Vibrational excitations in weakly coupled single-molecule junctions: a computational analysis

Charge-State Dependent Vibrational Relaxation in a Single-Molecule Junction

The outcome of an electron-transfer process is determined by the quantum-mechanical interplay between electronic and vibrational degrees of freedom. Nonequilibrium vibrational dynamics are known to direct electron-transfer mechanisms in molecular systems; however, the structural features of a molecule that lead to certain modes being pushed out of equilibrium are not well understood. Herein, we report on electron transport through a porphyrin dimer molecule, weakly coupled to graphene electrodes, that displays sequential tunneling within the Coulomb-blockade regime. The sequential transport is initiated by current-induced phonon absorption and proceeds by rapid sequential transport via a nonequilibrium vibrational distribution of low-energy modes, likely related to torsional molecular motions. We demonstrate that this is an experimental signature of slow vibrational dissipation, and obtain a lower bound for the vibrational relaxation time of 8 ns, a value dependent on the molecular charge state.

Charge transport through extended molecular wires with strongly correlated electrons

Electron–electron interactions are at the heart of chemistry and understanding how to control them is crucial for the development of molecular-scale electronic devices. Here, we investigate single-electron tunneling through a redox-active edge-fused porphyrin trimer and demonstrate that its transport behavior is well described by the Hubbard dimer model, providing insights into the role of electron–electron interactions in charge transport. In particular, we empirically determine the molecule's on-site and inter-site electron–electron repulsion energies, which are in good agreement with density functional calculations, and establish the molecular electronic structure within various oxidation states. The gate-dependent rectification behavior confirms the selection rules and state degeneracies deduced from the Hubbard model. We demonstrate that current flow through the molecule is governed by a non-trivial set of vibrationally coupled electronic transitions between various many-body ground and excited states, and experimentally confirm the importance of electron–electron interactions in single-molecule devices.

Experimental studies of electron transport through an edge-fused porphyrin oligomer in a graphene junction are interpreted within a Hubbard dimer framework.

Plexcitons, electric field gradient and electron-phonon coupling in tip-enhanced Raman spectroscopy (TERS)

Tip-Enhanced Raman Spectroscopy (TERS) provides very high spatial resolution and detection sensitivity, so it has important applications in nano-scale molecular analysis. Plexciton is a polarization mode caused by a strongly coupled interaction between plasma excitons and excitons. It is a hot topic in plasma photonics research. We introduce the characteristics, production methods, observation methods and some applications of TERS. The electric field gradient (EFG) is an important factor affecting TERS resolution. The electron-phonon interaction is a fundamental inelastic interaction and plays an important role in current-carrying single-molecular junctions. This article summarizes the characteristics and applications of these three parts for readers to gain a preliminary understanding.

Quantum Algorithm for Simulating Single-Molecule Electron Transport

An accurate description of electron transport at a molecular level requires a precise treatment of quantum effects. These effects play a crucial role in determining the electron transport properties of single molecules, which can be challenging to simulate classically. Here we introduce a quantum algorithm to efficiently calculate electronic current through single-molecule junctions in the weak-coupling regime. We show that a quantum computer programmed to simulate vibronic transitions between different charge states of a molecule can be used to compute electron-transfer rates and electronic current. In the harmonic approximation, the algorithm can be implemented using Gaussian boson sampling devices, which are a near-term platform for photonic quantum computing. We apply the algorithm to simulate the current and conductance of a magnesium porphine molecule. The algorithm provides a means for better understanding the mechanism of electron transport at a molecular level, which paves the way for building practical molecular electronic devices.

Polymorphism Dependent 9-Phosphoanthracene Derivative Exhibiting Thermally Activated Delayed Fluorescence: A Computational Investigation

Polymorphs of anthracene derivatives exhibit diverse photophysical properties that can help to develop efficient organic-based photovoltaic devices. 10-Anthryl-9-phosphoanthracene (10-APA) shows different photophysical behaviors for the solid state due to its variety in crystalline arrangement. Herein, we investigate the ground and excited-state properties of the monomer and two different polymorphs of 10-APA from first-principles. Calculations reveal that strong spin-orbit coupling (SOC) between first excited singlet state (S₁) and triplet manifolds at their S₁-optimized geometries enabling the reverse intersystem crossing (RISC). The electron-vibration coupling (Huang-Rhys factor) in the excited state is the most relevant factor here. For both ISC and RISC, a similarity in Huang-Rhys factors for the molecular vibration along the π···π stacking at low-frequency region makes the rates effective. On the other side, the nonvanishing vibronic relaxation modes provide a relatively slower RISC rate in the red crystal. However, for the red crystal, small reorganization energy (λ) and large Huang-Rhys factor toward S₁ → S₀ conversion reduce nonradiative decay, leading to a prompt fluorescence. As the feasibility of S₁ ↔ T₁ conversion increases in the yellow dimer, it allows a delay in fluorescence emission, leading to thermally activated delayed fluorescence (TADF).

