Close relation between quantum interference in molecular conductance and diradical existence.

An empirical observation of a relationship between a striking feature of electronic transmission through a π-system, destructive quantum interference (QI), on one hand, and the stability of diradicals on the other, leads to the proof of a general theorem that relates the two. Subject to a number of simplifying assumptions, in a π-electron system, QI occurs when electrodes are attached to those positions of an N-carbon atom N-electron closed-shell hydrocarbon where the matrix elements of the Green's function vanish. These zeros come in two types, which are called easy and hard. Suppose an N+2 atom, N+2 electron hydrocarbon is formed by substituting 2 CH2 groups at two atoms, where the electrodes were. Then, if a QI feature is associated with electrode attachment to the two atoms of the original N atom system, the resulting augmented N+2 molecule will be a diradical. If there is no QI feature, i.e., transmission of current is normal if electrodes are attached to the two atoms, the resulting hydrocarbon will not be a diradical but will have a classical closed-shell electronic structure. Moreover, where a diradical exists, the easy zero is associated with a nondisjoint diradical, and the hard zero is associated with a disjoint one. A related theorem is proven for deletion of two sites from a hydrocarbon.

Complex band structure and electronic transmission eigenchannels.

It is natural to characterize materials in transport junctions by their conductance length dependence, ß. Theoretical estimations of ß are made employing two primary theories: complex band structure and density functional theory (DFT) Landauer transport. It has previously been shown that the ß value derived from total Landauer transmission can be related to the ß value from the smallest |ki| complex band; however, it is an open question whether there is a deeper relationship between the two. Here we probe the details of the relationship between transmission and complex band structure, in this case individual eigenchannel transmissions and different complex bands. We present calculations of decay constants for the two most conductive states as determined by complex band structure and standard DFT Landauer transport calculations for one semi-conductor and two molecular junctions. The molecular junctions show that both the length dependence of the total transmission and the individual transmission eigenvalues can be, almost always, found through the complex band structure. The complex band structure of the semi-conducting material, however, does not predict the length dependence of the total transmission but only of the individual channels, at some k-points, due to multiple channels contributing to transmission. We also observe instances of vertical bands, some of which are the smallest |ki| complex bands, that do not contribute to transport. By understanding the deeper relationship between complex bands and individual transmission eigenchannels, we can make a general statement about when the previously accepted wisdom linking transmission and complex band structure will fail, namely, when multiple channels contribute significantly to the transmission.

Breakdown of interference rules in azulene, a nonalternant hydrocarbon.

We have designed and synthesized five azulene derivatives containing gold-binding groups at different points of connectivity within the azulene core to probe the effects of quantum interference through single-molecule conductance measurements. We compare conducting paths through the 5-membered ring, 7-membered ring, and across the long axis of azulene. We find that changing the points of connectivity in the azulene impacts the optical properties (as determined from UV-vis absorption spectra) and the conductivity. Importantly, we show here that simple models cannot be used to predict quantum interference characteristics of nonalternant hydrocarbons. As an exemplary case, we show that azulene derivatives that are predicted to exhibit destructive interference based on widely accepted atom-counting models show a significant conductance at low biases. Although simple models to predict the low-bias conductance do not hold with all azulene derivatives, we demonstrate that the measured conductance trend for all molecules studied actually agrees with predictions based on the more complete GW calculations for model systems.

Understanding the length dependence of molecular junction thermopower.

Thermopower of molecular junctions is sensitive to details in the junction and may increase, decrease, or saturate with increasing chain length, depending on the system. Using McConnell's theory for exponentially suppressed transport together with a simple and easily interpretable tight binding model, we show how these different behaviors depend on the molecular backbone and its binding to the contacts. We distinguish between resonances from binding groups or undercoordinated electrode atoms, and those from the periodic backbone. It is demonstrated that while the former gives a length-independent contribution to the thermopower, possibly changing its sign, the latter determines its length dependence. This means that the question of which orbitals from the periodic chain that dominate the transport should not be inferred from the sign of the thermopower but from its length dependence. We find that the same molecular backbone can, in principle, show four qualitatively different thermopower trends depending on the binding group: It can be positive or negative for short chains, and it can either increase or decrease with length.

Energy level alignment and quantum conductance of functionalized metal-molecule junctions: density functional theory versus GW calculations.

