Local Potential Energy Minima Research Articles

Gate Electrodes Enable Tunable Nanofluidic Particle Traps.

The ability to control the location of nanoscale objects in liquids is essential for fundamental and applied research from nanofluidics to molecular biology. To overcome their random Brownian motion, the electrostatic fluid trap creates local minima in potential energy by shaping electrostatic interactions with a tailored wall topography. However, this strategy is inherently static; once fabricated, the potential wells cannot be modulated. Here, we propose and experimentally demonstrate that such a trap can be controlled through a buried gate electrode. We measure changes in the average escape times of nanoparticles from the traps to quantify the induced modulations of 0.7 kBT in potential energy and 50 mV in surface potential. Finally, we summarize the mechanism in a parameter-free predictive model, including surface chemistry and electrostatic fringing, that reproduces the experimental results. Our findings open a route toward real-time controllable nanoparticle traps.

Ab initio modeling of helically periodic nanostructures using CRYSTAL17: A general algorithm first applied to nanohelicenes

A general algorithm based on the line symmetry group theory is proposed for ab initio modeling of one-dimensional (1D) helical nanoobjects using computer codes designed for periodic structure calculations. The key point of the algorithm is the interpolation between the properties of a sequence of periodic structures to obtain the properties of 1D helical nanoobjects without translational periodicity. A special selection of periodic structures avoids excessively long periods, thereby providing control over computational costs. The developed approach gives an opportunity to simulate the continuous dependences of mechanical and electronic properties on the torsional strain for any helical 1D nanoobject using high-level quantum chemical methods. The superposition of torsional and axial deformations can be used to generate the two-parameter maps of the desired properties.The proposed algorithm is applied to obtain the structure and properties of selected nanohelicenes, which are the helicenes infinitely continued along the helical (screw) axis direction. The CRYSTAL17 computer code based on atomic basis set has been used for this purpose. The main advantage of this program in comparison with other widely available ab initio simulation codes is the built-in accounting for helical symmetry operations in 1D periodic systems. Performed calculations show that nanohelicenes have several local minima of potential energy, differing in the order of the helical axis. The irrational order of the helical axis found at all energy minima indicates the absence of translational symmetry in these structures. Two-parameter electronic band gap maps and the dependences of Young’s moduli on the torsion angle for the selected nanohelicenes are calculated and discussed.

Bistable Structures for Advanced Functional Systems

AbstractBistable mechanical systems having two local minima of potential energy can rest in either of the two stable equilibrium states in the absence of external loadings. A snap‐through action may occur under suitable stimuli and/or loading, during which such systems exhibit distinct properties from linear structures. Such kinds of structures have been widely exploited for designing advanced functional systems for a variety of applications. Here, the advances of bistable structures are summarized for novel advanced functional systems, including actuators, energy harvesters, microelectromechanical systems (MEMS), robotics, energy absorbers, and programmable devices as well as metamaterials. The controllable snap‐through motions are highlighted in the nonlinear structures of bistability/multistability. Finally, the major principles, structures, pros and cons, and the future research directions along with its challenges are discussed.

Numerical method for computing the free energy of glasses.

We propose a numerical technique to compute the equilibrium free energy of glasses that cannot be prepared quasireversibly. For such systems, standard techniques for estimating the free energy by extrapolation cannot be used. Instead, we use a procedure that samples the equilibrium partition function of the basins of attraction of the different inherent structures (local potential energy minima) of the system. If all relevant inherent structures could be adequately sampled in the (supercooled) liquid phase, our approach would be rigorous. In any finite simulation, we will miss the lower-energy inherent structures that become dominant at very low temperatures. We find that our free energy estimates for a Kob-Andersen glass are lower than those obtained by very slow cooling, even at temperatures down to one-third of the glass transition temperature. The current approach could be applied to compute the chemical potential of ultrastable glassy materials and should enable the estimation of their solubility.

