Interpretation of molecular electron transport in ab initio many-electron framework incorporating zero-point nuclear motion effects

A computational methodology, founded on chemical concepts, is presented for interpreting the role of nuclear motion in the electron transport through single-molecule junctions (SMJ) using many-electron ab initio quantum chemical calculations. Within this approach the many-electron states of the system, computed at the SOS-ADC(2) level, are followed along the individual normal modes of the encapsulated molecules. The inspection of the changes in the partial charge distribution of the many-electron states allows the quantification of the electron transport and the estimation of transmission probabilities. This analysis improves the understanding of the relationship between internal motions and electron transport. Two SMJ model systems are studied for validation purposes, constructed from a conductor (BDA, benzene-1,4-diamine) and an insulator molecule (DABCO, 1,4-diazabicyclo[2.2.2]octane). The trends of the resulting transmission probabilities are in agreement with the experimental observations, demonstrating the capability of the approach to distinguish between conductor and insulator type systems, thereby offering a straightforward and cost-effective tool for such classifications via quantum chemical calculations.

Optimal tree tensor network operators for tensor network simulations: Applications to open quantum systems

Tree tensor network states (TTNS) decompose the system wavefunction to the product of low-rank tensors based on the tree topology, serving as the foundation of the multi-layer multi-configuration time-dependent Hartree method. In this work, we present an algorithm that automatically constructs the optimal and exact tree tensor network operators (TTNO) for any sum-of-product symbolic quantum operator. The construction is based on the minimum vertex cover of a bipartite graph. With the optimal TTNO, we simulate open quantum systems, such as spin relaxation dynamics in the spin-boson model and charge transport in molecular junctions. In these simulations, the environment is treated as discrete modes and its wavefunction is evolved on equal footing with the system. We employ the Cole-Davidson spectral density to model the glassy phonon environment and incorporate temperature effects via thermo-field dynamics. Our results show that the computational cost scales linearly with the number of discretized modes, demonstrating the efficiency of our approach.

Tuning charge transport by manipulating concentration dependent single-molecule absorption configurations

Understanding and tuning charge transport in molecular junctions is pivotal for crafting molecular devices with tailored functionalities. Here, we report a novel approach to manipulate the absorption configuration within a 4,4'-bipyridine (4,4'-BPY) molecular junction, utilizing the scanning tunneling microscope break junction technique in a concentration-dependent manner. Single-molecule conductance measurements demonstrate that the molecular junctions exhibit a significant concentration dependence, with a transition from high conductance (HC) to low conductance (LC) states as the concentration decreases. Moreover, we identified an additional conductance state in the molecular junctions besides already known HC and LC states. Flicker noise analysis and theoretical calculations provided valuable insights into the underlying charge transport mechanisms and single-molecule absorption configurations concerning varying concentrations. These findings contribute to a fundamental comprehension of charge transport in concentration-dependent molecular junctions. Furthermore, they offer promising prospects for controlling single-molecule adsorption configurations, thereby paving the way for future molecular devices.

Squeezed Protons and Infrared Plasmonic Resonance Energy Transfer

Unusual nuclear quantum effects may emerge near noble metal nanostructures such as squeezed vibrational states in molecular junctions and plasmonic resonance energy transfer in the infrared domain. Herein, nuclear quantum effects near heavy metals are studied by nuclear-electronic orbital density functional theory (NEO-DFT) with an effective core potential. For a quantum proton sandwiched between a pair of gold tips modeled by two Au6 clusters, NEO-DFT calculations suggest that the quantum proton density can be squeezed as the tip distance decreases. For an HF molecule placed near a one-dimensional Au nanowire composed of up to 34 Au atoms, real-time NEO time-dependent density functional theory (RT-NEO-TDDFT) shows that the infrared plasmonic motion within the Au nanowire may resonantly transfer electronic energy to the HF proton vibrational stretch mode. Overall, these calculations illustrate the advantages of the NEO approach for probing nuclear quantum effects, such as squeezed proton vibrational states and infrared plasmonic resonance energy transfer.

