Molecular-scale Systems Research Articles

Towards optimal control: the probabilistic route in quantum systems

There is a fundamental limit to what is knowable about atomic and molecular scale systems. This fuzziness is not always due to the act of measurement. Other contributing factors include system parameter uncertainty, functional uncertainty that originates from input functions, and sensors noises to mention a few. This indeterminism has led to major challenges in the development of accurate control methods for atomic scale systems. To address the probabilistic and uncertain nature of these systems, this work proposes a novel control framework that considers the representation of the quantum system states and the quantification of its physical properties following a probabilistic approach. Our framework is fully probabilistic. It uses the Shannon relative entropy from information theory to design optimal randomised controllers that can achieve a desired outcome of an atomic scale system. Two experiments are carried out to illustrate the applicability and effectiveness of the proposed approach.

Investigation of Conductance and Capacitance of Mesoscopic and Molecular Scale Systems

Investigation of Conductance and Capacitance of Mesoscopic and Molecular Scale Systems

Mapping saddles and minima on free energy surfaces using multiple climbing strings.

Locating saddle points on free energy surfaces is key in characterizing multistate transition events in complicated molecular-scale systems. Because these saddle points represent transition states, determining minimum free energy pathways to these saddles and measuring their free energies relative to their connected minima are further necessary, for instance, to estimate transition rates. In this work, we propose a new multistring version of the climbing string method in collective variables to locate all saddles and corresponding pathways on free energy surfaces. The method uses dynamic strings to locate saddles and static strings to keep a history of prior strings converged to saddles. Interaction of the dynamic strings with the static strings is used to avoid the convergence to already-identified saddles. Additionally, because the strings approximate curves in collective-variable space, and we can measure free energy along each curve, identification of any saddle's two connected minima is guaranteed. We demonstrate this method to map the network of stationary points in the 2D and 4D free energy surfaces of alanine dipeptide and alanine tripeptide, respectively.

Renewable Time-Responsive DNA Circuits.

DNA devices have been shown to be capable of evaluating Boolean logic. Several robust designs for DNA circuits have been demonstrated. Some prior DNA-based circuits are use-once circuits since the gate motifs of the DNA circuits get permanently destroyed as a side effect of the computation, and hence cannot respond correctly to subsequent changes in inputs. Other DNA-based circuits use a large reservoir of buffered gates to replace the working gates of the circuit and can be used to drive a finite number of computation cycles. In many applications of DNA circuits, the inputs are inherently asynchronous, and this necessitates that the DNA circuits be asynchronous: the output must always be correct regardless of differences in the arrival time of inputs. This paper demonstrates: 1) renewable DNA circuits, which can be manually reverted to their original state by addition of DNA strands, and 2) time-responsive DNA circuits, where if the inputs change over time, the DNA circuit can recompute the output correctly based on the new inputs, that are manually added after the system has been reset. The properties of renewable, asynchronous, and time-responsiveness appear to be central to molecular-scale systems; for example, self-regulation in cellular organisms.

Divergence of relative difference in Gaussian distribution function and stochastic resonance in a bistable system with frictionless state transition

A bistable system efficiently detects a weak signal by adding noise, which is referred to as stochastic resonance. A previous theory deals with friction in state transition; however, this hypothesis is inadequate when friction force is negligible such as in nano- and molecular-scale systems. We show that, when the transition occurs without friction, the sensitivity of the bistable system to a Gaussian-noise-imposed weak signal becomes significantly high. The sensitivity is determined by the relative difference in noise distribution function. We find that the relative difference in Gaussian distribution function diverges in its tail edge, resulting in a high sensitivity in the present system.

Reversibly Bound Kinesin-1 Motor Proteins Propelling Microtubules Demonstrate Dynamic Recruitment of Active Building Blocks.

Biological materials and systems often dynamically self-assemble and disassemble, forming temporary structures as needed and allowing for dynamic responses to stimuli and changing environmental conditions. However, this dynamic interplay of localized component recruitment and release has been difficult to achieve in artificial molecular-scale systems, which are usually designed to have long-lasting, stable bonds. Here, we report the experimental realization of a molecular-scale system that dynamically assembles and disassembles its building blocks while retaining functionality. In our system, filaments (microtubules) recruit biomolecular motors (kinesins) to a surface engineered to allow for the reversible binding of the kinesin-1 motors. These recruited motors work to propel the cytoskeletal filaments along the surface. After the microtubules leave the motors behind, the trail of motors disassembles, releasing the motors back into solution. Engineering such dynamic systems may allow us to create materials that mimic the way in which biological systems achieve self-healing and adaptation.

