Global Energy Minimum Research Articles

Transient Trapping into Metastable States in Systems with Competing Orders

The quench dynamics of a system involving two competing orders is investigated using a Ginzburg-Landau theory with relaxational dynamics. We consider the scenario where a pump rapidly heats the system to a high temperature, after which the system cools down to its equilibrium temperature. We study the evolution of the order parameter amplitude and fluctuations in the resulting time dependent free energy landscape. Exponentially growing thermal fluctuations dominate the dynamics. The system typically evolves into the phase associated with the faster-relaxing order parameter, even if it is not the global free energy minimum. This theory offers a natural explanation for the widespread experimental observation that metastable states may be induced by laser induced collapse of a dominant equilibrium order parameter.

Ground and Excited States of Gas-Phase DNA Nucleobase Cation-Radicals. A UV-vis Photodisociation Action Spectroscopy and Computational Study of Adenine and 9-Methyladenine.

Cation radicals of adenine (A•+) and 9-methyladenine (MA•+) were generated in the gas phase by collision-induced intramolecular electron transfer in copper-terpyridine-nucleobase ternary complexes and characterized by collision-induced dissociation (CID) mass spectra and UV-vis photodissociation action spectroscopy in the 210-700 nm wavelength region. The action spectra of both A•+ and MA•+ displayed characteristic absorption bands in the near-UV and visible regions. Another tautomer of A•+ was generated as a minor product by multistep CID of protonated 9-(2-bromoethyl)adenine. Structure analysis by density functional theory and coupled-clusters ab initio calculations pointed to the canonical 9-H-tautomer Ad1•+ as the global energy minimum of adenine cation radicals. The canonical tautomer MA1•+ was also calculated to be a low-energy structure among methyladenine cation radicals. However, two new noncanonical tautomers were found to be energetically comparable to MA1•+. Vibronic absorption spectra were calculated for several tautomers of A•+ and MA•+ and benchmarked on equation-of-motion coupled-clusters excited-state calculations. Analysis of the vibronic absorption spectra of A•+ tautomers pointed to the canonical tautomer Ad1•+ as providing the best match with the action spectrum. Likewise, the canonical tautomer MA1•+ was the unequivocal best match for the MA•+ ion generated in the gas phase. According to potential-energy mapping, MA1•+ was separated from energetically favorable noncanonical cation radicals by a high-energy barrier that was calculated to be above the dissociation threshold for loss of a methyl hydrogen atom, thus preventing isomerization. Structures and energetics of all four DNA nucleobase cation radicals are compared and discussed.

B13+is a Tri‐Spoke Wheel: A New Revelation through Electronic Structure Analysis

AbstractB13+ cluster has drawn considerable attention of the scientific community due to its promising molecular motor behaviour where the outer ring of ten boron atoms freely rotates around a triangular core. During this rotor action, the cluster undergoes successive transformation between a transition state (TS) and a global minimum energy state (GS). The electron density distribution analysis reveals that the core is connected to the periphery at three regions by concentrated high electron density paths making the topology of the cluster analogous to that of a tri‐spoke wheel. Also the periphery and core act as two quasi‐independent entities. The pathway of inter conversion between TS and GS has been studied through surface electron density distribution, atomic connectivity index (CI), Fuzzy bond order (FBO), electron localization function (ELF), atom in molecules (AIM) analysis. The electron localization function (ELF) analysis has revealed that electron in GS is more globally delocalized compared to TS making it more stable.

Manifolds Pinned by a High-Dimensional Random Landscape: Hessian at the Global Energy Minimum

We consider an elastic manifold of internal dimension d and length L pinned in a N dimensional random potential and confined by an additional parabolic potential of curvature mu . We are interested in the mean spectral density rho (lambda ) of the Hessian matrix {{mathcal {K}}} at the absolute minimum of the total energy. We use the replica approach to derive the system of equations for rho (lambda ) for a fixed L^d in the N rightarrow infty limit extending d=0 results of our previous work (Fyodorov et al. in Ann Phys 397:1–64, 2018). A particular attention is devoted to analyzing the limit of extended lattice systems by letting Lrightarrow infty . In all cases we show that for a confinement curvature mu exceeding a critical value mu _c, the so-called “Larkin mass”, the system is replica-symmetric and the Hessian spectrum is always gapped (from zero). The gap vanishes quadratically at mu rightarrow mu _c. For mu <mu _c the replica symmetry breaking (RSB) occurs and the Hessian spectrum is either gapped or extends down to zero, depending on whether RSB is 1-step or full. In the 1-RSB case the gap vanishes in all d as (mu _c-mu )^4 near the transition. In the full RSB case the gap is identically zero. A set of specific landscapes realize the so-called “marginal cases” in d=1,2 which share both feature of the 1-step and the full RSB solution, and exhibit some scale invariance. We also obtain the average Green function associated to the Hessian and find that at the edge of the spectrum it decays exponentially in the distance within the internal space of the manifold with a length scale equal in all cases to the Larkin length introduced in the theory of pinning.

