Local Energy Minima Research Articles

First Principles Study on the Stability and Electronic Structures of 7,8-Dichloro-4-Oxo-4H-Chromene-3-Carbaldehyde

The molecular structures and electronic properties of 7,8-Dichloro-4-Oxo-4H-Chromene-3-Carbaldehyde, C10H4Cl2O3 have been studied using Density Functional Theory (DFT) method. The calculation of geometry optimization was conducted to find the local energy minimum of C10H4Cl2O3 molecular system. The equilibrium geometries were used to determine the HOMO-LUMO gaps, Mulliken atomic charges, and other electronic structures of C10H4Cl2O3. The significant findings from DFT/B3LYP functional within the basis sets of 6-31G**, 6-31++G**, 6-311G**, and 6-311++G** show that the optimized geometries of C10H4Cl2O3 are in good agreement with that of measurement data. To further investigate this, using a variety of basis sets (3-21G, 6-31G, 6-31++G, 6-31G**, 6-31++G**, 6-311G, 6-311++G, 6-311G**, and 6-311++G**), it is found that the calculated total energy values of C10H4Cl2O3 are close to each other. Similarly, the computed HOMO-LUMO energy gaps obtained are also close to each other. Using the scheme of Mulliken Population Analysis (MPA), the trend of findings are the same for both cases of B3LYP/6-31G and B3LYP/6-31G** level of calculations. For the method of B3LYP/6-31G, it is clearly found that C4 and C6 have the highest positively charge, with the corresponding values about +0.284 and +0.238, respectively. On the other hand, the charge values of +0.157 and +0.206 are found on Cl1 and Cl2 atoms. The atoms of O1, O2, and O3 have the negatively charges, with the values of about 0.398, -0.512, and -0.424, respectively. Similarly, in the case of DFT/B3LYP/6-31G** level of theory, the computed charge values of C2 and C4 are about +0.311 and +0.393, respectively. Furthermore, the Cl1 and Cl2 atoms have the positively charge values of about +0.043 and +0.070, whereas for the O1, O2, and O3 atoms, the charges values obtained are about -0.421, -0.467, and -0.498, respectively.

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.

Faceted interfaces: a key feature to quantitative understanding of transformation morphology

AbstractFaceted interfaces are a typical key feature of the morphology of many microstructures generated from solid-state phase transformations. Interpretation, prediction and simulation of this faceted morphology remain a challenge, especially for systems where irrational orientation relationships (ORs) between two phases and irrational interface orientations (IOs) are preferred. In terms of structural singularities, this work suggests an integrated framework, which possibly encompasses all candidates of faceted interfaces. The structural singularities are identified from a matching pattern, a dislocation structure and/or a ledge structure. The resultant singular interfaces have discrete IOs, described with low-index g’s (rational orientations) and/or Δg’s (either rational or irrational orientations). Various existing models are grouped according to their determined results regarding the OR and IO, and the links between the models are clarified in the integrated framework. Elimination of defect types as far as possible in a dominant singular interface often exerts a central restriction on the OR. An irrational IO is usually due to the elimination of dislocations in one direction, i.e., an O-line interface. Analytical methods using both three-dimensional and two-dimensional models for quantitative determinations of O-line interfaces are reviewed, and a detailed example showing the calculation for an irrational interface is given. The association between structural singularities and local energy minima is verified by atomistic calculations of interfacial energies in fcc/bcc alloys where it is found that the calculated equilibrium cross-sections are in a good agreement with observations from selected alloys.

Phase Field Simulations of Autocatalytic Formation of Alpha Lamellar Colonies in Ti-6Al-4V

We present phase field simulations incorporating contributions due to chemical free energy, anisotropic interfacial energy, and elastic energy due to transformation strain, to demonstrate the nucleation and growth of multiple variants of alpha from undercooled beta in Ti-6Al-4V under isothermal conditions. A new composite nucleation seeding approach is used within the phase field simulations to demonstrate that the presence of a pre-existing strain field can cause the nucleation of specific crystallographic variants of alpha based on minimization of local elastic strain energy. Under conditions where specific combinations of elastic strains exist, for example in the vicinity of one or more pre-existing alpha variants, the nucleation of a new alpha variant is followed by the successive nucleation of the same variant in the form of a lamellar colony by an autocatalytic mechanism. At a given thermodynamic undercooling, the colony structure was favored at a nucleation rate that was low enough to allow sufficient growth of previously nucleated variants before another nucleus formed in their vicinity. Basket weave morphology was formed at higher nucleation rates where multiple nuclei variants grew almost simultaneously under evolving strain fields of several adjacent nuclei.