Electrochemistry of single molecules and biomolecules, molecular scale nanostructures, and low-dimensional systems

Electrochemistry at ultra-small scales, where even the single molecule or biomolecule can be characterized and manipulated, is on the way to a consolidated status. At the same time, molecular electrochemistry is expanding into other areas of sophisticated nano- and molecular-scale systems including molecular scale metal and semiconductor nanoparticles (NPs) and other nanostructures, e.g. nanotubes, “nanoflowers” etc. The new structures offer both new electronic properties and highly confined novel charge transfer environments.

Dynamic DNA Origami Device for Measuring Compressive Depletion Forces

The ability to self-assemble nanodevices with programmed structural dynamics that can sense and respond to the local environment could enable transformative applications in fields including molecular robotics, nanomanufacturing, and nanomedicine. The responsive function of biomolecules is often driven by alterations in conformational distributions mediated by highly sensitive interactions with the local environment. Here, we mimic this approach by engineering inherent nanoscale structural dynamics (nanodynamics) into a DNA device that exhibits a distribution of conformations including two stable states separated by a transition state where the energy barrier height is on the scale of the thermal energy, kBT = 4.1 pN·nm, enabling spontaneous transitions between states. We further establish design principles to regulate the equilibrium and kinetic behavior by substituting a few DNA strand components. We use single-molecule Förster resonance energy transfer measurements to show these nanodynamic properties are sensitive to sub-piconewton depletion forces in the presence of molecular crowding agents, and the device can measure depletion forces with a resolution of ∼100 fN. We anticipate that this approach of engineering nanodynamic DNA devices will enable molecular-scale systems that sense and respond to their local environment with extremely high sensitivity.

Conceptual density functional theory for electron transfer and transport in mesoscopic systems.

Molecular and supramolecular systems are essentially mesoscopic in character. The electron self-exchange, in the case of energy fluctuations, or electron transfer/transport, in the case of the presence of an externally driven electrochemical potential, between mesoscopic sites is energetically driven in such a manner where the electrochemical capacitance (C[small mu, Greek, macron]) is fundamental. Thus, the electron transfer/transport through channels connecting two distinct energetic (ΔE[small mu, Greek, macron]) and spatially separated mesoscopic sites is capacitively modulated. Remarkably, the relationship between the quantum conductance (G) and the standard electrochemical rate constant (kr), which is indispensable to understanding the physical and chemical characteristics governing electron exchange in molecular scale systems, was revealed to be related to C[small mu, Greek, macron], that is, C[small mu, Greek, macron] = G/kr. Accordingly, C[small mu, Greek, macron] is the proportional missing term that controls the electron transfer/transport in mesoscopic systems in a wide-range, and equally it can be understood from first principles density functional quantum mechanical approaches. Indeed the differences in energy between states is calculated (or experimentally accessed) throughout the electrochemical capacitance as ΔE[small mu, Greek, macron] = β/C[small mu, Greek, macron], and thus constitutes the driving force for G and/or kr, where β is only a proportional constant that includes the square of the unit electron charge times the square of the number of electron particles interchanged.

Photoconductive response of a single Au nanorod coupled to LaAlO3/SrTiO3 nanowires

Terahertz (THz) spectroscopy is an important tool that provides resonant access to free carrier motion, molecular rotation, lattice vibrations, excitonic, spin, and other degrees of freedom. Current methods using THz radiation suffer from limits due to diffraction or low-sensitivity, preventing application at the scale of single nanoscale objects. Here, we present coupling between plasmonic degrees of freedom in a single gold nanorod and broadband THz emission generated from a proximal LaAlO3/SrTiO3 nanostructure. A strong enhancement of THz emission is measured for incident radiation that is linearly polarized along the long axis of the nanorod. This demonstration paves the way for the investigation of near-field plasmonic coupling in a variety of molecular-scale systems.

Electrochemically Controlled Multistability of Ultrathin Films of Double-Decker Lanthanides Phthalocyanines