Adsorption of 2-Butanone on Pristine Graphene: A First-principles Study

The adsorption mechanism of 2-butanone (ethyl methyl ketone) on the surface of graphene is investigated by using Density Functionals Theory (DFT). A 2-butanone molecule is chosen as a selected example of main volatile organic compounds (VOCs) in exhaled breath. To describe the absorption of 2-butanone and graphene substrate, we have performed DFT simulations including van de Waals (vdW) interactions implemented in the Vienna Ab-initio Simulation Package (VASP). The global minimum energy configurations and binding energies for a 2-butanone molecule adsorbed on graphene are determined by using Computational DFT-based Nanoscope tool for imaging the binding possibility of the adsorbed molecules on the graphene surface. The adsorption energy profiles are calculated by three functionals of van der Waals interactions: revPBE-vdW, optPBE-vdW, and vdW-DF2. It is shown that the adsorption energy is highly sensitive to the vdW functionals. The fundamental insights of the interactions between 2-butanone and graphene through molecular doping, i.e., charge transfer are discussed in detail.

A symmetry result in $${\mathbb {R}}^2$$ for global minimizers of a general type of nonlocal energy

In this paper, we are interested in a general type of nonlocal energy, defined on a ball $$B_R\subset {\mathbb {R}}^n$$ for some $$R>0$$ as $$\begin{aligned} {\mathcal {E}}(u, B_R)= \iint _{{\mathbb {R}}^{2n}{\setminus } ({\mathcal {C}}B_R)^2} F( u(x)-u(y),x-y)dx dy+\int _{B_R} W(u)\, dx.\end{aligned}$$We prove that in $${\mathbb {R}}^2$$, under suitable assumptions on the functions F and W, bounded continuous global energy minimizers are one-dimensional. This proves a De Giorgi conjecture for minimizers in dimension two, for a general type of nonlocal energy.

Path Planning and Control of Redundant Manipulators Using Bilevel Optimization

Abstract Redundancy is a useful feature in dynamic systems which can be exploited to enhance performance in various tasks. In this work, redundancy will be utilized to minimize the energy consumption of a linear manipulator, while in some cases an additional task of end-effector tracking will also be required and achieved. Optimal control theory has been extensively used for the optimization of dynamic systems; however, complex tasks and redundancy make these problems computationally expensive, numerically difficult to solve, and in many cases, ill-defined. In this paper, evolutionary bilevel optimization for the problem is presented. This is done by setting up an upper level optimization problem for a set of decision variables and a lower level one that actually calculates the optimal inputs and trajectories. The upper level problem is solved by a genetic algorithm (GA), whereas the lower level problem uses classical optimal control. As a result, the proposed algorithm allows the optimization of complex tasks that usually cannot be solved in practice using standard optimal control tools. In addition, despite the use of penalty functions to enforce saturation constraints, the algorithm leads to global energy minimization. Illustrative examples of a redundant x-y robotic manipulator with complex overall tasks will be presented, solved, and discussed.

Solution of Levinthal's Paradox and a Physical Theory of Protein Folding Times.

“How do proteins fold?” Researchers have been studying different aspects of this question for more than 50 years. The most conceptual aspect of the problem is how protein can find the global free energy minimum in a biologically reasonable time, without exhaustive enumeration of all possible conformations, the so-called “Levinthal’s paradox.” Less conceptual but still critical are aspects about factors defining folding times of particular proteins and about perspectives of machine learning for their prediction. We will discuss in this review the key ideas and discoveries leading to the current understanding of folding kinetics, including the solution of Levinthal’s paradox, as well as the current state of the art in the prediction of protein folding times.