Antenna triplet DFT calculations to drive the design of luminescent Ln3+ complexes

Density functional theory-based methods have been exploited to look into the structural, vibrational and electronic properties of antenna ligands, all of them being crucial factors for the reliable design of customized luminescent lanthanide (Ln3+) complexes. The X-ray structures, UV-Vis absorption spectra and triplet (T1) energies of three novel β-diketone ligands with a thienyl group and naphthyl (L1), phenanthryl (L2), and pyrenyl (L3) polycyclic aromatic hydrocarbons as substituents have been modelled. Vibronic progressions provide a strong contribution to the L1 and L2 absorption spectra, while the L3 absorption spectrum needs the assumption of different conformational isomers in solution. T1 energies have been estimated either through the vertical- or the adiabatic-transition approach. The comparison with the phosphorescence spectra of Gd3+ complexes allowed us to infer that the latter approach is the most suitable one, in particular when sizable ligands are involved. Results obtained for the isolated antennas can be directly compared with those of the corresponding Ln3+ complexes, due to the unanimously accepted assumption that the excitation is ligand-centred.

Beyond Marcus theory and the Landauer-Büttiker approach in molecular junctions. II. A self-consistent Born approach

Marcus and Landauer-Büttiker approaches to charge transport through molecular junctions describe two contrasting mechanisms of electronic conduction. In previous work, we have shown how these charge transport theories can be unified in the single-level case by incorporating lifetime broadening into the second-order quantum master equation. Here, we extend our previous treatment by incorporating lifetime broadening in the spirit of the self-consistent Born approximation. By comparing both theories to numerically converged hierarchical-equations-of-motion results, we demonstrate that our novel self-consistent approach rectifies shortcomings of our earlier framework, which are present especially in the case of relatively strong electron-vibrational coupling. We also discuss circumstances under which the theory developed here simplifies to the generalized theory developed in our earlier work. Finally, by considering the high-temperature limit of our new self-consistent treatment, we show how lifetime broadening can also be self-consistently incorporated into Marcus theory. Overall, we demonstrate that the self-consistent approach constitutes a more accurate description of molecular conduction while retaining most of the conceptual simplicity of our earlier framework.

Understanding resonant charge transport through weakly coupled single-molecule junctions

Off-resonant charge transport through molecular junctions has been extensively studied since the advent of single-molecule electronics and is now well understood within the framework of the non-interacting Landauer approach. Conversely, gaining a qualitative and quantitative understanding of the resonant transport regime has proven more elusive. Here, we study resonant charge transport through graphene-based zinc-porphyrin junctions. We experimentally demonstrate an inadequacy of non-interacting Landauer theory as well as the conventional single-mode Franck–Condon model. Instead, we model overall charge transport as a sequence of non-adiabatic electron transfers, with rates depending on both outer and inner-sphere vibrational interactions. We show that the transport properties of our molecular junctions are determined by a combination of electron–electron and electron-vibrational coupling, and are sensitive to interactions with the wider local environment. Furthermore, we assess the importance of nuclear tunnelling and examine the suitability of semi-classical Marcus theory as a description of charge transport in molecular devices.

The mechanism of nonadiabatic electron transfer in molecular systems is an important research topic for understanding various chemical reactions. Thomas et al. quantify resonant charge transport through single-molecule junctions as a model system for examining quantum and Marcus theories.

Auxiliary Master Equation for Nonequilibrium Dual-Fermion Approach

We introduce an auxiliary quantum master equation dual fermion method and argue that it presents a convenient way to describe steady states of correlated impurity models. The scheme yields an expansion around a reference that is much closer to the true nonequilibrium state than that in the original dual fermion formulation. In steady-state situations, the scheme is numerically inexpensive and avoids time propagation. The Anderson impurity model is used to test the approach against numerically exact benchmarks.

