arXiv subjects

Robert Stadler

Publications and source records attributed to Robert Stadler.

At least 19 recordsLinked to original sources

arXiv2018

A Density Functional Theory Based Electron Transport Study of Coherent Tunneling Through Cyclic Molecules Containing Ru and Os as Redox Active Centers

In our theoretical study in which we combine a nonequilibrium Green's function (NEGF) approach with density functional theory (DFT) we investigate branched compounds containing Ru or Os metal complexes in two branches, which due to their identical or different metal centers are symmetric or asymmetric. In these compounds the metal atoms are connected to pyridyl anchor groups via acetylenic and phenyl spacer groups in a meta-connection. We find there is no destructive quantum interference (DQI) feature in the transmission function near the Fermi level for the investigated molecules regardless of their symmetry, neither in their neutral states nor in their charged states. We map the structural characteristics of the range of molecules onto a simplified tight-binding model in order to identify the main differences between the molecules in this study and previously investigated ferrocene compounds in order to clarify the structural sources for DQI, which we found for the latter but not for the former. We also find that local charging on one of the branches only changes the conductance by about one order of magnitude which we explain in terms of the spatial distributions and charge-induced energy shifts of the relevant molecular orbitals for the branched compounds.

physics.chem-ph↗

arXiv2018

A Density Functional Theory based study of Electron Transport Through Ferrocene Compounds with Different Anchor Groups in Different Adsorption Configurations of A STM-setup

In our theoretical study where we combine a nonequilibrium Green's function (NEGF) approach with density functional theory (DFT) we investigate compounds containing a ferrocene moiety which is connected to i) thiol anchor groups on both sides in a para-connection, ii) a pyridyl anchor group on one side in a meta-connection and a thiol group on the other side in a para-connection, in both cases with acetylenic spacers in between the Ferrocene and the anchors. We predict possible single molecule junction geometries within a scanning tunneling microscopy (STM) setup where we find that the conductance trend for the set of conformations are intriguing in the sense that the conductance does not decrease while the junction length increases which we analyze and explain in terms of Fermi level alignment. We also find a pattern for the current-voltage (IV) curves within the linear-response regime for both molecules we study, where the conductance variation with the molecular configurations is surprisingly small.

physics.chem-ph↗

arXiv2017

Charge Transport and Conductance Switching of Redox-active Azulene Derivatives

Azulene (Az) is a non-alternating, aromatic hydrocarbon composed of a five-membered, electron-rich and a seven-membered, electron-poor ring; an electron distribution that provides intrinsic redox activity. By varying the attachment points of the two electrode-bridging substituents to the Az centre, the influence of the redox functionality on charge transport is evaluated. The conductance of the 1,3 Az derivative is at least one order of magnitude lower than those of the 2,6 Az and 4,7 Az derivatives, in agreement with density functional theory (DFT) calculations. In addition, only 1,3 Az exhibits pronounced nonlinear current-voltage characteristics with hysteresis, indicating a bias-dependent conductance switching. DFT identifies the LUMO to be nearest to the Fermi energy of the electrodes, but to be an active transport channel only in the case of the 2,6 and the 4,7 Az derivatives, whereas the 1,3 Az derivative uses the HOMO at low and the LUMO+1 at high bias. In return, the localized, weakly coupled LUMO of 1,3 Az creates a slow electron-hopping channel responsible for the voltage-induced switching due to the occupation of a single MO.

cond-mat.mes-hall↗

arXiv2017

Quantum interference in coherent tunnelling through branched molecular junctions containing ferrocene centers