TMDOCK: An Energy-Based Method for Modeling α-Helical Dimers in Membranes

TMDOCK is a novel computational method for the modeling of parallel homodimers formed by transmembrane (TM) α-helices. Three-dimensional (3D) models of dimers are generated by threading a target amino acid sequence through several structural templates, followed by local energy minimization. This is the first method that identifies helix dimerization modes and ranks them based on the calculated free energy of α-helix association. Free energy components include van der Waals, hydrogen bonding, and dipole interactions; side-chain conformational entropy; and solvation energy in the anisotropic lipid environment. TMDOCK reproduced 26 experimental dimeric structures formed by TM α-helices of 21 single-pass membrane proteins (including 4 mutants) with Cα atom rmsd from 1.0 to 3.3Å. Assessment of dimerization heterogeneity of these TM domains demonstrated that 7 of them have a unique dimer structure, 12 have at least 2 alternative conformations, and 2 have a large number of different association modes. All unique experimental structures of proteins from the first group and eight structures from the second group were reproduced in computations as top-ranked models. A fast version of the method is available through the web server (http://membranome.org/tm_server.php).

Understanding the viscosity of supercooled liquids and the glass transition through molecular simulations

We discuss a potential energy landscape (PEL) approach to calculate the characteristically sluggish viscous behaviour of supercooled liquids. This phenomenon is central to the theoretical understanding of the liquid-to-glass transition, a long-standing challenge in non-equilibrium statistical mechanics of amorphous states of matter. Experimentally, the shear viscosity of supercooled glass-forming liquids shows strong variations with the quench temperature. In particular, two types of behaviour are observed, Arrhenius and highly super-Arrhenius. Conceptually, the molecular description of the structural and dynamical processes underpinning the viscosity behaviour has become a topic of interest because of general implications for the kinetics of slow relaxation in the glassy state. We regard the supercooled liquid as an assembly of interacting particles undergoing thermal fluctuations such that the system evolves in space and time by crossing a series of potential energy barriers. To find these barriers and their corresponding atomic configurations, we apply an energy landscape sampling algorithm that maps out the evolution trajectories in the form of alternating sequences of local energy minima and saddle points. The energy sequences and the atomic coordinates constitute a body of atomic-scale data which we then process using two distinct methods. One is based on an effective activation barrier extracted from the transition-state pathway data, and the other is based on the linear response theory of statistical mechanics. The former is heuristic by being more physically transparent, while the latter is theoretically more rigorous. Through these two complementary calculations, an understanding of the temperature variations of shear viscosities of supercooled liquids, as well as the nature of fragile and strong behaviour of the glass transition, emerges. Our calculation provides a molecular-level account of the viscosities of supercooled liquids in a unified and consistent manner without invoking ad hoc assumptions. Relative to the nature of the glass transition, the usefulness of the PEL perspective is demonstrated, along with the concept of crossover between strong and fragile behaviour. In terms of advancing atomistic simulation capability, we believe the time-scale limitations of traditional molecular dynamics may be significantly extended through the use of metadynamics algorithms for sampling transition-state pathways.

Exhaustive Conformational Sampling of Complex Fused Ring Macrocycles Using Inverse Kinematics.

Natural product and synthetic macrocycles are chemically and topologically diverse. An efficient, accurate, and general method for generating macrocycle conformations would enable structure-based design of macrocycle drugs or host-guest complexes. Computational sampling also provides insight into transiently populated states, complementing crystallographic and NMR data. Here, we report a new algorithm, BRIKARD, that addresses this challenge through computational algebraic geometry and inverse kinematics together with local energy minimization. BRIKARD is demonstrated on 67 diverse macrocycles with structural data, encompassing various ring topologies. We find this approach enumerates diverse structures with macrocyclic RMSD < 1.0 Å to the experimental conformation for 85% of our data set in contrast to success rates of 67-75% with other approaches, while for the subset of 21 more challenging compounds in the data set, these rates are 57% and 10-29%, respectively. Because the algorithm can be efficiently run in parallel on many processors, exhaustive conformational sampling of complex cycles can be obtained in minutes rather than hours: with a 40 processor implementation protocol, BRIKARD samples the conformational diversity of a potential energy landscape in a median of 1.3 minutes of wallclock time, much faster than 3.1-10.3 hours necessary with current programs. By rigorously testing BRIKARD on a broad range of scaffolds with highly complex ring systems, we push the frontiers of macrocycle sampling to encompass multiring compounds, including those with more than 50 ring atoms and up to seven interlaced flexible rings.

