coordinate

35. Transition state theory of electron transfer Adiabatic and non-adiabatic ET processes Landau-Zener problem Alternatively – solvent control (For harmonic diabatic surfaces (1/2)KR 2 )

36. Solvent controlled electron transfer Correlation between the fluorescence lifetime and the longitudinal dielectric relaxation time, of 6-N-(4-methylphenylamino-2-naphthalene-sulfon-N,N- dimethylamide) (TNSDMA) and 4-N,N-dimethylaminobenzonitrile (DMAB) in linear alcohol solvents. The fluorescence signal is used to monitor an electron transfer process that precedes it. The line is drawn with a slope of 1. (From E. M. Kosower and D. Huppert, Ann. Rev. Phys. Chem. 37, 127 (1986))

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

38. Electron transfer – Marcus theory  Free energy associated with a nonequilibrium fluctuation of P n “reaction coordinate” that characterizes the nuclear polarization

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

40. Electron transfer: Activation energy Reorganization energy Activation energy

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

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

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

44. Bridge assisted electron transfer EBEB

46. Effective donor-acceptor coupling

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

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

49. Bridge mediated ET rate Charge recombination lifetimes in the compounds shown in the inset in dioxane solvent. (J. M. Warman et al, Adv. Chem. Phys. Vol 106, 1999). The process starts with a photoinduced electron transfer – a charge separation process. The lifetimes shown are for the back electron transfer (charge recombination) process.

50. Incoherent hopping constant STEADY STATE SOLUTION

51. ET rate from steady state hopping

52. 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.

53. The photosythetic reaction center Michel - Beyerle et al

54. Dependence on bridge length

55. DNA (Giese et al 2001)

56. ELECTROCHEMISTRY

57. 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

58. PART C Molecular conduction

59. (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 AN, Oxford University Press, 2006 Řež, June 2006

60. Steady state evaluation of rates Rate of water flow depends linearly on water height in the cylinder Two ways to get the rate of water flowing out: (1)Measure h(t) and get the rate coefficient from k=(1/h)dh/dt (1)Keep h constant and measure the steady state outwards water flux J. Get the rate from k=J/h = Steady state rate h

61. Steady state quantum mechanics V0lV0l Starting from state 0 at t=0: P 0 = exp(-   t)   = 2  |V 0l | 2  L (Golden Rule) Steady state derivation:

62. pumping damping

63. Resonance scattering V 1r V 1l

64. Resonance scattering j = 0, 1, {l}, {r} For each r and l

65. Resonance scattering For each r and l

66. SELF ENERGY

67. V 1r V 1l

68. Resonant tunneling V 1r V 1l

69. Resonant Tunneling Transmission Coefficient

71. Resonant Transmission – 3d 1d 3d: Total flux from L to R at energy E 0 : If the continua are associated with a metal electrode at thermal equilibrium than (Fermi-Dirac distribution)

72. CONDUCTION 2 spin states Zero bias conduction L R  –  e|   f(E 0 ) (Fermi function)

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

74. Molecular level structure between electrodes LUMO HOMO

75. “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)

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

77. The N-level bridge (n.n. interactions) G 1N (E)

78. ET vs Conduction

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

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

81. Comparing conduction to rates (M. Newton, 2003)

82. 2-level bridge (local representation) Dependence on: Molecule-electrode coupling  L,  R Molecular energetics E 1, E 2 Intramolecular coupling V 1,2

83. 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

84. “Switching”

85. Reasons for switching Conformational changes Conformational changes STM under water S.Boussaad et. al. JCP (2003) Tsai et. al. PRL 1992: RTS in Me-SiO 2 -Si junctions Transient charging Transient charging time Polaron formation Polaron formation

86. 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)

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

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

89. Electron transfer in DNA

90. Conjugated vs. Saturated Molecules: Importance of Contact Bonding Kushmerick et al., PRL (2002) – positive bias --negative bias 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

91. 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

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

93. Experiment Theoretical Model

94. Experimental i/V behavior

95. 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.

96. Potential distribution

97. NEGF - HF calculation

98. HS - CH 2 CH 2 CH 2 CH 2 CH 2 CH 3... CH 3 CH 2 - SH MO Segment Orbital

99. A B A B

100. AN, Oxford University Press, 2006 SUMMARY (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 (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 (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 13-15Chapter 16 Chapter 17 THANK YOU A. Nitzan, Tel Aviv University INTRODUCTION TO ELECTRON TRANSFER AND MOLRCULAR CONDUCTION

102. THANK YOU A. Nitzan, Tel Aviv University INTRODUCTION TO ELECTRON TRANSFER AND MOLRCULAR CONDUCTION

103. AN, Oxford University Press, 2006 SUMMARY (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 (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 (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 13-15Chapter 16 Chapter 17

104. S S SS