In our theoretical study where we combine a nonequilibrium Green's function (NEGF) approach with density functional theory (DFT) we investigate branched compounds containing ferrocene moieties in both branches which due to their metal centers are designed to allow for asymmetry induced by local charging. In these compounds the ferrocene moieties are connected to pyridyl anchor groups either directly or via acetylenic spacers in a meta-connection where we also compare our results with those obtained for the respective single-branched molecules with both meta- and para-connections between the metal center and the anchors. We find a destructive quantum interference (DQI) feature in the transmission function slightly below the lowest unoccupied molecular orbital (LUMO) which dominates the conductance even for the uncharged branched compound with spacer groups inserted. In an analysis based on mapping the structural characteristics of the range of molecules in our article onto tight-binding models, we identify the structural source of the DQI minimum as the through-space coupling between the pyridyl anchor groups. We also find that local charging on one of the branches only changes the conductance by about one order of magnitude which we explain in terms of the spatial distributions of the relevant molecular orbitals for the branched compounds.

cond-mat.mes-hall↗

arXiv2016

Destructive quantum interference in electron transport: A reconciliation of the molecular orbital and the atomic orbital perspective

Destructive quantum interference (DQI) in single molecule electronics is a purely quantum mechanical effect and entirely defined by inherent properties of the molecule in the junction such as its structure and symmetry. This definition of DQI by molecular properties alone suggests its relation to other more general concepts in chemistry as well as the possibility of deriving simple models for its understanding and molecular device design. Recently, two such models have gained wide spread attention, where one was a graphical scheme based on visually inspecting the connectivity of carbon sites in conjugated pi systems in an atomic orbital (AO) basis and the other one put the emphasis on the amplitudes and signs of the frontier molecular orbitals (MOs). There have been discussions on the range of applicability for these schemes, but ultimately conclusions from topological molecular Hamiltonians should not depend on whether they are drawn from an AO or a MO representation, as long as all the orbitals are taken into account. In this article we clarify the relation between both models in terms of the zeroth order Green's function and compare their predictions for a variety of systems. From this comparison we conclude that for a correct description of DQI from a MO perspective it is necessary to include the contributions from all MOs rather than just those from the frontier orbitals. The cases where DQI effects can be successfully predicted within a frontier orbital approximation we show to be limited to alternant even-membered hydrocarbons, as a a direct consequence of the Coulson-Rushbrooke pairing theorem in quantum chemistry.

cond-mat.mes-hall↗

arXiv2016

Comment on "Breakdown of Interference Rules in Azulene, a Nonalternant Hydrocarbon"

Quantum interference (QI) effects in molecular systems are a topic of emerging interest in electron transport studies of single molecule junctions. In a recent Letter, Xia et al. employed a graphical scheme introduced by my colleagues and myself that enables to distinguish between molecular topologies in conjugated pi systems which exhibit QI effects in their conductance from those who do not. They claimed that this scheme is not applicable for nonalternant hydrocarbons, in particular Azulenes (Az), whose transport properties were studied both theoretically and experimentally by connecting the electrodes at Az's 1,3-, 2,6-, 4,7-, and 5,7-positions, respectively. An apparent disagreement has been identified between the predictions of our scheme referred to as "atom- or bond-counting model" and theoretical simulations for featureless, wide band electrodes in the GW approximation as well as for the tight-binding (TB) model our method was originally derived from. In the following I would like to clarify that this apparent disagreement vanishes if the graphical scheme is applied correctly, providing a different result for the 1,3 Az compound than claimed by Xia et al. It will further be argued that the graphical scheme is completely general for any molecular topology in conjugated pi systems regardless of whether they are alternant or non-alternant hydrocarbons as long as the basic assumptions of its derivation are fulfilled.

cond-mat.mes-hall↗

arXiv2016

Field-induced Conductance Switching by Charge-state Alternation in Organometallic Single-Molecule Junctions

Charge transport through single molecules can be influenced by the charge and spin states of redox-active metal centres placed in the transport pathway. These molecular intrinsic properties are usually addressed by varying the molecules electrochemical and magnetic environment, a procedure that requires complex setups with multiple terminals. Here we show that oxidation and reduction of organometallic compounds containing either Fe, Ru or Mo centres can solely be triggered by the electric field applied to a two-terminal molecular junction. Whereas all compounds exhibit bias-dependent hysteresis, the Mo-containing compound additionally shows an abrupt voltage-induced conductance switching, yielding high to low current ratios exceeding 1000 at voltage stimuli of less than 1.0 V. DFT calculations identify a localized, redox active molecular orbital that is weakly coupled to the electrodes and closely aligned with the Fermi energy of the leads because of the spin-polarised ground state unique to the Mo centre. This situation opens an additional slow and incoherent hopping channel for transport, triggering a transient charging effect of the entire molecule and a strong hysteresis with unprecedented high low-to-high current ratios.