Time-Dependent Density Matrix Renormalization Group Method for Quantum Transport with Phonon Coupling in Molecular Junction

Quantum transport in molecular junctions has attracted great attention. The charge motion in a molecular junction can cause geometric deformation, leading to strong electron phonon coupling, which was often overlooked. We have formulated a nearly exact method to assess the time-dependent current and occupation number in the molecular junction modeled by the electron-phonon coupled bridge state using the time-dependent density matrix renormalization group (TD-DMRG) method. The oscillation period and amplitude of the current are found to be dependent on the electron phonon coupling strength and energy level alignment with the electrodes. In an attempt to better understand these phenomena, we have devised a new approximation that explains the bistability phenomenon and the behavior of steady currents in the strong electron-phonon coupling regime. Comparisons have been made with the multilayer-multiconfiguration time-dependent Hartree (ML-MCTDH) method and the analytical result in the purely electronic limit. Furthermore, we explore the entropy of different orderings, extending to the electron phonon model problems. Regarding finite temperature, the thermal Bogoliubov transformation of both fermions and bosons is used and compared with imaginary time evolution results.

Anisotropic coupling of individual vibrational modes to a Cu(110) substrate

We present a study on the excitation of individual vibrational modes with ballistic charge carriers propagating along the Cu(110) surface. By means of the molecular nanoprobe technique, where the reversible switching of a molecule-in this case tautomerization of porphycene-is utilized to detect excitation events, we reveal anisotropic coupling of two distinct vibrational modes to the substrate. The N-H bending mode, excited below |E| ≈ 376 meV, exhibits maxima perpendicular to the rows of the Cu(110) substrate and minima along the rows. In contrast, the N-H stretching mode, excited above |E| ≈ 376 meV, displays maxima along the rows and is constant otherwise. This inversion of the anisotropy reflects the orthogonality between the N-H bending and stretching mode. Additionally, we observe an energy-dependent asymmetry in the propagation direction of charge carriers injected into the Cu(110) surface state. Hereby, the anisotropic band structure results in a correlation between the group velocity and the tunneling probability into electronic states of the substrate.

Quantum Chemical Studies on Possible Molecular Devices Based on Electric Field-Induced Intramolecular Charge Transfer

We report quantum chemical studies on possible molecular devices working based on electric field-induced intramolecular charge transfer (EFIMCT). In the case of donor-acceptor (DA)-type molecular systems, intramolecular charge transfer (IMCT) can be induced by applying the external electric field to molecular systems along the charge transport direction, providing a possible switching mechanism which does not depend upon the electron-phonon coupling effect and is different from the negative differential resistance mechanism observed in the well-known NO2-substituted phenylene ethynylene oligomers. When the EFIMCT proceeds, the molecular systems have strong static electron correlation effects, where the standard nonequilibrium Green's function-density functional theory (DFT) approach cannot be applied to the molecular junction. As a first step toward practical switching devices, we do quantum chemical studies on the EFIMCT in such molecular systems as an isolated molecule, instead of using the electrode-junction-electrode open quantum system model. A prototype molecule P1 is designed as a tentative candidate molecule where the EFIMCT can proceed. The complete active space self-consistent field (CASSCF) molecular orbital calculations on P1 indicate that the EFIMCT can proceed at the external electric field intensity of 0.003 au, corresponding to about 2.25 V bias voltage. This calculated result strongly suggests that the development of this type of switching devices working at practically low bias voltage is feasible if the molecular system is properly designed. Broken symmetry unrestricted Hartree-Fock and spin-polarized Kohn-Sham DFT calculations also qualitatively reproduce the CASSCF results on P1, to some extent, indicating that these approaches can be employed for rough estimations on the EFIMCT such as the first screening of a large quantity of candidate molecules for this type of molecular devices. The possibility of molecular memory devices based on the EFIMCT is also discussed by analyzing the ground and excited potential energy surface model. Remaining challenges to develop practical molecular devices are discussed.

Joule Heating in Single-Molecule Point Contacts Studied by Tip-Enhanced Raman Spectroscopy

Heating and cooling in current-carrying molecular junctions is a crucial issue in molecular electronics. The microscopic mechanism involves complex factors such as energy inputs, molecular properties, electrode materials, and molecule-electrode coupling. To gain an in-depth understanding, it is a desired experiment to assess vibrational population that represents the energy distribution stored within the molecule. Here, we demonstrate the direct observation of vibrational heating in a single C₆₀ molecule by means of tip-enhanced Raman spectroscopy (TERS). The heating of respective vibrational modes is monitored by anti-Stokes Raman scattering in the TERS spectra. The precise control of the gap distance in the single-molecule junction allows us to reveal a qualitatively different heating mechanism in distinct electron transport regimes, namely, the tunneling and single-molecule point contact (SMPC) regimes. Strong Joule heating via inelastic electron-vibration scattering occurs in the SMPC regime, whereas optical heating is predominant in the tunneling regime. The strong Joule heating at the SMPC also leads to a pronounced red shift of the Raman peak position and line width broadening. Furthermore, by examining the SMPC with several types of contact surfaces, we show that the heating efficiency is related to the current density at the SMPC and the vibrational dissipation channels into the electrode.

