The molecular yo-yo method: live jump detection improves throughput of single-molecule force spectroscopy for out-of-equilibrium transitions.

By monitoring multiple molecular transitions, force-clamp, and trap-position-clamp methods have led to precise determinations of the free energies and free energy landscapes for molecular states populated in equilibrium at the same or similar forces. Here, we present a powerful new elaboration of the force-clamp and force-jump methods, applicable to transitions far from equilibrium. Specifically, we have implemented a live jump detection and force-clamp algorithm that intelligently adjusts and maintains the force on a single molecule in response to the measured state of that molecule. We are able to collect hundreds of individual molecular transitions at different forces, many times faster than previously, permitting us to accurately determine force-dependent lifetime distributions and reaction rates. Application of our method to unwinding and rewinding the nucleosome inner turn, using optical tweezers reveals experimental lifetime distributions that comprise a statistically meaningful number of transitions, and that are accurately single exponential. These measurements significantly reduce the error in the previously measured rates, and demonstrate the existence of a single, dominant free energy barrier at each force studied. A key benefit of the molecular yo-yo method for nucleosomes is that it reduces as far as possible the time spent in the tangentially bound state, which minimizes the loss of nucleosomes by dissociation.

Unwinding and rewinding the nucleosome inner turn: force dependence of the kinetic rate constants.

A simple model for the force-dependent unwinding and rewinding rates of the nucleosome inner turn is constructed and quantitatively compared to the results of recent measurements [A. H. Mack et al., J. Mol. Biol. 423, 687 (2012)]. First, a coarse-grained model for the histone-DNA free-energy landscape that incorporates both an elastic free-energy barrier and specific histone-DNA bonds is developed. Next, a theoretical expression for the rate of transitions across a piecewise linear free-energy landscape with multiple minima and maxima is presented. Then, the model free-energy landscape, approximated as a piecewise linear function, and the theoretical expression for the transition rates are combined to construct a model for the force-dependent unwinding and rewinding rates of the nucleosome inner turn. Least-mean-squares fitting of the model rates to the rates observed in recent experiments rates demonstrates that this model is able to well describe the force-dependent unwinding and rewinding rates of the nucleosome inner turn, observed in the recent experiments, except at the highest forces studied, where an additional ad hoc term is required to describe the data, which may be interpreted as an indication of an alternate high-force nucleosome disassembly pathway, that bypasses simple unwinding. The good agreement between the measurements and the model at lower forces demonstrates that both specific histone-DNA contacts and an elastic free-energy barrier play essential roles for nucleosome winding and unwinding, and quantifies their relative contributions.

Probing the conductance superposition law in single-molecule circuits with parallel paths.

According to Kirchhoff's circuit laws, the net conductance of two parallel components in an electronic circuit is the sum of the individual conductances. However, when the circuit dimensions are comparable to the electronic phase coherence length, quantum interference effects play a critical role, as exemplified by the Aharonov-Bohm effect in metal rings. At the molecular scale, interference effects dramatically reduce the electron transfer rate through a meta-connected benzene ring when compared with a para-connected benzene ring. For longer conjugated and cross-conjugated molecules, destructive interference effects have been observed in the tunnelling conductance through molecular junctions. Here, we investigate the conductance superposition law for parallel components in single-molecule circuits, particularly the role of interference. We synthesize a series of molecular systems that contain either one backbone or two backbones in parallel, bonded together cofacially by a common linker on each end. Single-molecule conductance measurements and transport calculations based on density functional theory show that the conductance of a double-backbone molecular junction can be more than twice that of a single-backbone junction, providing clear evidence for constructive interference.

Environmental control of single-molecule junction transport.

The conductance of individual 1,4-benzenediamine (BDA)-Au molecular junctions is measured in different solvent environments using a scanning tunneling microscope based point-contact technique. Solvents are found to increase the conductance of these molecular junctions by as much as 50%. Using first principles calculations, we explain this increase by showing that a shift in the Au contact work function is induced by solvents binding to undercoordinated Au sites around the junction. Increasing the Au contact work function reduces the separation between the Au Fermi energy and the highest occupied molecular orbital of BDA in the junction, increasing the measured conductance. We demonstrate that the solvent-induced shift in conductance depends on the affinity of the solvent to Au binding sites and also on the induced dipole (relative to BDA) upon adsorption. Via this mechanism, molecular junction level alignment and transport properties can be statistically altered by solvent molecule binding to the contact surface.