cond-mat.mes-hall↗

arXiv2015

Quantum interference effects in electron transport: How to select suitable molecules for logic gates and thermoelectric devices

Since the concepts for the implementation of data storage and logic gates used in conventional electronics cannot be simply downscaled to the level of single molecule devices, new architectural paradigms are needed, where quantum interference (QI) effects are likely to provide an useful starting point. In order to be able to use QI for design purposes in single molecule electronics, the relation between their occurrence and molecular structure has to be understood at such a level that simple guidelines for electrical engineering can be established. We made a big step towards this aim by developing a graphical scheme that allows for the prediction of the occurrence or absence of QI induced minima in the transmission function and the derivation of this method will form the center piece of this review article. In addition the possible usefulness of QI effects for thermoelectric devices is addressed, where the peak shape around a transmission minimum is of crucial importance and different rules for selecting suitable molecules have to be found.

cond-mat.mes-hall↗

arXiv2015

High-Conductive Organometallic Molecular Wires with Delocalized Electron Systems Strongly Coupled to Metal Electrodes

Besides active, functional molecular building blocks such as diodes or switches, passive components as, e.g., molecular wires, are required to realize molecular-scale electronics. Incorporating metal centers in the molecular backbone enables the molecular energy levels to be tuned in respect to the Fermi energy of the electrodes. Furthermore, by using more than one metal center and sp-bridging ligands, a strongly delocalized electron system is formed between these metallic "dopants", facilitating transport along the molecular backbone. Here, we study the influence of molecule--metal coupling on charge transport of dinuclear X(PP)$_2$FeC$_4$Fe(PP)$_2$X molecular wires (PP = Et$_2$PCH$_2$CH$_2$PEt$_2$); X = CN (1), NCS (2), NCSe (3), C$_4$SnMe$_3$ (4) and C$_2$SnMe$_3$ (5)) under ultra-high vacuum and variable temperature conditions. In contrast to 1 which showed unstable junctions at very low conductance ($8.1\cdot10^{-7}$ G$_0$), 4 formed a Au-C$_4$FeC$_4$FeC$_4$-Au junction 4' after SnMe$_3$ extrusion which revealed a conductance of $8.9\cdot10^{-3}$ G$_0$, three orders of magnitude higher than for 2 ($7.9\cdot10^{-6}$ G$_0$) and two orders of magnitude higher than for 3 ($3.8\cdot10^{-4}$ G$_0$). Density functional theory (DFT) confirmed the experimental trend in the conductance for the various anchoring motifs. The strong hybridization of molecular and metal states found in the C--Au coupling case enables the delocalized electronic system of the organometallic Fe$_2$ backbone to be extended over the molecule-metal interfaces to the metal electrodes to establish high-conductive molecular wires.

cond-mat.mes-hall↗

arXiv2015

Partial vs. integer electron transfer in molecular assemblies: On the importance of a multideterminant theoretical description and the necessity to find a solution within DFT

Nonequilibrium Greens function techniques (NEGF) combined with density functional theory (DFT) calculations have become a standard tool for the description of electron transport through single molecule nanojunctions in the coherent tunneling regime. However, the applicability of these methods for transport in the Coulomb blockade regime is questionable. For a molecular assembly model, with multideterminant calculations as a benchmark, we show how a closed shell ansatz, the usual ingredient of meanfield methods, fails to properly describe the step like electron transfer characteristic in weakly coupled systems. Detailed analysis of this misbehavior allows us to propose a practical scheme to extract the addition energies in the CB regime for single-molecule junctions from NEGF DFT within the local density approximation (closed shell). We show also that electrostatic screening effects are taken into account within this simple approach.

