1. A. Nitzan, Tel Aviv University The Abdus Salam African College on Science at the Nanoscale Cape Town, November 2007 1. Relaxation, reactions and electron transfer in condensed molecular systems 2. Fundamentals of molecular conduction 3. Inelastic effects in electron transfer and molecular conduction

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 Fabrication Stability Characterization Funcionality Control

7. FABRICATION Nanopore Reed et al. APL 71 (97) Molecule lying on a surface Molecule between two electrodes: Break junction : 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 Nanotube on Au Lieber et al. Nature 391 (98) Van Ruitenbeek, Wittenberg Lectures 2004

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

9. AN, Oxford University Press, 2006 Cape Town, November 2006 (1a) 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 (1b) 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 (2) 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 (3) Inelastic effects in molecular conduction Dependence on nuclear configurations Electron-vibration coupling Timescales Coherent and incoherent transport Heating Current induced nuclear changes Heat conduction Inelastic tunneling spectroscopy

10. 1A Relaxation and reactions in molecular systems

11. The importance of timescales

12. 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 Electronic 10 -16 -10 -15 s Vibraional period 10 -14 s Vibrational xxxxrelaxation 1-10 -12 s Diffusion D~10 -5 cm 2 /s 10nm 10- 7 - 10 -8 s Chemical reactions xxxxxxxxx10 12 -10 -12 s Rotational period 10 -12 s Collision times 10 -12 s

13. 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

14. 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)).

15. Frequency dependent friction WIDE BAND APPROXIMATION MARKOVIAN LIMIT

16. 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

17. 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 Poisson equation

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

19. “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

20. 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)

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

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

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

24. excitation reaction Thermal interactions Unimolecular reactions (Lindemann)

25. Activated rate processes KRAMERS THEORY: Low friction limit High friction limit Transition State theory (action) Diffusion controlled rates 00 BB

26. 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

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

28. 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

29. Quantum considerations 1 in the classical case

30. Cape Town, November 2006 (1a) 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

32. A. Nitzan, Tel Aviv University The Abdus Salam African College on Science at the Nanoscale Cape Town, November 2007 1. Relaxation, reactions and electron transfer in condensed molecular systems 2. Fundamentals of molecular conduction 3. Inelastic effects in electron transfer and molecular conduction

33. Cape Town, November 2006 (1a) 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

34. The importance of timescales

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

36. Activated rate processes KRAMERS THEORY: Low friction limit High friction limit Transition State theory (action) Diffusion controlled rates 00 BB

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

38. Quantum considerations 1 in the classical case

39. PART 1B Electron transfer

40. (1b) 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 Cape Town, November 2006

41. Theory of Electron Transfer Rate – Transition state theory Rate – Transition state theory Transition rate Boltzmann Boltzmann Activation energy Activation energy Transition probability Transition probability

42. 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

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

44. Electron transfer Solvent polarization coordinate EAEA

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

46. 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 

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

48. 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.   

49. Electron transfer: Activation energy Reorganization energy Activation energy

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

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

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

53. Bridge assisted electron transfer EBEB

54. V DB D A B V AD EE D A V eff

55. V DB D A B1B1 V AD D A EE V eff B2B2 BNBN … V 12 Green’s Function

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

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

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

59. Incoherent hopping constant STEADY STATE SOLUTION

60. ET rate from steady state hopping

61. 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.

62. The photosythetic reaction center Michel - Beyerle et al

63. Dependence on bridge length

64. DNA (Giese et al 2001)

65. ELECTROCHEMISTRY

66. 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

67. (1b) 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 AN, Oxford University Press, 2006 Cape Town, November 2006

69. A. Nitzan, Tel Aviv University The Abdus Salam African College on Science at the Nanoscale Cape Town, November 2007 1. Relaxation, reactions and electron transfer in condensed molecular systems 2. Fundamentals of molecular conduction 3. Inelastic effects in electron transfer and molecular conduction

70. Cape Town, November 2006 (1a) 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

71. (1b) 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 Cape Town, November 2006

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

73. Electron transfer rate Bridge mediated electron transfer

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

75. Incoherent hopping

76. 2 Molecular conduction

77. (2) 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 Electron transfer by hopping Inelastic tunneling spectroscopy Chapter 17 AN, Oxford University Press, 2006 Cape Town, November 2006

78. 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

79. 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:

80. pumping damping

81. Resonance scattering V 1r V 1l

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

83. Resonance scattering For each r and l

84. SELF ENERGY

85. V 1r V 1l

86. Resonant tunneling V 1r V 1l V 10

87. Resonant Tunneling Transmission Coefficient

88. 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)

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

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

91. f L (E) – f R (E) T(E) ee f L (E) – f R (E) T(E) ee I  Weber et al, Chem. Phys. 2002 g

92. Molecular level structure between electrodes LUMO HOMO

93. GATING IONIC GATING

94. “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)

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

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

97. ET vs Conduction

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

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

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

101. 2-level bridge (local representation) Dependence on: Molecule-electrode coupling  L,  R Molecular energetics E 1, E 2 Intramolecular coupling V 1,2

102. 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

103. Temperature and chain length dependence Giese et al, 2002 Michel- Beyerle et al Xue and Ratner 2003 M. Poot et al (Van der Zant), Nanolet 2006

104. Barrier dynamics effects on electron transmission through molecular wires HEAT CONDUCTION -- RECTIFICATION INELASTIC TUNNELING SPECTROSCOPY STRONG e-ph COUPLING: (a) resonance inelastic tunneling spectroscopy (b) multistability and hysteresis NOISE RELEVANT TIMESCALES INELASTIC CONTRIBUTIONS TO CURRENT DEPHASING AND ACTIVATION HEATING

105. INELSTIC ELECTRON TUNNELING SPECTROSCOPY

106. incident scattered Light Scattering

107. Localization of Inelastic Tunneling and the Determination of Atomic-Scale Structure with Chemical Specificity B.C.Stipe, M.A.Rezaei and W. Ho, PRL, 82, 1724 (1999) STM image (a) and single-molecule vibrational spectra (b) of three acetylene isotopes on Cu(100) at 8 K. The vibrational spectra on Ni(100)are shown in (c). The imaged area in (a), 56Å x 56Å, was scanned at 50 mV sample bias and 1nA tunneling current

108. Electronic Resonance and Symmetry in Single- Molecule Inelastic Electron Tunneling J.R.Hahn,H.J.Lee,and W.Ho, PRL 85, 1914 (2000) Single molecule vibrational spectra obtained by STM-IETS for 16 O 2 (curve a), 18 O 2 (curve b), and the clean Ag(110)surface (curve c).The O2 spectra were taken over a position 1.6 Å from the molecular center along the [001] axis. The feature at 82.0 (76.6)meV for 16 O 2 ( 18 O 2 ) is assigned to the O-O stretch vibration, in close agreement with the values of 80 meV for 16O2 obtained by EELS. The symmetric O2 -Ag stretch (30 meV for 16O2) was not observed.The vibrational feature at 38.3 (35.8)meV for 16 O 2 ( 18 O 2 )is attributed to the antisymmetric O 2 -Ag stretch vibration.

109. Inelastic Electron Tunneling Spectroscopy of Alkanedithiol Self-Assembled Monolayers W. Wang, T. Lee, I. Kretzschmar and M. A. Reed (Yale, 2004) Inelastic electron tunneling spectra of C8 dithiol SAM obtained from lock-in second harmonic measurements with an AC modulation of 8.7 mV (RMS value) at a frequency of 503 Hz (T =4.2 K).Peaks labeled *are most probably background due to the encasing Si3N4 Nano letters, 2004

110. INELSTIC ELECTRON TUNNELING SPECTROSCOPY

111. INELASTIC ELECTRON TUNNELING SPECTROSCOPY

112. Conductance of Small Molecular Junctions N.B.Zhitenev, H.Meng and Z.Bao PRL 88, 226801 (2002) Conductance of the T3 sample as a function of source-drain bias at T =4.2 K. The steps in conductance are spaced by 22 mV. Left inset: conductance vs source-drain bias curves taken at different temperatures for the T3 sample (the room temperature curve is not shown because of large switching noise). Right inset: differential conductance vs source-drain bias measured for two different T3 samples at T = 4.2 K. 38mV 22 125 35,45,24

113. AN, Oxford University Press, 2006 SUMMARY (1a) 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 (1b) 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 (2) 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 Electronic conduction by hopping Inelastic tunneling spectroscopy Chapter 13-15Chapter 16 Chapter 17 THANK YOU A. Nitzan, Tel Aviv University INTRODUCTION TO ELECTRON TRANSFER AND MOLRCULAR CONDUCTION Download: http://atto.tau.ac.il/~nitzan/Capehttp://atto.tau.ac.il/~nitzan/Cape Town 07.ppt