True Polymorphic Phase Transition or Dynamic Crystal Disorder? An Investigation into the Unusual Phase Behavior of Barbituric Acid Dihydrate

Crystalline barbituric acid dihydrate (BTADH) was previously thought to undergo a subtle temperature-dependent phase transition from a high-temperature orthorhombic Pnma space group to a nonmerohedrally twinned monoclinic P21/n phase below a transition temperature of ∼217 K. Questions remain on the true nature of the unusual transformation and the structure of the high-temperature crystal phase due to difficulties in resolving the Pnma structure from X-ray diffraction data and because of the subtlety of the structural transition. In this study, terahertz (THz) spectroscopy and solid-state density functional theory (DFT) were utilized to explore this suspected phase transition and uncover the principle physical mechanisms contributing to this anomalous transition. Our findings suggest that at temperatures above the previously reported phase transition temperature of 217 K, the crystal does not exist in the Pnma space group configuration. However, two equivalent favorable energetic states with P21/n symmetry related by the twinning plane lie on either side of the proposed Pnma structure. It is these same local potential energy minima that guide the crystal system to a nonmerohedrally twinned configuration identified in the low-temperature crystal structures. At temperatures above 217 K, the system possesses the thermal energy necessary to readily transition between these degenerate states separated by the low-lying Pnma structural barrier. The evidence acquired by THz spectroscopy and DFT indicate the absence of a true temperature-dependent phase change, and rather a system that exists in a tenuous thermally disordered state above the previously alleged transition temperature.

High-resolution simulations of cylindrical gravity currents in a rotating system

Cylindrical gravity currents, produced by a full-depth lock release, in a rotating system are investigated by means of three-dimensional high-resolution simulations of the incompressible variable-density Navier–Stokes equations with the Coriolis term and using the Boussinesq approximation for a small density difference. Here, the depth of the fluid is chosen to be the same as the radius of the cylindrical lock and the ambient fluid is non-stratified. Our attention is focused on the situation when the ratio of Coriolis to inertia forces is not large, namely $0.1\leqslant {\mathcal{C}}\leqslant 0.3$, and the non-rotating case, namely ${\mathcal{C}}=0$, is also briefly considered. The simulations reproduce the major features observed in the laboratory and provide more detailed flow information. After the heavy fluid contained in a cylindrical lock is released in a rotating system, the influence of the Coriolis effects is not significant during the initial one-tenth of a revolution of the system. During the initial one-tenth of a revolution of the system, Kelvin–Helmholtz vortices form and the rotating cylindrical gravity currents maintain nearly perfect axisymmetry. Afterwards, three-dimensionality of the flow quickly develops and the outer rim of the spreading heavy fluid breaks away from the body of the current, which gives rise to the maximum dissipation rate in the system during the entire adjustment process. The detached outer rim of heavy fluid then continues to propagate outward until a maximum radius of propagation is attained. The body of the current exhibits a complex contraction–relaxation motion and new outwardly propagating pulses form regularly in a period slightly less than half-revolution of the system. Depending on the ratio of Coriolis to inertia forces, such a contraction–relaxation motion may be initiated after or before the attainment of a maximum radius of propagation. In the contraction–relaxation motion of the heavy fluid, energy is transformed between potential energy and kinetic energy, while it is mainly the kinetic energy that is consumed by the dissipation. As a new pulse initially propagates outward, the potential energy in the system increases at the expense of decreasing kinetic energy, until a local maximum of potential energy is reached. During the latter part of the new pulse propagation, the kinetic energy in the system increases at the expense of decreasing potential energy, until a local minimum of potential energy is reached and another new pulse takes form. With the use of three-dimensional high-resolution simulations, the lobe-and-cleft structure at the advancing front can be clearly observed. The number of lobes is maintained only for a limited period of time before merger between existing lobes occurs when a maximum radius of propagation is approached. The high-resolution simulations complement the existing shallow-water formulation, which accurately predicts many important features and provides insights for rotating cylindrical gravity currents with good physical assumptions and simple mathematical models.

The nature of carrier localisation in polar and nonpolar InGaN/GaN quantum wells

In this paper, we compare and contrast the experimental data and the theoretical predictions of the low temperature optical properties of polar and nonpolar InGaN/GaN quantum well structures. In both types of structure, the optical properties at low temperatures are governed by the effects of carrier localisation. In polar structures, the effect of the in-built electric field leads to electrons being mainly localised at well width fluctuations, whereas holes are localised at regions within the quantum wells, where the random In distribution leads to local minima in potential energy. This leads to a system of independently localised electrons and holes. In nonpolar quantum wells, the nature of the hole localisation is essentially the same as the polar case but the electrons are now coulombically bound to the holes forming localised excitons. These localisation mechanisms are compatible with the large photoluminescence linewidths of the polar and nonpolar quantum wells as well as the different time scales and form of the radiative recombination decay curves.

Long range stress correlations in the inherent structures of liquids at rest.

