¶ bridge-assisted electron transfer
https://wires.onlinelibrary.wiley.com/doi/full/10.1002/wcms.1102?saml_referrer
¶ Model
Molecular and bulk level charge-transfer processes are well understood.
- However, characterization of processes on the nanoscale (1 to 100 nm) is in its early stages
Ratner's Donor−Bridge−Acceptor classification provides a framework for nanoscale charge-transfer processes.
- A bridge may function as a spacer or a wire and may comprise a molecule or a nanoparticle
- Within this framework the charge transfer is viewed as proceeding from a donor to an acceptor via a bridge or a wire
- The donor and / or acceptor may be a molecule or an electrode
There are two major types of charge transfers
- Excess Electron Transfer ( EET )
- Hole Transfer ( HT )
Three major mechanisms for charge transfer are presently in focus
1. Electron hopping
- Multistep charge transport involves charge injection from d* (or d+) to {Bj}, charge hopping within {Bj}, and charge trapping by a
- phonon-assisted or local vibrationally assisted ET between neighboring sites with relaxation of the energy in each state proceed sequentially, with activation of each transition to a subsequent state
- Key features are low electronic energies of the intermediate states and strong interaction with the vibrational system.
2. ET in the superexchange mode
- The energy levels of the intermediate states in superexchange are strongly off-resonance of the energy of the tunneling electron, and the interaction with the environment is weaker
3. “direct” tunneling
- Happens when the contribution of the intermediate states is negligible
- The bridge molecule in direct tunneling simply represents a barrier for electron, which is, however, lower than that in the absence of the bridge because of long-range electrostatic or short-range interactions of the tunneling electron with the bridge molecule, e.g., the interactions with the polarization of the molecule.
increasingly systems of interest involve the tip of a scanning tunneling microscope (STM) as one electrode.
- The STM tip−bridge−bulk electrode has been studied, usually with nonbonded interactions between tip and molecule and nonbonded interactions between molecule and bulk electrode.
- The STM tip−bridge−nanoparticle combination has also been studied recently, 15,16 typically with a bonded interaction between the nanoparticle and bridge, although a Coulombic bonding is also possible
In a number of these studies the charge-transfer process is accompanied by a charging process and double-layer effects
It was shown that electron transport in a “molecular wire’, characterised by a conjugated π system and having a relatively rigid-rod structure, could be switched from coherent superexchange tunnelling at low temperatures to incoherent temperature dependent hopping at higher temperatures
control of molecular conformation at the metal-molecule interface offers possibilities to realise molecular rectifiers through, for instance, electrical field or current driven switching between conformers
On the theoretical side, the transport properties of small molecules cannot be modeled by solving Boltzmann’s equation as is done in conventional electronics. Transport properties must be calculated directly from electron wave func- tions using a full quantum-mechanical treatment. So far, only semiempirical approaches have been employed to investigate transport in molecular systems, providing useful insights into the fundamental mechanism
the molecule behaves as a resonant-tunneling transistor and b no charging effect occurs in the molecule because the elec- trons do not spend enough time in the device to prevent additional charge from entering the molecule.
We have found that the effects of charge redistribution as a function of molecular configuration and/or external field are important, since the mismatch between the work functions of Au and molecular bridge results in a considerable charge flow between the molecule and gold electrodes. Without external bias, the lowest unoccupied molecular orbital LUMO lies closer to the Fermi level of Au compared to the highest oc- cupied molecular orbital HOMO. The current through the molecule strongly depends on both the tilting angle and the self-consistent charge redistribution across the molecule
If the system has two contacts, its electronic conductivity can be measured in situ as a function of the charge carrier density that is varied by the electrochemical potential. This is called electrochemical gating.
¶ Theory
Current is determined as a function of tip position and potential bias. While nuclear factors introduce an activation barrier to charge-transport kinetics, the conductance can be expected to be dominated by electronic overlaps
A particular dynamical issue of central importance in charge transport is the role of tunneling of carriers between contacts and extended molecular spacers.
- A number of specialized, formal models for such tunneling are available in the chemistry and physics literature,7,8,29-33 but their applicability to realistic situations of chemical complexity requires specification of crucial energy (gaps) and electronic (transfer integrals) parameters.
ET is viewed as a molecular conduction process and one measures the voltage dependence of an electrical current between electrodes connected by DNA or its analogues.