Conformational analysis of macrocycles: comparing general and specialized methods

Macrocycles represent an important class of medicinally relevant small molecules due to their interesting biological properties. Therefore, a firm understanding of their conformational preferences is important for drug design. Given the importance of macrocycle-protein modelling in drug discovery, we envisaged that a systematic study of both classical and recent specialized methods would provide guidance for other practitioners within the field. In this study we compare the performance of the general, well established conformational analysis methods Monte Carlo Multiple Minimum (MCMM) and Mixed Torsional/Low-Mode sampling (MTLMOD) with two more recent and specialized macrocycle sampling techniques: MacroModel macrocycle Baseline Search (MD/LLMOD) and Prime macrocycle conformational sampling (PRIME-MCS). Using macrocycles extracted from 44 macrocycle-protein X-ray crystallography complexes, we evaluated each method based on their ability to (i) generate unique conformers, (ii) generate unique macrocycle ring conformations, (iii) identify the global energy minimum, (iv) identify conformers similar to the X-ray ligand conformation after Protein Preparation Wizard treatment (X-rayppw), and (v) to the X-rayppw ring conformation. Computational speed was also considered. In addition, conformational coverage, as defined by the number of conformations identified, was studied. In order to study the relative energies of the bioactive conformations, the energy differences between the global energy minima and the energy minimized X-rayppw structures and, the global energy minima and the MCMM-Exhaustive (1,000,000 search steps) generated conformers closest to the X-rayppw structure, were calculated and analysed. All searches were performed using relatively short run times (10,000 steps for MCMM, MTLMOD and MD/LLMOD). To assess the performance of the methods, they were compared to an exhaustive MCMM search using 1,000,000 search steps for each of the 44 macrocycles (requiring ca 200 times more CPU time). Prior to our analysis, we also investigated if the general search methods MCMM and MTLMOD could also be optimized for macrocycle conformational sampling. Taken together, our work concludes that the more general methods can be optimized for macrocycle modelling by slightly adjusting the settings around the ring closure bond. In most cases, MCMM and MTLMOD with either standard or enhanced settings performed well in comparison to the more specialized macrocycle sampling methods MD/LLMOD and PRIME-MCS. When using enhanced settings for MCMM and MTLMOD, the X-rayppw conformation was regenerated with the greatest accuracy. The, MD/LLMOD emerged as the most efficient method for generating the global energy minima.Graphic abstract

Edge Domain Walls in Ultrathin Exchange-Biased Films

We present an analysis of edge domain walls in exchange-biased ferromagnetic films appearing as a result of a competition between the stray field at the film edges and the exchange bias field in the bulk. We introduce an effective two-dimensional micromagnetic energy that governs the magnetization behavior in exchange-biased materials and investigate its energy minimizers in the strip geometry. In a periodic setting, we provide a complete characterization of global energy minimizers corresponding to edge domain walls. In particular, we show that energy minimizers are one-dimensional and do not exhibit winding. We then consider a particular thin-film regime for large samples and relatively strong exchange bias and derive a simple and comprehensive algebraic model describing the limiting magnetization behavior in the interior and at the boundary of the sample. Finally, we demonstrate that the asymptotic results obtained in the periodic setting remain true in the case of finite rectangular samples.

Advances in Docking.