Molecular-scale systems that exhibit intramolecular electron transfer (IET) induced by various external stimuli occupy a special place among the systems whose behaviour is determined by charge transfer processes. Such redox-isomeric materials are indeed promising for applications in the development of nanoscale information storage devices. Complexes in which both metal and ligand are redox-active are target objects for the study of redox isomerism phenomenon (reversible intramolecular metal−ligand electron transfer). From this standpoint, tetrapyrrole complexes of metals with variable oxidation states are one of the most promising compounds. Lanthanides phthalocyaninates proved to be very promising objects for the development of “molecular switches” and memory devices. Herein, we report on the electrochemical properties of Langmuir-Blodgett films of series of lanthanides complexes with bis-tetra-15-crown-5-phthalocyanines1,2. A previously unknown phenomenon of orientation-induced redox isomerism in a Langmuir monolayer is revealed in the case of cerium bis-[tetra-(15-crown-5)-phthalocyaninate] – (Ce[(15C5)4Pc]2)3,4 (Fig.1). The mechanism of genuine redox isomerism was confirmed by the results of in-situUV-Vis spectral measurements performed on monolayers and Langmuir-Blodgett films, AFM, and XPS studies of Langmuir-Blodgett films transferred at different surface pressures. The understanding of this reversible IET mechanism is especially important due to possible applications of such redox-isomeric systems in the development of nanoscale multibit information storage devices. 1. Selector, S. L.; Arslanov, V. V.; Gorbunova, Y. G.; Raitman, O. A.; Sheinina, L. S.; Birin, K. P.; Tsivadze, A. Y. Journal of Porphyrins and Phthalocyanines 2008, 12, 1154. 2. Selector, S. L.; Shokurov, A. V; Arslanov, V. V; Gorbunova, Y. G.; Raitman, O. A.; Isakova, A. A.; Birin, K. P.; Tsivadze, A. Y. Rus. J. of Electrochemistry 2012, 48, 218. 3. Selektor, S. L.; Shokurov, A. V.; Raitman, O. A.; Sheinina, L. S.; Arslanov, V. V.; Birin, K. P.; Gorbunova, Y. G.; Tsivadze, A. Y. Colloid J. 2012, 74, 334. 4. Selektor, S.L.; Shokurov, A.V.; Arslanov, V.V.; Gorbunova, Y.G.; Birin, K.P.; Raitman, O.A.; Morote, F.; Cohen-Bouhacina, T.; Grauby-Heywang, Ch.; Tsivadze, A.Yu. J. Phys. Chem. C ., 2014, 118, 4250. Figure 1

A test of systematic coarse-graining of molecular dynamics simulations: Transport properties

To what extent can a "bottom-up" mesoscale fluid model developed through systematic coarse-graining techniques recover the physical properties of a molecular scale system? In a previous paper [C.-C. Fu, P. M. Kulkarni, M. S. Shell, and L. G. Leal, J. Chem. Phys. 137, 164106 (2012)], we addressed this question for thermodynamic properties through the development of coarse-grained (CG) fluid models using modified iterative Boltzmann inversion methods that reproduce correct pair structure and pressure. In the present work we focus on the dynamic behavior. Unlike the radial distribution function and the pressure, dynamical properties such as the self-diffusion coefficient and viscosity in a CG model cannot be matched during coarse-graining by modifying the pair interaction. Instead, removed degrees of freedom require a modification of the equations of motion to simulate their implicit effects on dynamics. A simple but approximate approach is to introduce a friction coefficient, γ, and random forces for the remaining degrees of freedom, in which case γ becomes an additional parameter in the coarse-grained model that can be tuned. We consider the non-Galilean-invariant Langevin and the Galilean-invariant dissipative particle dynamics (DPD) thermostats with CG systems in which we can systematically tune the fraction φ of removed degrees of freedom. Between these two choices, only DPD allows both the viscosity and diffusivity to match a reference Lennard-Jones liquid with a single value of γ for each degree of coarse-graining φ. This friction constant is robust to the pressure correction imposed on the effective CG potential, increases approximately linearly with φ, and also depends on the interaction cutoff length, rcut, of the pair interaction potential. Importantly, we show that the diffusion constant and viscosity are constrained by a simple scaling law that leads to a specific choice of DPD friction coefficient for a given degree of coarse-graining. Moreover, we find that the pair interaction distance cutoffs used for DPD random and dissipative forces should be considered separately from that of the conservative interaction potential.

Thermal sensation and cell adaptability.

Whole person adaptive comfort is discussed with reference to recent findings in molecular scale systems biology. The observations are upscaled to hypotheses relating to less traditional interpretations of thermal processes, which have new implications for indoor climate management and design. Arguments are presented for a revision of current focus, model and paradigm. The issue is seen as a problem of integrating theoretical development, conceptual modeling and as an investigation of the extent to which environments and acclimatization can be used to achieve individual fitness and health, not only at the subjective comfort level, as hitherto promoted. It is argued that there are many questions yet to be asked about adaptability before celebrating a particular adaptive state.