Generalized master equation for charge transport in a molecular junction: Exact memory kernels and their high order expansion

We derive a set of generalized master equations (GMEs) to study charge transport dynamics in molecular junctions using the Nakajima-Zwanzig-Mori projection operator approach. In the new GME, time derivatives of population on each quantum state of the molecule, as well as the tunneling current, are calculated as the convolution of time non-local memory kernels with populations on all system states. The non-Markovian memory kernels are obtained by combining the hierarchical equations of motion (HEOM) method and a previous derived Dyson relation for the exact kernel. A perturbative expansion of these memory kernels is then calculated using the extended HEOM developed in our previous work [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. By using the resonant level model and the Anderson impurity model, we study properties of the exact memory kernels and analyze convergence properties of their perturbative expansions with respect to the system-bath coupling strength and the electron-electron repulsive energy. It is found that exact memory kernels calculated from HEOM exhibit short memory times and decay faster than the population and current dynamics. The high order perturbation expansion of the memory kernels can give converged results in certain parameter regimes. The Padé and Landau-Zener resummation schemes are also found to give improved results over low order perturbation theory.

Real-time dynamics of strongly correlated fermions using auxiliary field quantum Monte Carlo

Spurred by recent technological advances, there is a growing demand for computational methods that can accurately predict the dynamics of correlated electrons. Such methods can provide much-needed theoretical insights into the electron dynamics probed via time-resolved spectroscopy experiments and observed in non-equilibrium ultracold atom experiments. In this article, we develop and benchmark a numerically exact Auxiliary Field Quantum Monte Carlo (AFQMC) method for modeling the dynamics of correlated electrons in real time. AFQMC has become a powerful method for predicting the ground state and finite temperature properties of strongly correlated systems mostly by employing constraints to control the sign problem. Our initial goal in this work is to determine how well AFQMC generalizes to real-time electron dynamics problems without constraints. By modeling the repulsive Hubbard model on different lattices and with differing initial electronic configurations, we show that real-time AFQMC is capable of accurately capturing long-lived electronic coherences beyond the reach of mean field techniques. While the times to which we can meaningfully model decrease with increasing correlation strength and system size as a result of the exponential growth of the dynamical phase problem, we show that our technique can model the short-time behavior of strongly correlated systems to very high accuracy. Crucially, we find that importance sampling, combined with a novel adaptive active space sampling technique, can substantially lengthen the times to which we can simulate. These results establish real-time AFQMC as a viable technique for modeling the dynamics of correlated electron systems and serve as a basis for future sampling advances that will further mitigate the dynamical phase problem.

Hopping Conductance in Molecular Wires Exhibits a Large Heavy-Atom Kinetic Isotope Effect

We report a large kinetic isotope effect (KIE) for intramolecular charge transport in π-conjugated oligophenyleneimine (OPI) molecules connected to Au electrodes. ¹³C and ¹⁵N substitution on the imine bonds produces a conductance KIE of ∼2.7 per labeled atom in long OPI wires >4 nm in length, far larger than typical heavy-atom KIEs for chemical reactions. In contrast, isotopic labeling in shorter OPI wires <4 nm does not produce a conductance KIE, consistent with a direct tunneling mechanism. Temperature-dependent measurements reveal that conductance for a long ¹⁵N-substituted OPI wire is activated, and we propose that the exceptionally large conductance KIEs imply a thermally assisted, through-barrier polaron tunneling mechanism. In general, observation of large conductance KIEs opens up considerable opportunities for understanding microscopic conduction mechanisms in π-conjugated molecules.