Enhancement of the Raman Effect by Infrared Pumping

We propose a method for increasing Raman scattering from an ensemble of molecules by up to 4 orders of magnitude. Our method requires an additional coherent source of IR radiation with the half-frequency of the Stokes shift. This radiation excites the molecule electronic subsystem that in turn, via Fröhlich coupling, parametrically excites nuclear oscillations at a resonant frequency. This motion is coherent and leads to a boost of the Raman signal in comparison to the spontaneous signal because its intensity is proportional to the squared number of molecules in the illuminated volume.

Photoinduced Anomalous Coulomb Blockade and the Role of Triplet States in Electron Transport through an Irradiated Molecular Transistor

In this study, we explore photoinduced electron transport through a molecule weakly coupled to two electrodes by combining first-principles quantum chemistry calculations with a Pauli master equation approach that accounts for many-electron states. In the incoherent limit, we demonstrate that energy-level alignment of triplet and charged states plays a crucial role, even when the rate of intersystem crossing is much smaller than the rate of fluorescence. Furthermore, the field intensity dependence and an upper bound to the photoinduced electric current can be analytically derived in our model. Under an optical field, the conductance spectra (charge stability diagrams) exhibit unusual Coulomb diamonds, which are associated with molecular excited states, and their widths can be expressed in terms of energies of the molecular electronic states. This study offers new directions for exploring optoelectronic response in nanoelectronics.

Predicting transport regime and local electrostatic environment from Coulomb blockade diamond sizes

Electron transport through a molecule is often described in one of the two regimes: the coherent tunnelling regime or the Coulomb blockade regime. The twilight zone of the two regimes still possesses many unsolved questions. A theoretical analysis of the oligophenylenevinylene OPV3 experiments by Bjørnholm and co-workers is performed. The experiments showed how two OPV3 derivatives performed very differently despite the strong similarity of the molecular structure, hence the experimental data showed two different transport mechanisms. The different transport mechanisms of the two OPV3 derivatives are explained from quantum mechanical calculations of the molecular redox energies and from the experimentally accessible window size.

Sequential Electron Transport and Vibrational Excitations in an Organic Molecule Coupled to Few-Layer Graphene Electrodes

Graphene electrodes are promising candidates to improve reproducibility and stability in molecular electronics through new electrode-molecule anchoring strategies. Here we report sequential electron transport in few-layer graphene transistors containing individual curcuminoid-based molecules anchored to the electrodes via π-π orbital bonding. We show the coexistence of inelastic co-tunneling excitations with single-electron transport physics due to an intermediate molecule-electrode coupling; we argue that an intermediate electron-phonon coupling is the origin of these vibrational-assisted excitations. These experimental observations are complemented with density functional theory calculations to model electron transport and the interaction between electrons and vibrational modes of the curcuminoid molecule. We find that the calculated vibrational modes of the molecule are in agreement with the experimentally observed excitations.

The effect of Duschinsky rotation on charge transport properties of molecular junctions in the sequential tunneling regime

We present here a systematic theoretical study on the effect of Duschinsky rotation on charge transport properties of molecular junctions in the sequential tunneling regime. In the simulations we assume that only two electronic charging states each coupled to a two dimensional vibrational potential energy surface (PES) are involved in the transport process. The Duschinsky rotation effect is accounted by varying the rotational angle between the two sets of displaced PESs. Both harmonic potential and anharmonic Morse potential have been considered for the cases of the intermediate to strong electron-vibration couplings. Our calculations show that the inclusion of the Duschinsky rotation effect can significantly change the charge transport properties of a molecular junction. Such an effect makes the otherwise symmetric Coulomb diamond become asymmetric in harmonic potentials. Depending on the angle of the rotation, the low bias current could be significantly suppressed or enhanced. This effect is particularly prominent in the Franck-Condon (FC) blockade regime where the electron-vibration coupling is strong. These changes are caused by the variation of the FC factors which are closely related to the rotational angle between the two sets of PESs involved in the charge transport process. For a molecular junction with Morse potentials, the changes caused by Duschinsky rotation are much more complicated. Both the amplitude and shape of the Coulomb diamond are closely dependent on the rotational angle in the whole range from 0 to 2π. One interesting result is that with a rotation angle of π (and also π/2 for certain cases) symmetric Coulomb diamonds can even be formed from the intrinsically asymmetric Morse potential. These results could be important for the interpretation of experimental observations.