Modeling Spin Transport in Helical Fields: Derivation of an Effective Low-Dimensional Hamiltonian

This study is devoted to a consistent derivation of an effective model Hamiltonian to describe spin transport along a helical pathway and in the presence of spin–orbit interaction, the latter being induced by an external field with helical symmetry. It is found that a sizable spin polarization of an unpolarized incoming state can be obtained without introducing phase breaking processes. For this, at least two energy levels per lattice site in the tight-binding representation are needed. Additionally, asymmetries in the effective electronic-coupling parameters as well as in the spin–orbit interaction strength must be present to achieve net polarization. For a fully symmetric system—in terms of electronic and spin–orbit couplings—no spin polarization is found. The model presented is quite general and is expected to be of interest for the treatment of spin-dependent effects in molecular scale systems with helical symmetry.

Experimental Electron Density Studies of Inorganic Materials

AbstractThe electron density of a molecular scale system is probably the most information‐rich observable in natural science, and experimental electron density determination based on X‐ray diffraction is a strong field of modern crystallography. Most studies concern small molecule organic or metal‐organic crystals, and indeed the experimental method and the subsequent data modeling and analysis have become a very versatile tool for such systems. However, inorganic materials in the form of high‐symmetry dense solids, often with extended structures and containing heavy atoms, represent one of the most serious challenges to the X‐ray electron density technique. For inorganic materials the scattering from the valence electrons is minute compared with the core electron scattering, and systematic errors such as extinction and absorption can be severe. In some sense studies of inorganic materials can be used as a benchmark for the current level of electron density analysis using X‐ray diffraction. Here we discuss the special challenges that face X‐ray electron density studies of inorganic materials. We discuss the special experimental requirements – basically the ideal X‐ray electron density experiment shines stable, intense, high energy, monochromatic X‐rays on minute single crystals at the lowest possible temperature, and the diffracted intensities are recorded on detectors with low background noise and large dynamic range. We also address the specific problems encountered when modeling very diffuse valence electrons in heavy atoms. Furthermore, for light atom materials topological analysis is often used as an analysis tool to extract information e.g. about chemical bonding, but for inorganic materials many of the commonly used descriptors are less informative, and other approaches are called for.

Towards a General Theory of Molecular-Scale Energy Transfer

Specialized proteins inside cells work on a molecular scale to convert chemical energy into mechanical motion. Brownian motion on a multi-dimensional tilted periodic free-energy potential is a possible unifying theory for the description of far-from-equilibrium molecular-scale energy transfer. In this framework each degree of freedom is a generalized coordinate representing displacements in real space or along reaction coordinates. The minima of the periodic potential define microscopic (meta-)stable states and the potential barriers between minima determine the probability of hopping transitions. The linear potential represents a constant macroscopic thermodynamic force driving the system out of thermal equilibrium. This framework provides a compelling physical picture of a molecular-scale system undergoing Brownian motion on a potential landscape that directs the average behavior of the system thereby enabling energy coupling between degrees of freedom.In this work we derive analytic solutions to the continuous stochastic diffusion equation describing overdamped Brownian motion on a multi-dimensional tilted periodic potential in the limit of deep potential wells. using an approach similar to the tight-binding model of quantum mechanics, we derive a master equation describing discrete hopping between localized (meta-)stable states of the untilted periodic potential. This discrete master equation represents a significant simplification of the system valid in a well-defined parameter regime and can be solved analytically. For non-separable potentials the master equation describes energy transfer between degrees of freedom. We derive expressions for the dependence of the rate and efficiency of energy transfer on the tilt valid beyond the near-equilibrium limit. These results provide an opportunity to connect with experiments, phenomenological models, and other general results from non-equilibrium thermodynamics.

A test of systematic coarse-graining of molecular dynamics simulations: Thermodynamic properties

Coarse-graining (CG) techniques have recently attracted great interest for providing descriptions at a mesoscopic level of resolution that preserve fluid thermodynamic and transport behaviors with a reduced number of degrees of freedom and hence less computational effort. One fundamental question arises: how well and to what extent can a "bottom-up" developed mesoscale model recover the physical properties of a molecular scale system? To answer this question, we explore systematically the properties of a CG model that is developed to represent an intermediate mesoscale model between the atomistic and continuum scales. This CG model aims to reduce the computational cost relative to a full atomistic simulation, and we assess to what extent it is possible to preserve both the thermodynamic and transport properties of an underlying reference all-atom Lennard-Jones (LJ) system. In this paper, only the thermodynamic properties are considered in detail. The transport properties will be examined in subsequent work. To coarse-grain, we first use the iterative Boltzmann inversion (IBI) to determine a CG potential for a (1-φ)N mesoscale particle system, where φ is the degree of coarse-graining, so as to reproduce the radial distribution function (RDF) of an N atomic particle system. Even though the uniqueness theorem guarantees a one to one relationship between the RDF and an effective pairwise potential, we find that RDFs are insensitive to the long-range part of the IBI-determined potentials, which provides some significant flexibility in further matching other properties. We then propose a reformulation of IBI as a robust minimization procedure that enables simultaneous matching of the RDF and the fluid pressure. We find that this new method mainly changes the attractive tail region of the CG potentials, and it improves the isothermal compressibility relative to pure IBI. We also find that there are optimal interaction cutoff lengths for the CG system, as a function of φ, that are required to attain an adequate potential while maintaining computational speedup. To demonstrate the universality of the method, we test a range of state points for the LJ liquid as well as several LJ chain fluids.