Reversal of the Direction of Rectification Induced by Fermi Level Pinning at Molecule-Electrode Interfaces in Redox-Active Tunneling Junctions

Control over the energy level alignment in molecular junctions is notoriously difficult, making it challenging to control basic electronic functions such as the direction of rectification. Therefore, alternative approaches to control electronic functions in molecular junctions are needed. This paper describes switching of the direction of rectification by changing the bottom electrode material M = Ag, Au, or Pt in M-S(CH₂)₁₁S-BTTF//EGaIn junctions based on self-assembled monolayers incorporating benzotetrathiafulvalene (BTTF) with EGaIn (eutectic alloy of Ga and In) as the top electrode. The stability of the junctions is determined by the choice of the bottom electrode, which, in turn, determines the maximum applied bias window, and the mechanism of rectification is dominated by the energy levels centered on the BTTF units. The energy level alignments of the three junctions are similar because of Fermi level pinning induced by charge transfer at the metal-thiolate interface and by a varying degree of additional charge transfer between BTTF and the metal. Density functional theory calculations show that the amount of electron transfer from M to the lowest unoccupied molecular orbital (LUMO) of BTTF follows the order Ag > Au > Pt. Junctions with Ag electrodes are the least stable and can only withstand an applied bias of ±1.0 V. As a result, no molecular orbitals can fall in the applied bias window, and the junctions do not rectify. The junction stability increases for M = Au, and the highest occupied molecular orbital (HOMO) dominates charge transport at a positive bias resulting in a positive rectification ratio of 83 at ±1.5 V. The junctions are very stable for M = Pt, but now the LUMO dominates charge transport at a negative bias resulting in a negative rectification ratio of 912 at ±2.5 V. Thus, the limitations of Fermi level pinning can be bypassed by a judicious choice of the bottom electrode material, making it possible to access selectively HOMO- or LUMO-based charge transport and, as shown here, associated reversal of rectification.

Functional Redox-Active Molecular Tunnel Junctions

Redox-active molecular junctions have attracted considerable attention because redox-active molecules provide accessible energy levels enabling electronic function at the molecular length scales, such as, rectification, conductance switching, or molecular transistors. Unlike charge transfer in wet electrochemical environments, it is still challenging to understand how redox-processes proceed in solid-state molecular junctions which lack counterions and solvent molecules to stabilize the charge on the molecules. In this minireview, we first introduce molecular junctions based on redox-active molecules and discuss their properties from both a chemistry and nanoelectronics point of view, and then discuss briefly the mechanisms of charge transport in solid-state redox-junctions followed by examples where redox-molecules generate new electronic function. We conclude with challenges that need to be addressed and interesting future directions from a chemical engineering and molecular design perspectives.

Sharp Negative Differential Resistance from Vibrational Mode Softening in Molecular Junctions

We unravel the critical role of vibrational mode softening in single-molecule electronic devices at high bias. Our theoretical analysis is carried out with a minimal model for molecular junctions, with mode softening arising due to quadratic electron-vibration couplings, and by developing a mean-field approach. We discover that the negative sign of the quadratic electron-vibration coupling coefficient can realize, at high voltage, a sharp negative differential resistance (NDR) effect with a large peak-to-valley ratio. Calculated current-voltage characteristics, obtained based on physical parameters for a nitro-substituted oligo(phenylene ethynylene) junction, agree very well with the measurements. Our results establish that vibrational mode softening is a crucial effect at high voltage, underlying NDR, a substantial diode effect, and the breakdown of current-carrying molecular junctions.

Transition in nanoscale electrical conductivity in the Langmuir-Blodgett film of a novel liquid crystalline oligomer

We have studied the nanoscale electrical conductivity of a monolayer film of a novel star shaped liquid crystalline molecule, hexatriphenylene substituted anthraquinone (AQD6). The molecule has a central core of electron deficient anthraquinone moiety connected to six electron rich triphenylene moieties by flexible alkyl chains. The monolayer formed at air-water interface was transferred onto the solid substrates by Langmuir-Blodgett (LB) technique and its surface topography was imaged using an atomic force microscope (AFM). The limiting area obtained from the surface pressure-area per molecule isotherm and the topography of the AFM images suggest that the anthraquinone moiety of the AQD6 molecule is organized in face-on configuration on the substrate and the triphenylene moieties are in edge-on configuration extended away from the substrate. We have studied the electrical conductivity of the AQD6 monolayer deposited on gold coated silicon substrate using a current sensing AFM. Analysis of current (I) − voltage (V) characteristics of the metal-monolayer film-metal junction showed a transition from direct tunneling to an injection tunneling. Further, we have estimated the barrier height and the effective mass of electron in the metal-monolayer film-metal junction.

