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Lecture 5

A. Nitzan, Tel Aviv University SELECTED TOPICS IN CHEMICAL DYNAMICS IN CONDENSED SYSTEMS Boulder, Aug 2007. Lecture 5. Boulder Aug 2007. (1) Relaxation and reactions in condensed molecular systems Kinetic models Transition state theory Kramers theory and its extensions

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Lecture 5

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  1. A. Nitzan, Tel Aviv University SELECTED TOPICS IN CHEMICAL DYNAMICS IN CONDENSED SYSTEMS Boulder, Aug 2007 Lecture 5

  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 Coming March 2006 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 Coming March 2006 Chapter 16

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

  6. 2-level bridge (local representation) • Dependence on: • Molecule-electrode coupling GL , GR • Molecular energetics E1, E2 • Intramolecular coupling V1,2

  7. 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)

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

  9. 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

  10. 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

  11. Potential distribution

  12. NEGF - HF calculation

  13. PART E Inelastic effects in molecular conductions

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

  15. A look from above on a water film

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

  17. 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.

  18. Resonant tunneling? V1r V1l

  19. Resonance transmission through water

  20. Tunneling supporting structures in water

  21. 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.

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

  23. Configurations Resonance (eV)energy Decay time(fsec) 0ps (4.5029, -0.0541) 6 0ps (4.6987, -0.0545) 6 50ps (4.4243, -0.0424) 7.6 50ps (4.8217, 0.0463) 7 Electron transmission through water: Resonance Lifetimes

  24. Traversal time for tunneling? 1 2 3 4 B A

  25. Traversal Time

  26. "Tunnelling Times"

  27. For: D=10A (N=2-3) UB-E = E~1eV m=me • Notes: • Both time estimates are considerably shorter than vibrational period • Potential problem: Near resonance these times become longer Estimates

  28. Tunneling time and transmission probability Vacuum barrier

  29. Instantaneous normal modes for water The density ρ of instantaneous normal modes for bulk water systems at 60K (full line) and 300K (dotted line) shown together with the result for a water layer comprised of three monolayers of water molecules confined between two static Pt(100) surfaces, averaged over 20 configurations sampled from an equilibrium (T=300K)(dashed line). The densities of modes shown are normalized to 1.The usual convention of displaying unstable modes on the negative frequency axis is applied here.

  30. Solvation correlation functions for electron in water Linearized INM and MD solvation response functions for upward (a) and downward (b) transitions. The solid lines are the MD results obtained from the fluctuations of the energy gap, the red lines are results of INM calculation using stable normal modes,and the blue lines stand for a calculation with all modes included. (Chao- Yie Yang, Kim F. Wong, Munir S. Skaf, and Peter J. Rossky; J. Chem. Phys. 2001)

  31. Fig. 5 The ratio between the inelastic (integrated over all transmitted energies) and elastic components of the transmission probability calculated for different instantaneous structures of a water layer consisting of 3 monolayers of water molecules confined between two Pt(100) surfaces. Vacuum barrier

  32. Barrier dynamics effects on electron transmission through molecular wires • Relevant timescales • Inelastic contributions to the tunneling current • Dephasing and activation • Heating of current carrying molecular wires • HEAT CONDUCTION -- RECTIFICATION • INELASTIC TUNNELING SPECTROSCOPY • MULTISTABILITY AND HYSTERESIS • LIGHTNOISE

  33. INELSTIC ELECTRON TUNNELING SPECTROSCOPY

  34. What is typically observed Negative signals possible too

  35. Light Scattering incident scattered

  36. 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 Recall: van Ruitenbeek et al (Pt/H2)- dips

  37. Electronic Resonance and Symmetry in Single-Molecule Inelastic Electron TunnelingJ.R.Hahn,H.J.Lee,and W.Ho, PRL 85, 1914 (2000) Single molecule vibrational spectra obtained by STM-IETS for 16O2 (curve a),18O2 (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 16O2 (18O2) 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 16O2 (18O2)is attributed to the antisymmetric O2 -Ag stretch vibration.

  38. Inelastic Electron Tunneling Spectroscopy ofAlkanedithiol Self-Assembled MonolayersW. 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, in press

  39. INELASTIC ELECTRON TUNNELING SPECTROSCOPY

  40. Conductance of Small Molecular JunctionsN.B.Zhitenev, H.Meng and Z.BaoPRL 88, 226801 (2002) 38mV 22 125 35,45,24 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.

  41. Nanomechanical oscillations in a single C60 transistorH. Park, J. Park, A.K.L. Lim, E.H. Anderson, A. P. Alivisatos and P. L. McEuen [NATURE, 407, 57 (2000)] Vsd(mV) Two-dimensional differential conductance (I/V)plots as a function of the bias voltage (V) and the gate voltage (Vg ). The dark triangular regions correspond to the conductance gap, and the bright lines represent peaks in the differential conductance. Vg(Volt)

  42. A contour map of d2I/dV2 plotted against the source-drain, and gate, potentials, obtained from a simple junction model with on-site e-e interaction U. This characteristic “diamond’ structure shows the thresholds for conduction with varying VSD and VG, and satellite peaks associated with vibrational transitions (inelastic contributions to conduction). Lower panels: An experimental realization (42) with an oligophenylenevinylene molecule an gold electrodes with an Al2O3 gate.

  43. Experimental (black) and computed (red) IETS spectra for the molecule in the inset. Blue lines indicate the computed frequency and IETS intensity of the individual modes. (A. Troisi et. al, submitted to PNAS)

  44. V Parameters Constant in the wide band approximation GL GR electrons e1 M Molecular vibrations w0 U Thermal environment M – from reorganization energy (~M2/w0) U – from vibrational relaxation rates

  45. NEGF ({ }=anticommutator)

  46. electrons M vibrations A1 A2M A3M2 elastic inelastic elastic

  47. Changing position of molecular resonance:

  48. Changing tip-molecule distance

  49. V IETS (intrinsic?) linewidth GL GR electrons e1 M Molecular vibrations w0 U Thermal environment M – from reorganization energy (~M2/w0) U – from vibrational relaxation rates

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