Core and surface/interface magnetic anisotropies in nanocrystalline nickel

By making use of the micromagnetic theory for the ‘approach-to-saturation’ in magnetization, the effective magnetic anisotropy (MA) constant (MA energy density), Keff, as a function of temperature in the range 2 K ≤ T ≤ 300 K, is deduced from the magnetization versus magnetic field isotherms taken on nanocrystalline Ni samples with average crystallite size, d, ranging from 10 to 40 nm. For a fixed d and at any given temperature, the contributions to Keff(T) arising from the volume (core) magnetocrystalline anisotropy, K1c(T), the surface/interface anisotropy, Ks(T), and shape anisotropy, Kshape(T), are assumed to be additive. The result that a linear relationship exists between Keff × d and d not only validates this assumption in the present case but also permits an accurate determination of K1c(T), Ks(T) and Kshape(T). Thermal activation over an effective anisotropy energy barrier (which separates two local energy minima and depends on both temperature and magnetic field), as the mechanism for magnetization reversal, is shown to account for the observed temperature dependence of the coercive field. Another important finding is that the magnetic moment per Ni atom, μNi, deduced from the saturation magnetization at 2 K, increases with d in accordance with the relation μNi(d) = μNi(d = ∞) [1 − b × d−3/2], with the magnetic moment per Ni atom in the bulk at T = 2 K, μNi(d = ∞) = 0.616 μB, and b = 0.50(5).

Centralized versus Distributed Cooperative Operating Rules for Multiple Cascaded Hydropower Reservoirs

AbstractMultiple cascaded hydropower reservoir systems serving the same area need to cooperate to increase overall benefits and reliability. To meet system demand while balancing among cascaded systems, both centralized and distributed five segment energy available based operating rules, making power decisions for subsystems and the whole system, are proposed for cooperation across multiple cascaded hydropower reservoirs. Unlike existing methods, the cooperative operating rules are optimized to the global objective of maximizing the minimum system power production, with constraints on local cascade minimum energy generation to confine the possible local profit earnings or losses because of cooperation, making the operating rules more acceptable for cooperative operations among local cascade system agents. The operating rule optimization models are solved using a genetic algorithm. A case study for three cascaded systems in southwest China shows that distributed and centralized cooperative operating rules ...

Strain-Induced Energy Band Gap Opening in Two-Dimensional Bilayered Silicon Film

This work presents a theoretical study of the structural and electronic properties of bilayered silicon films under in-plane biaxial strain/stress using density functional theory. Atomic structures of the two-dimensional silicon films are optimized by using both the local-density approximation and generalized gradient approximation. In the absence of strain/stress, five buckled hexagonal honeycomb structures of the bilayered silicon film have been obtained as local energy minima and their structural stability has been verified. These structures present a Dirac-cone shaped energy band diagram with zero energy band gaps. Applying tensile biaxial strain leads to a reduction of the buckling height. Atomically flat structures with zero bucking height have been observed when the AA-stacking structures are under a critical biaxial strain. Increase of the strain between 10.7% ~ 15.4% results in a band-gap opening with a maximum energy band gap opening of ~168.0 meV obtained when 14.3% strain is applied. Energy band diagram, electron transmission efficiency, and the charge transport property are calculated.

Helical coil buckling mechanism for a stiff nanowire on an elastomeric substrate

When a stiff nanowire is deposited on a compliant soft substrate, it may buckle into a helical coil form when the system is compressed. Using theoretical and finite element method (FEM) analyses, the detailed three-dimensional coil buckling mechanism for a silicon nanowire (SiNW) on a polydimethylsiloxane (PDMS) substrate is studied. A continuum mechanics approach based on the minimization of the strain energy in the SiNW and elastomeric substrate is developed. Due to the helical buckling, the bending strain in SiNW is significantly reduced and the maximum local strain is almost uniformly distributed along SiNW. Based on the theoretical model, the energy landscape for different buckling modes of SiNW on PDMS substrate is given, which shows that both the in-plane and out-of-plane buckling modes have the local minimum potential energy, whereas the helical buckling model has the global minimum potential energy. Furthermore, the helical buckling spacing and amplitudes are deduced, taking into account the influences of the elastic properties and dimensions of SiNWs. These features are verified by systematic FEM simulations and parallel experiments. As the effective compressive strain in elastomeric substrate increases, the buckling profile evolves from a vertical ellipse to a lateral ellipse, and then approaches to a circle when the effective compressive strain is larger than 30%. The study may shed useful insights on the design and optimization of high-performance stretchable electronics and 3D complex nano-structures.