Nonadiabatic Molecular Dynamics at Metal Surfaces

Dynamics at molecule-metal interfaces are a subject of intense current interest and come in many different flavors of experiments: gas-phase scattering, chemisorption, electrochemistry, nanojunction transport, and heterogeneous catalysis, to name a few. These dynamics involve nuclear degrees of freedom entangled with many electronic degrees of freedom (in the metal), and as such there is always the possibility for nonadiabatic phenomena to appear: the nuclei do not necessarily need to move slower than the electrons to break the Born-Oppenheimer (BO) approximation. In this Feature Article, we review a set of dynamical methods developed recently to deal with such nonadiabatic phenomena at a metal surface, methods that serve as alternatives to Tully's independent electron surface hopping (IESH) model. In the weak molecule-metal coupling regime, a classical master equation (CME) can be derived and a simple surface hopping approach is proposed to propagate nuclear and electronic dynamics stochastically. In the strong molecule-metal interaction regime, a Fokker-Planck equation can be derived for the nuclear dynamics, with electronic DoFs incorporated into the overall friction and random force. Lastly, a broadened classical master equation (BCME) can interpolate between the weak and strong molecule-metal interactions. Here, we briefly review these methods and the relevant benchmarking data, showing in particular how the methods can be used to calculate nonequilibrium transport properties. We highlight several open questions and pose several avenues for future study.

Ultrafast dynamics of the dipole moment reversal in a polar organic monolayer

Pyridine layers on Cu(110) possess a strong electric field due to the large dipole of adsorbed pyridine. This electric field is visible as an enhanced sum frequency response from both the copper surface electrons and the aromatic C-H stretch of pyridine via a third order susceptibility. In response to a visible pump pulse, both surface electron and C-H stretch sum frequency signals are reduced on a subpicosecond time scale. In addition, the relative phase between the two signals changes over a few hundred femtoseconds, which indicates a change in the electronic structure of the adsorbate. We explain the transients as a consequence of the previously observed pyridine dipole field reversal when the pump pulse excites electrons into the pyridine π^* orbital. The pyridine anions in the pyridine layer cause a large-scale structural change which alters the pyridine-copper bond, reflected in the altered sum frequency response.

Hubbard Nonequilibrium Green's Function Analysis of Photocurrent in Nitroazobenzene Molecular Junction

We present a combined experimental and theoretical study of photoinduced current in molecular junctions consisting of monolayers of nitroazobenzene oligomers chemisorbed on carbon surfaces and illuminated by ultraviolet-visible light through a transparent electrode. Experimentally observed dependence of the photocurrent on light frequency, temperature, and monolayer thickness is analyzed within first-principles simulations employing the Hubbard nonequilibrium Green's function diagrammatic technique. We reproduce qualitatively correct behavior and discuss mechanisms leading to the characteristic behavior of dark and photoinduced currents in response to changes in bias, frequency of radiation, temperature, and thickness of molecular layer.

Cross-plane conductance through a graphene/molecular monolayer/Au sandwich

The functionalities offered by single-molecule electrical junctions are yet to be translated into monolayer or few-layer molecular films, where making effective and reproducible electrical contact is one of the challenging bottlenecks. Here we take a significant step in this direction by demonstrating that excellent electrical contact can be made with a monolayer biphenyl-4,4'-dithiol (BPDT) molecular film, sandwiched between gold and graphene electrodes. This sandwich device structure is advantageous, because the current flows through the molecules to the gold substrate in a 'cross-plane' manner, perpendicular to the plane of graphene, yielding high-conductance devices. We elucidate the nature of the cross-plane graphene/molecule/Au transport using quantum transport calculations and introduce a simple analytical model, which captures generic features of the current-voltage characteristic. Asymmetry in junction properties results from the disparity in electrode electrical properties, the alignment of the BPDT HOMO-LUMO energy levels and the specific characteristics of the graphene electrode. The experimental observation of scalability of junction properties within the junction area, in combination with a theoretical description of the transmission probability of the thiol-graphene contact, demonstrates that between 10% and 100% of the molecules make contact with the electrodes, which is several orders of magnitude greater than that achieved to date in the literature.