We study the effect of functional groups (CH3*4, OCH3, CH3, Cl, CN, F*4) on the electronic transport properties of 1,4-benzenediamine molecular junctions using the non-equilibrium Green function method. Exchange and correlation effects are included at various levels of theory, namely density functional theory (DFT), energy level-corrected DFT (DFT+Σ), Hartree-Fock and the many-body GW approximation. All methods reproduce the expected trends for the energy of the frontier orbitals according to the electron donating or withdrawing character of the substituent group. However, only the GW method predicts the correct ordering of the conductance amongst the molecules. The absolute GW (DFT) conductance is within a factor of two (three) of the experimental values. Correcting the DFT orbital energies by a simple physically motivated scissors operator, Σ, can bring the DFT conductances close to experiments, but does not improve on the relative ordering. We ascribe this to a too strong pinning of the molecular energy levels to the metal Fermi level by DFT which suppresses the variation in orbital energy with functional group.

Dynamic breaking of a single gold bond.

While one might assume that the force to break a chemical bond gives a measure of the bond strength, this intuition is misleading. If the force is loaded slowly, thermal fluctuations may break the bond before it is maximally stretched, and the breaking force will be less than the bond can sustain. Conversely, if the force is loaded rapidly it is more likely that the maximum breaking force is measured. Paradoxically, no clear differences in breaking force were observed in experiments on gold nanowires, despite being conducted under very different conditions. Here we explore the breaking behaviour of a single Au-Au bond and show that the breaking force is dependent on the loading rate. We probe the temperature and structural dependencies of breaking and suggest that the paradox can be explained by fast breaking of atomic wires and slow breaking of point contacts giving very similar breaking forces.

The atomic simulation environment-a Python library for working with atoms.

The atomic simulation environment (ASE) is a software package written in the Python programming language with the aim of setting up, steering, and analyzing atomistic simulations. In ASE, tasks are fully scripted in Python. The powerful syntax of Python combined with the NumPy array library make it possible to perform very complex simulation tasks. For example, a sequence of calculations may be performed with the use of a simple 'for-loop' construction. Calculations of energy, forces, stresses and other quantities are performed through interfaces to many external electronic structure codes or force fields using a uniform interface. On top of this calculator interface, ASE provides modules for performing many standard simulation tasks such as structure optimization, molecular dynamics, handling of constraints and performing nudged elastic band calculations.

Towards quantitative accuracy in first-principles transport calculations: The GW method applied to alkane/gold junctions.

The calculation of the electronic conductance of nanoscale junctions from first principles is a long-standing problem in the field of charge transport. Here we demonstrate excellent agreement with experiments for the transport properties of the gold/alkanediamine benchmark system when electron-electron interactions are described by the many-body GW approximation. The conductance follows an exponential length dependence: G(n) = G(c) exp(-ßn). The main difference from standard density functional theory (DFT) calculations is a significant reduction of the contact conductance, G(c), due to an improved alignment of the molecular energy levels with the metal Fermi energy. The molecular orbitals involved in the tunneling process comprise states delocalized over the carbon backbone and states localized on the amine end groups. We find that dynamic screening effects renormalize the two types of states in qualitatively different ways when the molecule is inserted in the junction. Consequently, the GW transport results cannot be mimicked by DFT calculations employing a simple scissors operator.

Anomalous conductance oscillations and half-metallicity in atomic Ag-O chains.

Using spin density functional theory, we study the electronic and magnetic properties of atomically thin, suspended chains containing silver and oxygen atoms in an alternating sequence. Chains longer than 4 atoms develop a half-metallic ground state implying fully spin-polarized charge carriers. The conductances of the chains exhibit weak even-odd oscillations around an anomalously low value of 0.1G0 (G0=2e2/h) which coincide with the averaged experimental conductance in the long chain limit. The unusual conductance properties are explained in terms of a resonating-chain model, which takes the reflection probability and phase shift of a single bulk-chain interface as the only input. The model also explains the conductance oscillations for other metallic chains.

Conductance of sidewall-functionalized carbon nanotubes: universal dependence on adsorption sites.

We use density functional theory to study the effect of molecular adsorbates on the conductance of metallic carbon nanotubes (CNT). The five molecules considered (NO2, NH2, H, COOH, OH) lead to very similar scattering of the electrons. The adsorption of a single molecule suppresses one of the two available transport channels at the Fermi level while the other is left undisturbed. If more molecules are adsorbed on the same sublattice, the remaining open channel may or may not be blocked, depending on the relative position of the adsorbates. If the relative positions satisfy a simple geometric condition, this channel remains fully open independently of the number of adsorbed molecules.