First Principles Density Functional Theory Investigation on the Structural, Energetic and Electronic Properties of 6–Bromo–4–Oxo–4H–Chromene–3–Carbaldehyde

In this paper, we report the first principles Density Functional Theory (DFT) calculation to study the structural, energetic, and electronics properties of the 6–Bromo–4–Oxo–4H–Chromene–3–Carbaldehyde, C10H5BrO3 molecular framework. Geometry optimization technique was carried out to find the local energy minimum of the title compound using four hybrid DFT functionals with the basis set of 6–311++G**. The optimized molecular structure of C10H5BrO3 cluster was then used to determine the HOMO–LUMO gaps, Molecular Electrostatic Potential (MEP), Mulliken atomic charges, and others. Using the four hybrid DFT techniques, the optimized geometries of C10H5BrO3 molecular cluster is close to that of measurement data. Our calculation results also show that the total energies obtained are close to each other with the four hybrid DFT procedures. The diagram of electrostatic potential surface show that the regions of negative electrostatic potential around the oxygen atoms, O1 and O2. Using the scheme of Mulliken Population Analysis (MPA), the distributions of atomic charges follow the same arguments for the B3LYP/6–311++G**, B3PW91/6–311++G**, M06/6–311++G**, and PBE1PBE/6–311++G** simulation approaches. For example, the atom of C5 has the highest positively charge, whereas the highest negatively charge was found in the C4 atom. For Br atom, the atomic charge values obtained are –0.158, –0.222, –0.277, and –0.224, respectively for the B3LYP/6–311++G**, B3PW91/6–311++G**, M06/6–311++G**, and PBE1PBE/6–311++G** computational methods.

Skyrmions in thin films with easy-plane magnetocrystalline anisotropy

We demonstrate that chiral skyrmionic magnetization configurations can be found as the minimum energy state in B20 thin film materials with easy-plane magnetocrystalline anisotropy with an applied magnetic field perpendicular to the film plane. Our observations contradict results from prior analytical work, but are compatible with recent experimental investigations. The size of the observed skyrmions increase with the easy-plane magnetocrystalline anisotropy. We use a full micromagnetic model including demagnetization and a three-dimensional geometry to find local energy minimum (metastable) magnetization configurations using numerical damped time integration. We explore the phase space of the system and start simulations from a variety of initial magnetization configurations to present a systematic overview of anisotropy and magnetic field parameters for which skyrmions are metastable and global energy minimum (stable) states.

Regularity of Local Minimizers of the Interaction Energy Via Obstacle Problems

The repulsion strength at the origin for repulsive/attractive potentials determines the regularity of local minimizers of the interaction energy. In this paper, we show that if this repulsion is like Newtonian or more singular than Newtonian (but still locally integrable), then the local minimizers must be locally bounded densities (and even continuous for more singular than Newtonian repulsion). We prove this (and some other regularity results) by first showing that the potential function associated to a local minimizer solves an obstacle problem and then by using classical regularity results for such problems.

Schematics and Energetics of Bucky Shuttle Memory on Graphene Nanoribbon Array.

Conjugated carbon nanomaterials such as fullerene-nanotube, fullerene-graphene, and nanotube-graphene hybrids have great potential for various applications. This paper presents the schematics and energetics of a nonvolatile nanomemory element based on a fullerene-nanotube-graphene hybrid. The system proposed was composed of C60 fullerene and a nanotube placed on two graphene-nanoribbons with a gap. The C60 fullerene encapsulated in the nanotube can shuttle between two graphene-nanoribbons along the nanotube under the alternatively applied force fields. When the encapsulated C60 fullerene settles on the graphene-nanoribbons, the local energy minima are achieved from the attractive van der Waals potential energies. Since the C60 fullerene retains its position on the graphene-nanoribbon without external force fields, the proposed system can then operate a nonvolatile memory device.

Metabolic Precursor of Cholesterol Causes Formation of Chained Aggregates of Liquid-Ordered Domains

7-Dehydrocholesterol, an immediate metabolic predecessor of cholesterol, can accumulate in tissues due to some metabolic abnormalities, causing an array of symptoms known as Smith-Lemli-Opitz syndrome. Enrichment of cellular membranes with 7-dehydrocholesterol interferes with normal cell-signaling processes, which involve interaction between rafts and formation of the so-called signaling platforms. In model membranes, cholesterol-based ordered domains usually merge upon contact. According to our experimental data, ordered domains in the model systems where cholesterol is substituted for 7-dehydrocholesterol never merge on the time scale of the experiment, but clusterize into necklace-like aggregates. We attribute such different dynamical behavior to altered properties of the domain boundary. In the framework of thickness mismatch model, we analyzed changes of interaction energy profiles of two approaching domains caused by substitution of cholesterol by 7-dehydrocholesterol. The energy barrier for domain merger is shown to increase notably, with simultaneous appearance of another distinct local energy minimum. Such energy profile is in perfect qualitative agreement with the experimental observations. The observed change of domain dynamics can impair proper interaction between cellular rafts underlying pathologies associated with deviations in cholesterol metabolism.