Molecular Coupling between Organic Molecules and Metal

Molecular couplings at interfaces play important roles in determining the performance of nanophotonics and molecular electronics. In this Letter, using femtosecond sum frequency generation to trace free-induction decay of vibrationally excited aromatic thiol molecules immobilized on metal with and without the bridged methylene group(s), metal surface free electron-coupled and uncoupled phenyl C-H stretching vibrational modes were identified, with dephasing times of ∼0.28 and ∼0.60 ps, respectively. For thiols on Au with the bridged methylene group(s) (benzyl mercaptan and phenylethanethiol), both the coupled and uncoupled modes were observed; for thiol on Au without the bridged methylene group (thiophenol), only the coupled mode was observed. This indicates that the bridged methylene group(s) serving as a spacer can be used to adjust the molecular coupling between the phenyl vibration and surface free electrons. The experimental approach can be used to tune molecular couplings in advanced nanophotonics and molecular electronics.

Density-functional tight-binding approach for metal clusters, nanoparticles, surfaces and bulk: application to silver and gold

Density-functional based tight-binding (DFTB) is an efficient quantum mechanical method that can describe a variety of systems, going from organic and inorganic compounds to metallic and hybrid materials. The present topical review addresses the ability and performance of DFTB to investigate energetic, structural, spectroscopic and dynamical properties of gold and silver materials. After a brief overview of the theoretical basis of DFTB, its parametrization and its transferability, we report its past and recent applications to gold and silver systems, including small clusters, nanoparticles, bulk and surfaces, bare and interacting with various organic and inorganic compounds. The range of applications covered by those studies goes from plasmonics and molecular electronics, to energy conversion and surface chemistry. Finally, perspectives of DFTB in the field of gold and silver surfaces and NPs are outlined.

Tunneling explains efficient electron transport via protein junctions

Metalloproteins, proteins containing a transition metal ion cofactor, are electron transfer agents that perform key functions in cells. Inspired by this fact, electron transport across these proteins has been widely studied in solid-state settings, triggering the interest in examining potential use of proteins as building blocks in bioelectronic devices. Here, we report results of low-temperature (10 K) electron transport measurements via monolayer junctions based on the blue copper protein azurin (Az), which strongly suggest quantum tunneling of electrons as the dominant charge transport mechanism. Specifically, we show that, weakening the protein-electrode coupling by introducing a spacer, one can switch the electron transport from off-resonant to resonant tunneling. This is a consequence of reducing the electrode's perturbation of the Cu(II)-localized electronic state, a pattern that has not been observed before in protein-based junctions. Moreover, we identify vibronic features of the Cu(II) coordination sphere in transport characteristics that show directly the active role of the metal ion in resonance tunneling. Our results illustrate how quantum mechanical effects may dominate electron transport via protein-based junctions.

Negative Differential Resistance Behavior of the Iron Storage Protein Ferritin

Realization of useful nanometer length scale devices in which metalloproteins are junction-confined in a distinct molecular arrangement for generating practical electronic signals (e.g., in bioelectronic switch configuration) is elusive till date. This is mostly due to difficulties in observing an electronically appropriate signal (i.e., reproducible and controllable), when studied under junction-assembled condition. A useful "ON"-"OFF" behavior, based on the negative differential resistance (NDR) peak characteristics in the current-voltage response curves, acquired using metal-insulator-metal (MIM) configuration, has been observed only in the case of a few proteins, namely, azurin, cytochrome c, bacteriorhodopsin, so far. The case of NDR in ferritin, an iron storage protein having a semiconducting iron core consisting of few thousands of iron atoms connected in an oxide network, has not been studied in the MIM configuration where single (or a few) molecule(s) are junction-trapped, for example, as in the case of local probe configuration of scanning probe microscopy. The present study by scanning tunneling microscopy (STM), using the naturally occurring iron-containing ferritin (human liver), as well as different iron-loaded ferritins, provides clear indication of the capability of ferritins to be NDR capable, at varying sweep conditions. As ferritin can be tailor-made in a structurally conserved manner, metal core-reconstituted ferritins, that is, Mn(III)-ferritin, Cu(II)-ferritin, and Ag-ferritin, were prepared. A correlation between the NDR peak signatures, as observed in the respective current-voltage response curves of these reconstituted ferritins, and the nature of the metal core is demonstrated. In support of our earlier proposition, here, we affirm that the ferritin protein behaves as a conductor-insulator (metal core-polypeptide shell) composite, where the overall electronic structure of the material can alter as a function of the nature of the conducting filler placed inside the insulated matrix.

Understanding the charge transport properties of redox active metal-organic conjugated wires

For Rh₂-organic molecular wires, we found that weaker coupling systems built using longer bridging ligands exhibit better electrical conductance.

