© A. Nitzan, TAU PART B: Molecular conduction: Main results and phenomenology A. Nitzan ( ; ) PART A: Introduction: electron transfer in molecular systems PART C: Inelastic effects in molecular conduction Introduction to electron transport in molecular systems (X=A,B,C)

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

© A. Nitzan, TAU log e of GCGC(AT)mGCGC conductance vs length (total number of base pairs). The solid line is a linear fit that reflects the exponential dependence of the conductance on length. The decay constant,, is determined from the slope of the linear fit. (b) Conductance of (GC)n vs 1/length (in total base pairs). Xu et al (Tao), NanoLet (2004)  =0.43Å -1

© 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

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

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

© A. Nitzan, TAU 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: pumpingdamping

© A. Nitzan, TAU Resonant tunneling V 1r V 1l

© A. Nitzan, TAU Resonant Tunneling Transmission Coefficient

© 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

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

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

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

© A. Nitzan, TAU “The resistance of a single octanedithiol molecule was 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)

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

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

© A. Nitzan, TAU ET vs Conduction

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

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

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

© 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

© A. Nitzan, TAU I / arb. units I V (V) Ratner and Troisi, 2004

© A. Nitzan, TAU “Switching”

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

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

© 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

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

© A. Nitzan, TAU Experiment Theoretical Model

© A. Nitzan, TAU Experimental i/V behavior

© A. Nitzan, TAU Potential distribution

© A. Nitzan, TAU NEGF - HF calculation

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

© 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

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

© 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

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

© A. Nitzan, TAU incident scattered Light Scattering

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

© 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

© 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.

© 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

© 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

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

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

© A. Nitzan, TAU Changing tip- molecule distance

© 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