Convergence Properties of Crystal Structure Prediction by Quasi-Random Sampling.

Generating sets of trial structures that sample the configurational space of crystal packing possibilities is an essential step in the process of ab initio crystal structure prediction (CSP). One effective methodology for performing such a search relies on low-discrepancy, quasi-random sampling, and our implementation of such a search for molecular crystals is described in this paper. Herein we restrict ourselves to rigid organic molecules and, by considering their geometric properties, build trial crystal packings as starting points for local lattice energy minimization. We also describe a method to match instances of the same structure, which we use to measure the convergence of our packing search toward completeness. The use of these tools is demonstrated for a set of molecules with diverse molecular characteristics and as representative of areas of application where CSP has been applied. An important finding is that the lowest energy crystal structures are typically located early and frequently during a quasi-random search of phase space. It is usually the complete sampling of higher energy structures that requires extended sampling. We show how the procedure can first be refined, through targetting the volume of the generated crystal structures, and then extended across a range of space groups to make a full CSP search and locate experimentally observed and lists of hypothetical polymorphs. As the described method has also been created to lie at the base of more involved approaches to CSP, which are being developed within the Global Lattice Energy Explorer (Glee) software, a few of these extensions are briefly discussed.

The dynamics of aloof baby Skyrmions

The aloof baby Skyrme model is a (2+1)-dimensional theory with solitons that are lightly bound. It is a low-dimensional analogue of a similar Skyrme model in (3+1)-dimensions, where the lightly bound solitons have binding energies comparable to nuclei. A previous study of static solitons in the aloof baby Skyrme model revealed that multi-soliton bound states have a cluster structure, with constituents that preserve their individual identities due to the short-range repulsion and long-range attraction between solitons. Furthermore, there are many different local energy minima that are all well-described by a simple binary species particle model. In this paper we present the first results on soliton dynamics in the aloof baby Skyrme model. Numerical field theory simulations reveal that the lightly bound cluster structure results in a variety of exotic soliton scattering events that are novel in comparison to standard Skyrmion scattering. A dynamical version of the binary species point particle model is shown to provide a good qualitative description of the dynamics.

Modified Wenzel and Cassie Equations for Wetting on Rough Surfaces

We study a stationary wetting problem on rough and inhomogeneous solid surfaces. We derive a new formula for the apparent contact angle by an asymptotic two-scale homogenization method. The formula reduces to a modified Wenzel equation for geometrically rough surfaces and a modified Cassie equation for chemically inhomogeneous surfaces. Unlike the classical Wenzel and Cassie equations, the modified equations correspond to local minimizers of the total interface energy in the solid-liquid-air system, so that they are consistent with experimental observations. The homogenization results are proved rigorously by a variational method.

Comparative Molecular Mechanics and Quantum Mechanics Study of Monohydration of Nucleic Acid Bases

DNA is the most important biological molecule and its hydration contributes essentially to the structure and functions of the double helix. We analyze the monohydration of the individual bases of nucleic acids and their methyl derivatives using methods of Molecular Mechanics (MM) with the Poltev-Malenkov (PM), AMBER and OPLS force fields, as well as ab initio Quantum Mechanics (QM) calculations at MP2/6-31G(d,p) level of theory. A comparison is made between the calculated interaction energies and the experimental enthalpies of microhydration of bases, obtained from mass spectrometry at low temperatures. Each local water-base interaction energy minimum obtained with MM corresponds to the minimum obtained with QM. General qualitative agreement was observed in the geometrical characteristics of the local minima obtained via the two groups of methods. MM minima correspond to slightly more coplanar structures than those obtained via QM methods, and the absolute MM energy values overestimate corresponding values obtained with QM. For Adenine and Thymine the QM local minima energy values are closer to those obtained by the PM potential (average of 0.72 kcal/mol) than by the AMBER force field (1.86 kcal/mol). The differences in energy between MM and QM results are more pronounced for Guanine and Cytosine, especially for minima with the water molecule forming H-bonds with two proton-acceptor centers of the base. Such minima are the deepest ones obtained via MM methods while QM calculations result in the global minima corresponding to water molecule H-bonded to one acceptor and one donor site of the base. Calculations for trimethylated bases with a water molecule corroborate the MM results. The energy profiles were obtained with some degrees of freedom of the water molecule being frozen. This data will contribute to the improvement of the molecular mechanics force fields.