Layer-by-layer assembly of the dirhodium complex [Rh₂(O₂CCH₃)₄] (Rh₂) with linear N,N′-bidentate ligands pyrazine (L_S) or 1,2-bis(4-pyridyl)ethene (L_L) on a gold substrate has developed two series of redox active molecular wires, (Rh₂L_S)_n@Au and (Rh₂L_L)_n@Au (n = 1–6). By controlling the number of assembling cycles, the molecular wires in the two series vary systematically in length, as characterized by UV-vis spectroscopy, cyclic voltammetry and atomic force microscopy. The current–voltage characteristics recorded by conductive probe atomic force microscopy indicate a mechanistic transition for charge transport from voltage-driven to electrical field-driven in wires with n = 4, irrespective of the nature and length of the wires. Whilst weak length dependence of electrical resistance is observed for both series, (Rh₂L_L)_n@Au wires exhibit smaller distance attenuation factors (β) in both the tunneling (β = 0.044 Å^–1) and hopping (β = 0.003 Å^–1) regimes, although in (Rh₂L_S)_n@Au the electronic coupling between the adjacent Rh₂ centers is stronger. DFT calculations reveal that these wires have a π-conjugated molecular backbone established through π(Rh₂)–π(L) orbital interactions, and (Rh₂L_L)_n@Au has a smaller energy gap between the filled π*(Rh₂) and the empty π*(L) orbitals. Thus, for (Rh₂L_L)_n@Au, electron hopping across the bridge is facilitated by the decreased metal to ligand charge transfer gap, while in (Rh₂L_S)_n@Au the hopping pathway is disfavored likely due to the increased Coulomb repulsion. On this basis, we propose that the super-exchange tunneling and the underlying incoherent hopping are the dominant charge transport mechanisms for shorter (n ≤ 4) and longer (n > 4) wires, respectively, and the Rh₂L subunits in mixed-valence states alternately arranged along the wire serve as the hopping sites.

Tuning the spin-related transport properties of FePc on Au(111) through single-molecule chemistry

Tuning the spin-related transport properties of FePc on Au(111) through single-molecule chemistry.

The influence of nearest-neighbour interactions and assembly dynamics on the transport properties of porphyrin supramolecular assemblies on Au(111)

Here we report on the effect of local molecular organization or "tertiary structure" on the charge transport properties of thiol-tethered tetraphenylporphyrin (ZnTPPF₄-SC₅SH) nanoscale clusters of ca. 5 nm in lateral dimension embedded within a dodecanethiol (C12) monolayer on Au(111). The structure of the clusters in the mixed monolayers and their resulting transport properties were monitored by Atomic Force Microscopy (AFM), Scanning Tunneling Microscopy (STM) and Spectroscopy (STS). The mixed films were deposited on Au(111) for a period of one to five days, during which the lateral dimensions of the ZnTPPF₄-SC₅SH islands that were formed after one day reduced by nearly 35% on average by five days, accompanied by a noticeable depletion of the surrounding C12 monolayer. These subtle changes in mixed monolayer morphology were accompanied by drastic differences in conductance. The ZnTPPF₄-SC₅SH clusters assembled for one day exhibited highly reproducible I-V spectra with simple tunneling behavior. By three days, this evolved into bias-induced switching of conductance, with a ∼100-1000 fold increase. Furthermore, current fluctuations started to become significant, and then dominated transport across the ZnTPPF₄-SC₅SH clusters assembled over five days. Our data suggests that this evolution can be understood by slow surface diffusion, enabling the ZnTPPF₄-SC₅SH molecules to overcome initial steric hindrance in the early stages of island formation in the C12 monolayer (at day one), to reach a more energetically-favored, close-packed organization, as noted by the decrease in island size (by day three). However, when desorption of the supporting matrix of C12 became pronounced (by day five), the ZnTPPF₄-SC₅SH clusters began to lose stabilization, and stochastic switching was then observed to dominate transport in the clusters, illustrating the critical nature of the local organization on these transport properties.