Single-molecule transistors

The use of a gate electrode allows us to gain deeper insight into the electronic structure of molecular junctions. It is widely used for spectroscopy of the molecular levels and its excited states, for changing the charge state of the molecule and investigating higher order processes such as co-tunneling and the Kondo effect. Gate electrodes have been implemented in several types of nanoscale devices such as electromigration junctions, mechanically controllable break junctions, and devices with carbon-based electrodes. Here we review the state-of-the-art in the field of single-molecule transitors. We discuss the experimental challenges and describe the advances made for the different approaches.

Two-level spatial modulation of vibronic conductance in conjugated oligophenylenes on boron nitride

Intramolecular current-induced vibronic excitations are reported in highly ordered monolayers of quaterphenylene dicarbonitriles at an electronically patterned boron nitride on copper platform (BN/Cu(111)). A first level of spatially modulated conductance at the nanometer-scale is induced by the substrate. Moreover, a second level of conductance variations at the molecular level is found. Low temperature scanning tunneling microscopy studies in conjunction with molecular dynamics calculations reveal collective amplification of the molecule's interphenylene torsion angles in the monolayer. Librational modes influencing these torsion angles are identified as initial excitations during vibronic conductance. Density functional theory is used to map phenylene breathing modes and other vibrational excitations that are suggested to be at the origin of the submolecular features during vibronic conductance.

Vibrational control of electron-transfer reactions: a feasibility study for the fast coherent transfer regime

Electron donors are connectedvialeft and right bridges to electron acceptors. Following electron-transfer initiation, the IR excitation of selected bridge vibrational modes can tune the directionality of electron transfer.

Franck-Condon blockade in a single-molecule transistor

We investigate vibron-assisted electron transport in single-molecule transistors containing an individual Fe4 Single-Molecule Magnet. We observe a strong suppression of the tunneling current at low bias in combination with vibron-assisted excitations. The observed features are explained by a strong electron-vibron coupling in the framework of the Franck-Condon model supported by density-functional theory.

Density-matrix approach for the electroluminescence of molecules in a scanning tunneling microscope

The electroluminescence (EL) of molecules confined inside a nanocavity in the scanning tunneling microscope possesses many intriguing but unexplained features. We present here a general theoretical approach based on the density-matrix formalism to describe the EL from molecules near a metal surface induced by both electron tunneling and localized surface plasmon excitations simultaneously. It reveals the underlying physical mechanism for the external bias dependent EL. The important role played by the localized surface plasmon on the EL is highlighted. Calculations for porphyrin derivatives have reproduced corresponding experimental spectra and nicely explained the observed unusual large variation of emission spectral profiles. This general theoretical approach can find many applications in the design of molecular electronic and photonic devices.

Charge transport through single molecules, quantum dots and quantum wires

We review recent progress in the theoretical description of correlation and quantum fluctuation phenomena in charge transport through single molecules, quantum dots and quantum wires. Various physical phenomena are addressed, relating to cotunneling, pair-tunneling, adiabatic quantum pumping, charge and spin fluctuations, and inhomogeneous Luttinger liquids. We review theoretical many-body methods to treat correlation effects, quantum fluctuations, non-equilibrium physics, and the time evolution into the stationary state of complex nanoelectronic systems.

Charge transport through molecular switches

We review the fascinating research on charge transport through switchable molecules. In the past decade, detailed investigations have been performed on a great variety of molecular switches, including mechanically interlocked switches (rotaxanes and catenanes), redox-active molecules and photochromic switches (e.g. azobenzenes and diarylethenes). To probe these molecules, both individually and in self-assembled monolayers (SAMs), a broad set of methods have been developed. These range from low temperature scanning tunneling microscopy (STM) via two-terminal break junctions to larger scale SAM-based devices. It is generally found that the electronic coupling between molecules and electrodes has a profound influence on the properties of such molecular junctions. For example, an intrinsically switchable molecule may lose its functionality after it is contacted. Vice versa, switchable two-terminal devices may be created using passive molecules ('extrinsic switching'). Developing a detailed understanding of the relation between coupling and switchability will be of key importance for both future research and technology.