cond-mat.mes-hall↗

arXiv2015

A density functional theory based direct comparison of coherent tunnelling and electron hopping in redox-active single molecule junctions

For defining the conductance of single molecule junctions with a redox functionality in an electrochemical cell, two conceptually different electron transport mechanisms, namely coherent tunnelling and vibrationally induced hopping compete with each other, where implicit parameters of the setup such as the length of the molecule and the applied gate voltage decide which mechanism is the dominant one. Although coherent tunnelling is most efficiently described within Landauer theory, while the common theoretical treatment of electron hopping is based on Marcus theory, both theories are adequate for the processes they describe without introducing accuracy limiting approximations. For a direct comparison, however, it has to be ensured that the crucial quantities obtained from electronic structure calculations, i.e. the transmission function T(E) in Landauer theory, and the transfer integral V, the reorganisation energy $λ$ and the driving force $ΔG^0$ in Marcus theory, are derived from similar grounds as pointed out by Nitzan and co-workers in a series of publications. In this article our framework is a single particle picture, where we perform density functional theory calculations for the conductance corresponding to both transport mechanisms for junctions with the central molecule containing one, two or three Ruthenium centers, respectively, where we extrapolate our results in order to define the critical length for the transition point of the two regimes which we identify at 5.76 nm for this type of molecular wire. We also discuss trends in dependence on an electrochemically induced gate potential.

cond-mat.mes-hall↗

arXiv2014

Density functional theory based calculations of the transfer integral in a redox-active single molecule junction

There are various quantum chemical approaches for an ab initio description of transfer integrals within the framework of Marcus theory in the context of electron transfer reactions. In our article we aim to calculate transfer integrals in redox-active single molecule junctions, where we focus on the coherent tunneling limit with the metal leads taking the position of donor and acceptor and the molecule acting as a transport mediating bridge. This setup allows us to derive a conductance, which can be directly compared with recent results from a non-equilibrium Green's function approach. Compared with purely molecular systems we face additional challenges due to the metallic nature of the leads, which rules out some of the common techniques, and due to their periodicity, which requires {\bf k} space integration. We present three different methods, all based on density functional theory, for calculating the transfer integral under these constraints, which we benchmark on molecular test systems from the relevant literature. We also discuss manybody effects and apply all three techniques to a junction with a Ruthenium complex in different oxidation states.

cond-mat.mes-hall↗

arXiv2013

Charge localisation on a redox-active single molecule junction and its influence on coherent electron transport

For adjusting the charging state of a molecular metal complex in the context of a density functional theory description of coherent electron transport through single molecule junctions, we correct for self interaction effects by fixing the charge on a counterion, which in our calculations mimics the effect of the gate in an electrochemical STM setup, with two competing methods, namely the generalized $Δ$ SCF technique and screening with solvation shells. One would expect a transmission peak to be pinned at the Fermi energy for a nominal charge of +1 on the molecule in the junction but we find a more complex situation in this multicomponent system defined by the complex, the leads, the counterion and the solvent. In particular equilibrium charge transfer between the molecule and the leads plays an importanty role, which we investigate in dependence on the total external charge in the context of electronegativity theory.

cond-mat.mes-hall↗

arXiv2012

Electron transfer through a single barrier inside a molecule: from strong to weak coupling

In all theoretical treatments of electron transport through single molecules between two metal electrodes, a clear distinction has to be made between a coherent transport regime with a strong coupling throughout the junction and a Coulomb blockade regime in which the molecule is only weakly coupled to both leads. The former case where the tunnelling barrier is considered to be delocalized across the system can be well described with common mean-field techniques based on density functional theory (DFT), while the latter case with its two distinct barriers localized at the interfaces usually requires a multideterminant description. There is a third scenario with just one barrier localized inside the molecule which we investigate here using a variety of quantum-chemical methods by studying partial charge shifts in biphenyl radical ions induced by an electric field at different angles to modulate the coupling and thereby the barrier within the $π$-system. We find steps rounded off at the edges in the charge versus field curves for weak and intermediate coupling, whose accurate description requires a correct treatment of both exchange and dynamical correlation effects is essential. We establish that DFT standard functionals fail to reproduce this feature, while a long range corrected hybrid functional fares much better, which makes it a reasonable choice for a proper DFT-based transport description of such single barrier systems

cond-mat.mes-hall↗

arXiv2011

Controlling the transmission line shape of molecular t-stubs and potential thermoelectric applications