Maximally Entangled States in the Hydrogen Molecule: The Role of Spin and Correlation

Many electron calculations on a simplest realistic two electron system i.e. H2molecule was applied and as the consequence correlation effects was reflected accurately in the wavefunctions of H2. Zanardi’s entanglement measurement, demonstrated that the maximum of entanglement for the ground state happens when U =J and this resolved the controversial conclusion of U = 0 for maximum entanglement. It was shown that the ground and third excited states are maximally entangled. These maximally entangled states and also the minimally entangled states are correlated to their spin’s property. The wavefunctions of the not magnetic (S = 0) ground and excited states explicitly depend on correlation parameters whereas the first excited states which is magnetic (S2 = 2 and Sz≠0) is not entangled. The second excited state is not magnetic but its wavefunction does not depend on correlation parameters therefore it is a moderately entangled state. In any case, by switching on a magnetic field an entangled state with Sz = 0 can be extracted from a not entangled degenerate magnetic state. We suggest that in a realistic molecular scale system, there is two criteria for finding maximally entangled electronic states, first the system should be in moderately correlated regime and second the system should have a non-magnetic (Sz = 0) electronic state.

Redox Control of Molecular Motion in Switchable Artificial Nanoscale Devices

The design, synthesis, and operation of molecular-scale systems that exhibit controllable motions of their component parts is a topic of great interest in nanoscience and a fascinating challenge of nanotechnology. The development of this kind of species constitutes the premise to the construction of molecular machines and motors, which in a not-too-distant future could find applications in fields such as materials science, information technology, energy conversion, diagnostics, and medicine. In the past 25 years the development of supramolecular chemistry has enabled the construction of an interesting variety of artificial molecular machines. These devices operate via electronic and molecular rearrangements and, like the macroscopic counterparts, they need energy to work as well as signals to communicate with the operator. Here we outline the design principles at the basis of redox switching of molecular motion in artificial nanodevices. Redox processes, chemically, electrically, or photochemically induced, can indeed supply the energy to bring about molecular motions. Moreover, in the case of electrically and photochemically induced processes, electrochemical and photochemical techniques can be used to read the state of the system, and thus to control and monitor the operation of the device. Some selected examples are also reported to describe the most representative achievements in this research area.

Recent Developments on Rotaxane-Based Shuttles

Artificial molecular machines capable of converting chemical, photochemical and electrochemical energy into mechanical motion represent a high-impact, fast-growing field of interdisciplinary research. These molecular-scale systems utilize a “bottom-up” technology centered upon the design and manipulation of molecular assemblies and are potentially capable of delivering efficient actuation at length scales dramatically smaller than traditional microscale actuators. Much of the inspiration to construct molecular devices and machines comes from the outstanding progress in molecular biology that has begun to reveal the secrets of the natural nanodevices that constitute the material base of life. Mechanically interlocked molecules, such as rotaxanes are one of the most suitable candidates for molecular machines because (i) the mechanical bond allows a large variety of mutual arrangements of the molecular components, while conferring stability on the system; (ii) the interlocked architecture limits the amplitude of the intercomponent motion in the three dimensions; (iii) the stability of a specific arrangement is determined by the strength of the intercomponent interactions; and (iv) such interactions can be modulated by external stimulation. These systems, initially gained interest due to their interesting topology and associated synthetic challenge, but recent efforts have showed that they, by virtue of their electrical properties and bi- or multistable behaviour, are also attractive as nanoscale switches for molecular electronics and nanoelectromechanical systems. This reivew will focused on the recent progress occurred in the development of new and more functional molecular shuttles based on rotaxane chemistry. Keywords: molecular shuttles, rotaxane chemistry, nanoelectromechanical systems, interlocked architecture