- so there are two ways for conduction of the bridge, the hole transfer and the excess electron transfer
- in both cases, a hole or electron will travel across the bridge to carry the charge
The superexchange mechanism is characterized by the rapid exponential decay of the ET rate
Which mechanism, direct electron tunneling or multistep hopping, will dominate can be qualitatively explored in terms of three quantities the driving force ΔG°, the energy gap between donor and bridge Δbarrier shown on Figure 2, and the donor–acceptor distance Rda.
Note that for charge hopping, d+ba → dba+, ΔG is (almost) independent of the donor–acceptor distance; by contrast, for charge separation dba → d+ba− or charge recombination d+ba− → dba, the Coulomb interaction of d+ and a−, proportional to 1/Rda, contributes to ΔG
ΔE12 of hole transformed is estimated as a difference of the HOMO (highest occupied molecular orbital) and HOMO−1 energies
The driving force for EET is expressed through the difference of electron affinities (EAs) of donor and acceptor. The orbital energies of LUMO (lowest unoccupied molecular orbital) and LUMO+1 of neutral stacks may be used to estimate the driving force of EET
The driving force of HT and EET through is affected by counterions and solvent.
- hole migration is gated by dynamics of the counterions
- simulation24 showed, however, that the local distribution of water molecules and their dynamics has a stronger impact on HT than counterions
- In both systems, with and without counterions, the total fractions of time, when A+ states are of lower energy than G+, are found to be similar. This result clearly suggests that water molecules rather than surrounding counterions affect the HT process in DNA.
By definition, electronic coupling Vda of donor and acceptor is equal to half of the splitting ΔE12 = E2 − E1 of adiabatic energies calculated at the crossing point
- The electronic coupling for symmetry-equivalent donor and acceptor can be estimated as one-half of the energy gap ΔE12 between adiabatic states calculated at a reasonable geometry of the system, Vda = ½ ΔE12
In general, EET couplings are found to be considerably smaller than the corresponding values for HT
The more extended the wave function, the better the conductance of the material.
- Delocalization of an excess charge over adjacent sites is controlled by the interplay between site energies, electronic couplings, and the reorganization energy
- It was found that the excess charge distribution in the ground and excited states of radical cations and radical anions is well described by Kohn–Sham orbitals of neutral dimers
- The interaction with polar environment is found to affects considerably the charge distribution in DNA resulting in more localized hole states
single-molecule bridge-mediated electronic nanojunctions
- These junctions may operate electrolyte solution
- The conducting orbitals of target molecules should be energetically well below electronic levels of the solvent
A key feature for these junctions is rectification in the current–voltage relation
- A common view is that asymmetric molecules or asymmetric links to the electrodes are needed to acquire rectification
- However, a structurally symmetric system can provide rectification because of the Debye screening of the electric field in the nanogap if the screening length is smaller than the bridge length
The prevailing mechanism depends on the electronic structure of the molecule and electrodes and on the environment
- It is not always straightforward to assert which mechanism dominates in a given junction
- Theory that offers distinct expressions for the current across the junction as a function of bias voltage, overpotential, temperature, length of the molecule, etc., may therefore shed light on the actual mechanism. In this work, we will study the superexchange mechanism.
Initially, the electronic states of the bridge groups were regarded as independent of the reactive modes
- However, it has become clear recently that nuclear configurational fluctuations, at least for flexible molecules, may strongly affect the single-molecule conductance through the dependence of the electronic tunneling factor (“matrix element”) on the nuclear configuration of both the molecule and the environment
The nuclear modes thus affect
- the overlap of the molecular orbitals of neighboring groups
- electronic energy levels
- dependence of the energy level of the bridge group on the reactive modes may affect strongly the activation energy of reaction
Our study thus offers a way toward building controllable single-molecule rectifying devices without involving asymmetric molecular structures.
building and tuning in situ (in operando) rectification in two symmetric molecular structures in electrochemical environment
- The molecules were designed to conduct electronically via either their LUMO ( electron transfer) or HOMO ( hole transfer )
rectification originates first from the asymmetric energy barrier height at positive and negative bias created by independent tuning of the tip and substrate electrochemical potentials
- the bias voltage variation was shown to depend strongly on the ionic strength in the electrochemically controlled tunneling gap to reinforce the rectification more strongly the higher the ionic strength or shorter the Debye or Gouy screening lengths