1. © A. Nitzan, TAU PART B: Main results and phenomenology A. Nitzan

2. © A. Nitzan, TAU Electron transfer in DNA

3. © A. Nitzan, TAU Weber et al, Chem. Phys. 2002

4. © A. Nitzan, TAU Electron transfer Electron transition takes place in unstable nuclear configurations obtained via thermal fluctuations Nuclear motion

5. © A. Nitzan, TAU Bridge assisted ET rates Bridge Green’s Function Donor-to-Bridge/ Acceptor-to-bridge Franck-Condon- weighted DOS Reorganization energy Effective donor-acceptor coupling Golden-rule- like equation

6. © A. Nitzan, TAU Electron transfer F V AD

7. © A. Nitzan, TAU Bridge mediated ET rate  ’ ( Å -1 ) = 0.2-0.6 for highly conjugated chains 0.9-1.2 for saturated hydrocarbons ~ 2 for vacuum

8. © A. Nitzan, TAU ET rate from steady state hopping Bridge length Activation to bridge Constant (k=rate on bridge)

9. © A. Nitzan, TAU A level interacting with a continnum V0lV0l Starting from state 0 at t=0: P 0 = exp(-   t)  = 2  |V sl | 2  L (Golden Rule) SELF ENERGY

10. © A. Nitzan, TAU 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) V 1r V 1l E0E0

11. © A. Nitzan, TAU CONDUCTION 2 spin states Zero bias conduction L R  L  R  e|  RR LL

12. © A. Nitzan, TAU Landauer formula (maximum=1) Maximum conductance per channel For a single “channel”:

13. © A. Nitzan, TAU Molecular level structure between electrodes LUMO HOMO

14. © A. Nitzan, TAU “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)

15. © A. Nitzan, TAU General case Unit matrix in the bridge space Bridge Hamiltonian B (R) + B (L) -- Self energy Wide band approximation

16. © A. Nitzan, TAU The N-level bridge (n.n. interactions) G 1N (E)

17. © A. Nitzan, TAU ET vs Conduction

18. © A. Nitzan, TAU A relation between g and k conductionElectron transfer rate Marcus Decay into electrodes Electron charge

19. © A. Nitzan, TAU A relation between g and k  eV

20. © A. Nitzan, TAU Comparing conduction to rates (M. Newton, 2003)

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

22. © A. Nitzan, TAU 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

23. © A. Nitzan, TAU “Switching”

24. 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

25. © A. Nitzan, TAU Temperature and chain length dependence Giese et al, 2002 Michel- Beyerle et al Selzer et al 2004 Xue and Ratner 2003

26. © A. Nitzan, TAU 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

27. © A. Nitzan, TAU Why is it important? D. Segal, AN, JCP 2002 Heat Release on junction Tian et al JCP 1998

28. © A. Nitzan, TAU Experiment Theoretical Model

29. © A. Nitzan, TAU Experimental i/V behavior

30. © A. Nitzan, TAU Potential distribution

31. © A. Nitzan, TAU NEGF - HF calculation

32. © A. Nitzan, TAU HS - CH 2 CH 2 CH 2 CH 2 CH 2 CH 3... CH 3 CH 2 - SH MO Segment Orbital

33. © A. Nitzan, TAU Electron and Phonon Transport in molecular wires Inelastic tunneling spectroscopy Relevant timescales Heating of current carrying molecular wires Inelastic contributions to the tunneling current Dephasing and activation - transition from coherent transmission to activated hoppinga (1) dissipation of electronic energy (2) Heat conduction away from junction

34. © A. Nitzan, TAU Elastic transmission vs. maximum heat generation: 

35. © A. Nitzan, TAU The quantum heat flux Bose Einstein populations for left and right baths. Transmission coefficient at frequency  With Dvira Segal and Peter Hanggi

36. © A. Nitzan, TAU Inelastic tunneling spectroscopy: Peaks and dips With Michael Galperin and Mark Ratner

37. © A. Nitzan, TAU incident scattered Light Scattering

38. © A. Nitzan, TAU INELSTIC ELECTRON TUNNELING SPECTROSCOPY V hh

39. © A. Nitzan, TAU 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

40. © A. Nitzan, TAU 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.

41. © A. Nitzan, TAU 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

42. © A. Nitzan, TAU Parameters electrons Molecular vibrations Thermal environment M U LL RR  00 V M – from reorganization energy (~M 2 /  0 ) U – from vibrational relaxation rates

43. © A. Nitzan, TAU electrons vibrations M A1A1 A2MA2M A3M2A3M2 elasticinelasticelastic

44. © A. Nitzan, TAU Changing position of molecular resonance:

45. © A. Nitzan, TAU Changing tip- molecule distance

46. © A. Nitzan, TAU Challenges and prospects  Characterization of the temperature dependence of conductance.  Characterization geometry and its evolution during transport.  Measurements with differing junction subunits (molecular conjugation, interface bonding “alligator clip” functional groups, electrodes). Use of semi-conductor electrodes  More extensive work on gating of molecular junctions. Finding other controls.  Elucidating the change in behavior from a single molecule conductance through junctions comprising a few molecules to molecular film conductors.  Effects of changing chemistry and doping on the bridge – can mechanisms be altered by chemical change, as in conducting polymers, and can we predict and control such behavior?  Characterizing transport junctions behavior in the presence of radiation.  Understanding noise  Understanding heating, heat conduction and current induced chemical changes