Asymmetric line shapes can occur in the transmission function describing electron transport in the vicinity of a minimum caused by quantum interference effects. Such asymmetry can be used to increase the thermoelectric efficiency of molecular junctions. So far, however, asymmetric line shapes have been only empirically found for just a few rather complex organic molecules where the origins of the line shapes relation to molecular structure were not resolved. In the present work we introduce a method to analyze the structure dependence of the asymmetry of interference dips from simple two site tight-binding models, where one site corresponds to a molecular $π$ orbital of the wire and the other to an atomic $p_z$ orbital of a side group, which allows us to analytically characterize the peak shape in terms of just two parameters. We assess our scheme with first-principles electron transport calculations for a variety of {\it t-stub} molecules and also address their suitability for thermoelectric applications.

cond-mat.mes-hall↗

arXiv2011

Graphical prediction of quantum interference-induced transmission nodes in functionalized organic molecules

Quantum interference (QI) in molecular transport junctions can lead to dramatic reductions of the electron transmission at certain energies. In a recent work [Markussen et al., Nano Lett. 2010, 10, 4260] we showed how the presence of such transmission nodes near the Fermi energy can be predicted solely from the structure of a conjugated molecule when the energies of the atomic p_z orbitals do not vary too much. Here we relax the assumption of equal on-site energies and generalize the graphical scheme to molecules containing different atomic species. We use this diagrammatic scheme together with tight-binding and density functional theory calculations to investigate QI in linear molecular chains and aromatic molecules with different side groups. For the molecular chains we find a linear relation between the position of the transmission nodes and the side group pi orbital energy. In contrast, the transmission functions of functionalized aromatic molecules generally display a rather complex nodal structure due to the interplay between molecular topology and the energy of the side group orbital.

cond-mat.mes-hall↗

arXiv2010

Relative Oscillation Theory for Dirac Operators

We develop relative oscillation theory for one-dimensional Dirac operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing zeros of solutions of one operator by weighted zeros of Wronskians of solutions of two different operators. In particular, we show that a Sturm-type comparison theorem still holds in this situation and demonstrate how this can be used to investigate the number of eigenvalues in essential spectral gaps. Furthermore, the connection with Krein's spectral shift function is established. As an application we extend a result by K.M. Schmidt on the finiteness/infiniteness of the number of eigenvalues in essential spectral gaps of perturbed periodic Dirac operators.

math.SP↗

arXiv2010

Conformation dependence of charge transfer and level alignment in nitrobenzene junctions with pyridyl anchor groups

The alignment of molecular levels with the Fermi energy in single molecule junctions is a crucial factor in determining their conductance or the observability of quantum interference effects. In the present study which is based on density functional theory calculations, we explore the zero-bias charge transfer and level alignment for nitro-bipyridyl-phenyl adsorbed between two gold surfaces which we find to vary significantly with the molecular conformation. The net charge transfer is the result of two opposing effects, namely Pauli repulsion at the interface between the molecule and the leads, and the electron accepting nature of the NO$_2$ group, where only the latter which we analyze in terms of the electronegativity of the isolated molecules depends on the two intra-molecular torsion angles. We provide evidence that the conformation dependence of the alignment of molecular levels and peaks in the transmission function can indeed be understood in terms of charge transfer for this system, and that other properties such as molecular dipoles do not play a significant role. Our study is relevant for device design in molecular electronics where nitrobenzene appears as a component in proposals for rectification, quantum interference or chemical gating.

cond-mat.mes-hall↗