Simulation studies of the atomic shear stress in the local potential energy minima (inherent structures) are reported for binary liquid mixtures in 2D and 3D. These inherent structure stresses are fundamental to slow stress relaxation and high viscosity in supercooled liquids. We find that the atomic shear stress in the inherent structures (IS's) of both liquids at rest exhibits slowly decaying anisotropic correlations. We show that the stress correlations contribute significantly to the variance of the total shear stress of the IS configurations and consider the origins of the anisotropy and spatial extent of the stress correlations.

TIGER2 with solvent energy averaging (TIGER2A): An accelerated sampling method for large molecular systems with explicit representation of solvent.

The recently developed "temperature intervals with global exchange of replicas" (TIGER2) accelerated sampling method is found to have inaccuracies when applied to systems with explicit solvation. This inaccuracy is due to the energy fluctuations of the solvent, which cause the sampling method to be less sensitive to the energy fluctuations of the solute. In the present work, the problem of the TIGER2 method is addressed in detail and a modification to the sampling method is introduced to correct this problem. The modified method is called "TIGER2 with solvent energy averaging," or TIGER2A. This new method overcomes the sampling problem with the TIGER2 algorithm and is able to closely approximate Boltzmann-weighted sampling of molecular systems with explicit solvation. The difference in performance between the TIGER2 and TIGER2A methods is demonstrated by comparing them against analytical results for simple one-dimensional models, against replica exchange molecular dynamics (REMD) simulations for sampling the conformation of alanine dipeptide and the folding behavior of (AAQAA)3 peptide in aqueous solution, and by comparing their performance in sampling the behavior of hen egg-white lysozyme in aqueous solution. The new TIGER2A method solves the problem caused by solvent energy fluctuations in TIGER2 while maintaining the two important characteristics of TIGER2, i.e., (1) using multiple replicas sampled at different temperature levels to help systems efficiently escape from local potential energy minima and (2) enabling the number of replicas used for a simulation to be independent of the size of the molecular system, thus providing an accelerated sampling method that can be used to efficiently sample systems considered too large for the application of conventional temperature REMD.

Structural conditionality of the piezoelectric properties of langasite family crystals

The atomic displacements upon isomorphic substitutions in crystals of the langasite family have been analyzed. The thermal parameters are determined and the probability density function of atoms is analyzed. Local potential energy minima are found which can be occupied by atoms under external effects. The contributions of cations in all four independent crystallographic positions and anions in all three such positions to the piezoelectric properties are established. One specific structural feature is the constant (at isomorphic substitutions) or possible (under external effects) but always opposite displacements of two cations along symmetry axis 2. Large cations in eight-vertex polyhedra make the main contribution to the piezoelectric properties. The cations in the tetrahedra on symmetry axis 2 weaken these properties. The cations in the octahedra in the origin of coordinates and in the tetrahedra on symmetry axes 3 only slightly affect the piezoelectricity.

Inherent structures for soft long-range interactions in two-dimensional many-particle systems

We generate inherent structures, local potential-energy minima, of the "k-space overlap potential" in two-dimensional many-particle systems using a cooling and quenching simulation technique. The ground states associated with the k-space overlap potential are stealthy (i.e., completely suppress single scattering of radiation for a range of wavelengths) and hyperuniform (i.e., infinite wavelength density fluctuations vanish). However, we show via quantitative metrics that the inherent structures exhibit a range of stealthiness and hyperuniformity depending on the fraction of degrees of freedom χ that are constrained. Inherent structures in two dimensions typically contain five-particle rings, wavy grain boundaries, and vacancy-interstitial defects. The structural and thermodynamic properties of the inherent structures are relatively insensitive to the temperature from which they are sampled, signifying that the energy landscape is relatively flat along the directions sampled, with wide shallow local minima and devoid of deep wells. Using the nudged-elastic-band algorithm, we construct paths from ground-state configurations to inherent structures and identify the transition points between them. In addition, we use point patterns generated from a random sequential addition (RSA) of hard disks, which are nearly stealthy, and examine the particle rearrangements necessary to make the configurations absolutely stealthy. We introduce a configurational proximity metric to show that only small local, but collective, particle rearrangements are needed to drive initial RSA configurations to stealthy disordered ground states. These results lead to a more complete understanding of the unusual behaviors exhibited by the family of "collective-coordinate" potentials to which the k-space overlap potential belongs.