Born-Oppenheimer Dynamics, Electronic Friction, and the Inclusion of Electron-Electron Interactions

We present a universal expression for the electronic friction as felt by a set of classical nuclear degrees of freedom (DOFs) coupled to a manifold of quantum electronic DOFs; no assumptions are made regarding the nature of the electronic Hamiltonian and electron-electron repulsions are allowed. Our derivation is based on a quantum-classical Liouville equation for the coupled electronic-nuclear motion, followed by an adiabatic approximation whereby electronic transitions are assumed to equilibrate faster than nuclear movement. The resulting form of friction is completely general, but does reduce to previously published expressions for the quadratic Hamiltonian (i.e., Hamiltonians without electronic correlation). At equilibrium, the second fluctuation-dissipation theorem is satisfied and the frictional matrix is symmetric. To demonstrate the importance of electron-electron correlation, we study electronic friction within the Anderson-Holstein model, where a proper treatment of electron-electron interactions shows signatures of a Kondo resonance and a mean-field treatment is completely inadequate.

Thermally Activated Tunneling Transition in a Photoswitchable Single-Molecule Electrical Junction

Exploring the charge transport process in molecular junctions is essential to the development of molecular electronics. Here, we investigate the temperature-dependent charge transport mechanism of carbon electrode-diarylethene single-molecule junctions, which possess photocontrollable molecular orbital energy levels due to reversible photoisomerization of individual diarylethenes between open and closed conformations. Both the experimental results and theoretical calculations consistently demonstrate that the vibronic coupling (thermally activated at the proper temperature) drives the transition of charge transport in the junctions from coherent tunneling to incoherent transport. Due to the subtle electron-phonon coupling effect, incoherent transport in the junctions proves to have different activation energies, depending on the photoswitchable molecular energy levels of two different conformations. These results improve fundamental understanding of charge transport mechanisms in molecular junctions and should lead to the rapid development of functional molecular devices toward practical applications.

Molecular floating-gate single-electron transistor

We investigated reversible switching behaviors of a molecular floating-gate single-electron transistor (MFG-SET). The device consists of a gold nanoparticle-based SET and a few tetra-tert-butyl copper phthalocyanine (ttbCuPc) molecules; each nanoparticle (NP) functions as a Coulomb island. The ttbCuPc molecules function as photoreactive floating gates, which reversibly change the potential of the Coulomb island depending on the charge states induced in the ttbCuPc molecules by light irradiation or by externally applied voltages. We found that single-electron charging of ttbCuPc leads to a potential shift in the Coulomb island by more than half of its charging energy. The first induced device state was sufficiently stable; the retention time was more than a few hours without application of an external voltage. Moreover, the device exhibited an additional state when irradiated with 700 nm light, corresponding to doubly charged ttbCuPc. The life time of this additional state was several seconds, which is much shorter than that of the first induced state. These results clearly demonstrate an alternative method utilizing the unique functionality of the single molecule in nanoelectronics devices, and the potential application of MFG-SETs for investigating molecular charging phenomena.

Time-Resolved Imaging of Negative Differential Resistance on the Atomic Scale

Negative differential resistance remains an attractive but elusive functionality, so far only finding niche applications. Atom scale entities have shown promising properties, but the viability of device fabrication requires a fuller understanding of electron dynamics than has been possible to date. Using an all-electronic time-resolved scanning tunneling microscopy technique and a Green's function transport model, we study an isolated dangling bond on a hydrogen terminated silicon surface. A robust negative differential resistance feature is identified as a many body phenomenon related to occupation dependent electron capture by a single atomic level. We measure all the time constants involved in this process and present atomically resolved, nanosecond time scale images to simultaneously capture the spatial and temporal variation of the observed feature.

Tuning electronic transport via hepta-alanine peptides junction by tryptophan doping

Charge migration for electron transfer via the polypeptide matrix of proteins is a key process in biological energy conversion and signaling systems. It is sensitive to the sequence of amino acids composing the protein and, therefore, offers a tool for chemical control of charge transport across biomaterial-based devices. We designed a series of linear oligoalanine peptides with a single tryptophan substitution that acts as a "dopant," introducing an energy level closer to the electrodes' Fermi level than that of the alanine homopeptide. We investigated the solid-state electron transport (ETp) across a self-assembled monolayer of these peptides between gold contacts. The single tryptophan "doping" markedly increased the conductance of the peptide chain, especially when its location in the sequence is close to the electrodes. Combining inelastic tunneling spectroscopy, UV photoelectron spectroscopy, electronic structure calculations by advanced density-functional theory, and dc current-voltage analysis, the role of tryptophan in ETp is rationalized by charge tunneling across a heterogeneous energy barrier, via electronic states of alanine and tryptophan, and by relatively efficient direct coupling of tryptophan to a Au electrode. These results reveal a controlled way of modulating the electrical properties of molecular junctions by tailor-made "building block" peptides.