A. Nitzan, Tel Aviv University ELECTRON TRANSFER AND TRANSMISSION IN MOLECULES AND MOLECULAR JUNCTIONS AEC, Grenoble, Sept 2005. Lecture 4. Grenoble Sept 2005. (1) Relaxation and reactions in condensed molecular systems Kinetic models Transition state theory
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ELECTRON TRANSFER AND TRANSMISSION IN MOLECULES AND MOLECULAR JUNCTIONS
AEC, Grenoble, Sept 2005
Coming March 2006
Coming March 2006
Coming March 2006
Donor gives an electron and goes from state “a” (reduced) to state “b” (oxidized). Eb,a=Eb-Ea is the energy of the electron given to the metal
Transition rate to a continuum (Golden Rule)
Rate of electron transfer to metal in vacuum
Rate of electron transfer to metal in electrolyte solution
Reorganization energy here – from donor only (~0.5 of “regular” value)
For a single “channel”:
Maximum conductance per channel
Unit matrix in the bridge space
B(R) + B(L) -- Self energy
Wide band approximation
“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”.
Electron transfer rate
Decay into electrodes
Or at T=300K.
Issues in molecular conductions
I / arb. units
Ratner and Troisi, 2004
Tsai et. al. PRL 1992: RTS in Me-SiO2-Si junctions
STM under waterS.Boussaad et. al. JCP (2003)
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.
Michel-Beyerle et al
Xue and Ratner 2003
Selzer et al 2004Temperature and chain length dependence
Especially of the future ”
attributed to Niels Bohr
Conjugated vs. Saturated Molecules: Importance of Contact Bonding
Kushmerick et al., PRL (2002)
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!
Xue, Ratner (2003)
Galperin et al JCP 2003Where does the potential bias falls, and how?
Galperin et al 2003
D. Segal, AN, JCP 2002 Heat Release on junction
aCurrent at the negative bias refers to the measurement with the Hg side of the junction biased negative relative to the Au side.
Does the tunneling electron interact with other degrees of freedom and what are the possible consequences of this interaction?
The case of electron tunneling in water
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.
Electron-Water..............Barnett et al +correction for many body polarizability
Water-Wall........Henziker et al (W-Pt), Hautman et al (W-Au)
Earlier studies – Tunneling through static water configurations
Fig. 1. A model system used to compute electron transmission between two electrodes, L and R separated by a narrow spatial gap (M) containing a molecular species. The surface S1 of L is shaped to mimic a tip. The lines A'B', C'D' and AB and CD are projections of boundary surfaces normal to the transmission direction (see text for details). The numerical solution is carried on a grid (Shown).
A cut of the external potential distribution between the tip and the flat substrate for a voltage drop of 0.5V between these electrodes
The image potential along different lines normal to the flat electrode: (1) x=0 (a line going through the tip axis); (2) x=11.96au (distance from the tip axis); (3) x=23.92au.
Figure - Ohmine et al
Absorbing boundary conditions Green's function method: Replace by i(r), smoothly rising towards edges of M system, provided LM and MR boundaries are set far enough
Current against bias voltage in a biased tip-planar electrode junction under water. Upper and lower lines are results for single water configurations characterized by tip-substrate separation of 5.85Å (2 water monolayers) and 12.15Å(4 water monolayers), respectively. The intermediate group of lines are results for 5 different water configurations at tip-substrate separation 9Å (3 water monolayers).
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.