Electronic and steric effects on the photo-induced C→E ring-opening of structurally modified furylfulgides

The ultrafast C→E ring-opening reactions of four selectively modified furylfulgides have been studied by means of ultrafast broadband transient absorption spectroscopy after femtosecond laser excitation at λ = 500 nm. A large difference in the dynamics was found in the case of benzannulation at the furyl moiety as an example for an electronic effect by extension of the conjugated π-electron system compared to furylfulgides carrying sterically different alkyl substituents at the central cyclohexadiene (CHD) ring. The measured very similar spectro-temporal absorption maps for the furylfulgides with a methyl or isopropyl group at the CHD ring or an intramolecular alkyl bridge from the CHD to the furyl moiety showed two distinctive excited-state absorptions with slightly different decay times. The first time constant (τ(1) = 0.39-0.57 ps) was assigned to the rapid departure of the excited wavepacket from the Franck-Condon region. The slightly longer second decay time of τ(2) = 0.66-0.92 ps, depending on the compound, was attributed to the electronic deactivation and ring-opening through a conical intersection to the S(0) state. In contrast, the benzannulation at the furyl moiety was found to lead to a bi-phasic excited-state decay with τ(2) = 4.7 ps and a much slower additional contribution of τ(3) = 17.4 ps, ≈25 times longer compared to the normal furylfulgides. The drastic change is attributed to a trapping of excited molecules in a local potential energy minimum en route to the conical intersection.

Controlled Formation of Nanostructures with Desired Geometries. 2. Robust Dynamic Paths

Part 2 of this series addresses the question of how to manipulate in time the positions and intensities of external controls so that a set of self-assembling nanoscale particles can always reach the nanostructure of desired geometry, starting from any random and unknown spatial distribution of the particles. It complements part 1 in which we examined how to position external controls and compute their intensities so that we can ensure that the final nanostructure with the desired geometry corresponds to a local potential energy minimum surrounded by sufficiently high energy barriers to ensure that the nanostructure is statistically robust, i.e., it remains at the desired geometry with an acceptably high probability. The proposed approach for the generation of robust dynamic self-assembly paths is based on a progressive reduction of the system phase space into subsets with progressively smaller numbers of locally allowable configurational states. In other words, it is based on a judicious progressive transition from ergodic to nonergodic subsystems. The subsets of allowable configurations in phase space are modeled by a wavelet-based spatial multiresolution view of the desired structure (in terms of the number of particles). This approach produces a prescription of the optimal control problem where the dynamic self-assembly of particles into the desired nanostructure is governed by the dynamic master equation of statistical mechanics. A genetic algorithm is used to solve the associated optimization problems at each time period and locate the position of the external controls in the physical domain, as well as their intensities over time. The approaches and methods are illustrated with 1- and 2-dimensional lattice example systems.

Nitrosonium nitrite isomer of N2O3: Quantum-chemical data

The geometrical, electronic, and thermodynamic parameters of three known isomers of dinitrogen trioxide N2O3 were calculated by the density functional theory DFT/B3LYP method using the 6-311++G(3df) basis. The structure of the new isomer, NONO2, was calculated. From the calculation of vibrational frequencies it follows that the structure of NONO2 has a local potential energy minimum and corresponds to the stationary state of the N2O3 isomer. The molecular structure of NONO2 is characterized by a substantial negative charge on the NO2 fragment and positive charge on the NO fragment. The electronic structure of the NO+NO2− isomer can be characterized as nitrosonium nitrite, which can be oxidized to nitrite and participate in nitrosylation in accordance with the biogenic characteristics of the NOx intermediate, assumed to be formed in biological systems during the oxidation of NO.

Quantum-chemical evidence for the possible existence of a new isomer of dinitrogen tetraoxide

The geometric, electronic, and thermodynamic parameters of six known isomers of the molecular structure of dinitrogen tetraoxide N2O4 were calculated by the quantum-chemical DFT/B3LYP density functional method with the 6-311++G(3df) basis set. The structure of a new isomer of dinitrogen tetraoxide NONO3, which is characterized by a local potential energy minimum and corresponds to a stationary state of the N2O4 isomer, was calculated. The DFT calculations showed that this structure NONO3 is characterized by a significant negative charge on the NO3 fragment and a positive charge on the NO fragment. The calculated dipole moment of nitrosonium nitrate NO+NO 3 − in the gas phase is 4.13 D.