Relating energy level alignment and amine-linked single molecule junction conductance.

Using photoemission spectroscopy, we determine the relationship between electronic energy level alignment at a metal-molecule interface and single-molecule junction transport data. We measure the position of the highest occupied molecular orbital (HOMO) relative to the Au metal Fermi level for three 1,4-benzenediamine derivatives on Au(111) and Au(110) with ultraviolet and resonant X-ray photoemission spectroscopy. We compare these results to scanning tunnelling microscope-based break-junction measurements of single molecule conductance and to first-principles calculations. We find that the energy difference between the HOMO and Fermi level for the three molecules adsorbed on Au(111) correlate well with changes in conductance and agree well with quasiparticle energies computed from first-principles calculations incorporating self-energy corrections. On the Au(110) that presents Au atoms with lower-coordination, critical in break-junction conductance measurements, we see that the HOMO level shifts further from the Fermi level. These results provide the first direct comparison of spectroscopic energy level alignment measurements with single molecule junction transport data.

Conductance and geometry of pyridine-linked single-molecule junctions.

We have measured the conductance and characterized molecule-electrode binding geometries of four pyridine-terminated molecules by elongating and then compressing gold point contacts in a solution of molecules. We have found that all pyridine-terminated molecules exhibit bistable conductance signatures, signifying that the nature of the pyridine-gold bond allows two distinct conductance states that are accessed as the gold-molecule-gold junction is elongated. We have identified the low-conductance state as corresponding to a molecule fully stretched out between the gold electrodes, where the distance between contacts correlates with the length of the molecule; the high-conductance state is due to a molecule bound at an angle. For all molecules, we have found that the distribution of junction elongations in the low-conductance state is the same, while in the high-conductance state, the most likely elongation length increases linearly with molecule length. The results of first-principles conductance calculations for the four molecules in the low-conductance geometry agree well with the experimental results and show that the dominant conducting channel in the conjugated pyridine-linked molecules is through the pi* orbital.

Measurement of voltage-dependent electronic transport across amine-linked single-molecular-wire junctions.

We measure the conductance and current-voltage characteristics of two amine-terminated molecular wires -- 4,4'-diaminostilbene and bis-(4-aminophenyl)acetylene -- by breaking Au point contacts in a molecular solution at room temperature. Histograms compiled from thousands of measurements show a slight increase in the molecular junction conductance (I/V) as the bias is increased to nearly 450 mV. Comparatively, similar conductance measurements made with 1,6-diaminohexane, a saturated molecule, demonstrate almost no bias dependence. We also present a new technique to measure a statistically defined current-voltage (I-V) curve. Application to all three molecules shows that 4,4'-diaminostilbene exhibits the largest increase in differential conductance as a function of applied bias. This indicates that the predominant transport channel for 4,4'-diaminostilbene (the highest occupied molecular orbital) is closer to the Fermi level of the metal than that of the other molecules, consistent with the trends observed in the molecular ionization potential. We find that junctions constructed with the conjugated molecules show greater noise in individual junctions and less structural stability, on average, at biases greater than 450 mV. In contrast, junctions formed with the alkane can sustain a bias of up to 900 mV. This significantly affects the statistically averaged I-V characteristic measured for the conjugated molecules at higher bias.

Formation and evolution of single-molecule junctions.

We analyze the formation and evolution statistics of single-molecule junctions bonded to gold electrodes using amine, methyl sulfide, and dimethyl phosphine link groups by measuring conductance as a function of junction elongation. For each link, the maximum elongation and formation probability increase with molecular length, strongly suggesting that processes other than just metal-molecule bond breakage play a key role in junction evolution under stress. Density functional theory calculations of adiabatic trajectories show sequences of atomic-scale changes in junction structure, including shifts in the attachment point, that account for the long conductance plateau lengths observed.