Quantum-chemical calculations on a novel reaction mechanism of CNN with NO

Quantum-chemical calculations of the possible interaction between CNN and NO have been performed at the CCSD(T)/aug-cc-PVTZ//B3LYP/6-31++G(d,p) level of theory. Fourteen conformers corresponding to local minima of potential energy and sixteen transition structures are located, and various possible reaction paths are probed. Products P3 – NCO + N 2 – and P4 – N 2O + CN – were the two leading channels with slight energy barriers as compared to the reactants CNN + NO. Employing the Fukui functions and HSAB theory, we are able to rationalize the calculated outcomes.

ロボットハンドによる把持・操り動作を実現する半球型ソフトフィンガの幾何学的・材料学的非線形性を考慮した弾性力モデル

This study focuses on the derivation of elastic force models of a hemispherical soft fingertip and reveals the existence of a local minimum of elastic potential energy (LMEE) induced by the deformation of the fingertip. The proposed model can be written in a straightforward equation when the geometric nonlinearity of the fingertip is applied in the derivation process, which is suitable for analyzing the stability of robotic handling system with soft fingertips. We also show complete elastic force and potential energy equations by incorporating the material nonlinearity into the derived model. Furthermore, we compare our models with the Hertzian contact theory that is applicable to the practical usage for the strength design of a lot of machines. Finally, we demonstrate the validity of our models by comparing simulation results and experimental results.

Giant Colloidal Diffusivity on Corrugated Optical Vortices

A single colloidal sphere circulating around a periodically modulated optical vortex trap can enter a dynamical state in which it intermittently alternates between freely running around the ringlike optical vortex and becoming trapped in local potential energy minima. Velocity fluctuations in this randomly switching state still are characterized by a linear Einstein-like diffusion law, but with an effective diffusion coefficient that is enhanced by more than 2 orders of magnitude.

半球型ソフトフィンガを有する最小自由度２指回転関節ハンドによる準静的把持・操り動作

This paper shows that a minimum d.o.f. robotic hand with two fingers is able to achieve the secure grasping of an object according to the local minimum of elastic potential energy (LMEE) . First, we derive an elastic force and an elastic potential energy equations due to deformation of soft fingers, which can be calculated into straightforward equations in an analytical way. These formulae lead to the fact that the potential energy of a soft fingertip is a function of two variables, and has a local minimum through the elastic rolling of a contacting object. Second, we formulate four geometric constraints in the grasping motion of a rigid object by means of two degrees of freedom robotic hand that has two rotational joints. Third, we define a basic motion that includes a translational and a rolling motions when two fingers rotate by infinitesimal angle, and propose a quasi-static manipulation and its algorithm by using the LMEE of soft fingers with the geometric constraints. In this theory, we define an energy function that includes the LMEE algorithm. By solving that function we simulate the path of the center of gravity and the change of orientation of the grasped object, and compare those values with measurements actually obtained from a CCD camera equipped above the manipulated object. Finally, we confirm the effectiveness of the quasi-static manipulation theory based on the LMEE algorithm from experiments.

Clusters of mobile molecules in supercooled water

We study the spatially heterogeneous dynamics in water via molecular dynamics simulations using the extended simple point charge potential. We identify clusters formed by mobile molecules and study their properties. We find that these clusters grow in size and become more compact as temperature decreases. We analyze the probability density function of cluster size, and we study the cluster correlation length. We find that clusters appear to be characterized by a fractal dimension consistent with that of lattice animals. We relate the cluster size and correlation length to the configurational entropy, S(conf). We find that these quantities depend weakly on 1/ S(conf). In particular, the linearity found between the cluster mass n(*) and 1/ S(conf) suggests that n(*) may be interpreted as the mass of the cooperatively rearranging regions that form the basis of the Adam-Gibbs approach to the dynamics of supercooled liquids. We study the motion of molecules within a cluster, and find that each molecule preferentially follows a neighboring molecule in the same cluster. Based on this finding we hypothesize that stringlike cooperative motion may be a general mechanism for molecular rearrangement of complex, as well as simple liquids. By mapping each equilibrium configuration onto its corresponding local potential energy minimum or inherent structure (IS), we are able to compare the mobile molecule clusters in the equilibrium system with the molecules forming the clusters identified in the transitions between IS. We find that (i) mobile molecule clusters obtained by comparing different system configurations and (ii) clusters obtained by comparing the corresponding IS are completely different for short time scales, but are the same on the longer time scales of diffusive motion.