Design of small molecules which are able to bind to the protein responsible for a disease is the key step of the entire process of the new medicine discovery. Atomistic computer modeling can significantly improve effectiveness of such design. The accurate calculation of the free energy of binding a small molecule (a ligand) to the target protein is the most important problem of such modeling. Docking is one of the most popular molecular modeling methods for finding ligand binding poses in the target protein and calculating the protein-ligand binding energy. This energy is used for finding the most active compounds for the given target protein. This short review aims to give a concise description of distinctive features of docking programs focusing on computation methods and approximations influencing their accuracy. This review is based on the peer-reviewed research literature including author's own publications. The main features of several representative docking programs are briefly described focusing on their characteristics influencing docking accuracy: force fields, energy calculations, solvent models, algorithms of the best ligand pose search, global and local optimizations, ligand and target protein flexibility, and the simplifications made for the docking accelerating. Apart from other recent reviews focused mainly on the performance of different docking programs, in this work, an attempt is made to extract the most important functional characteristics defining the docking accuracy. Also a roadmap for increasing the docking accuracy is proposed. This is based on the new generation of docking programs which have been realized recently. These programs and respective new global optimization algorithms are described shortly. Several popular conventional docking programs are considered. Their search of the best ligand pose is based explicitly or implicitly on the global optimization problem. Several algorithms are used to solve this problem, and among them, the heuristic genetic algorithm is distinguished by its popularity and an elaborate design. All conventional docking programs for their acceleration use the preliminary calculated grids of protein-ligand interaction potentials or preferable points of protein and ligand conjugation. These approaches and commonly used fitting parameters restrict strongly the docking accuracy. Solvent is considered in exceedingly simplified approaches in the course of the global optimization and the search for the best ligand poses. More accurate approaches on the base of implicit solvent models are used frequently for more careful binding energy calculations after docking. The new generation of docking programs are developed recently. They find the spectrum of low energy minima of a protein-ligand complex including the global minimum. These programs should be more accurate because they do not use a preliminary calculated grid of protein-ligand interaction potentials and other simplifications, the energy of any conformation of the molecular system is calculated in the frame of a given force field and there are no fitting parameters. A new docking algorithm is developed and fulfilled specially for the new docking programs. This algorithm allows docking a flexible ligand into a flexible protein with several dozen mobile atoms on the base of the global energy minimum search. Such docking results in improving the accuracy of ligand positioning in the docking process. The adequate choice of the method of molecular energy calculations also results in the better docking positioning accuracy. An advancement in the application of quantum chemistry methods to docking and scoring is revealed. The findings of this review confirm the great demand in docking programs for discovery of new medicine substances with the help of molecular modeling. New trends in docking programs design are revealed. These trends are focused on the increase of the docking accuracy at the expense of more accurate molecular energy calculations without any fitting parameters, including quantum-chemical methods and implicit solvent models, and by using new global optimization algorithms which make it possible to treat flexibility of ligands and mobility of protein atoms simultaneously. Finally, it is shown that all the necessary prerequisites for increasing the docking accuracy can be accomplished in practice.

A BPt4S4 cluster: a planar tetracoordinate boron system with three charges all at their global energy minima

The monoanion state of BPt4S4− possesses the lowest energy among the three oxidation states with planar tetracoordinate boron.

Dynamics of an active semi-flexible filament in a spherical cavity.

We perform numerical simulations of active semiflexible filaments inside a rigid spherical cavity. We study the problem as a function of the bending rigidity, degree of confinement, and strength of the active forces. For passive filaments, the multispool conformations already established in previous studies are recovered, yet even small amounts of activity, when aligned along the direction of the filament backbone, destabilize these passive conformations. What emerges from our study is a highly dynamic scenario, where a filament is capable of escaping local and global energy minima and sample, in a quasiperiodic fashion, an ensemble of conformations usually associated with higher bending energies, and previously observed for passive filaments only under very different degrees of confinement or identified as glassy metastable states. We detail the structural properties of the different states and uncover a new dynamic pathway associated with their formation.

Embedding a Planar Hypercoordinate Carbon Atom into a [4n+2] π-System.

Through delicate tuning of the electronic structure, we report herein a rational design of seventeen new putative global minimum energy structures containing a planar tetra- or pentacoordinate carbon atom embedded in an aromatic hydrocarbon. These structures are the result of replacing three consecutive hydrogen atoms of an aromatic hydrocarbon by less electronegative groups, forming a multicenter σ-bond with the planar hypercoordinate carbon atom and participating in the π-electron delocalization. This strategy that maximizes both mechanical and electronic effects through aromatic architectures can be extended to several molecular combinations to achieve new and diverse compounds containing planar hypercoordinate carbon centers.

Exploration of Superacidic Properties of HMnFn (n = 1–6) Using Density Functional Theory

AbstractSuperacids play a key role as catalysts in various processes, such as acylation, esterification, and protonation of diverse chemical compounds. In the present investigation, HMnFn (n = 1–6) superacid series are studied within the quantum chemical framework using density functional theory with the B3LYP functional. The new superacid series is created through protonation of MnFn superhalogen complexes. Various molecular geometries, for example, HMnF, HMnF2, HMnF3, HMnF4, HMnF5, and HMnF6, are optimized to their respective global energy minimum and molecular properties are analyzed. First, the normal mode frequencies are analyzed in order to verify that the geometries are associated with their respective global minimum. Second, the Gibbs free energy of deprotonation ΔGacid is computed to estimate acidity of the molecules in gas phase. A compound is classified as a superacid if ΔGacid value is below 300 kcal mol−1. The HMnFn superacid series is found to have ΔGacid values well below this threshold of 300 kcal mol−1 and strength is comparable with fluoroantimonic acid (HSbF6), which is the strongest superacid known having ΔGacid value of 255.5 kcal mol−1.

Hydrodynamics-dominated wetting phenomena on hybrid superhydrophobic surfaces

HypothesisBecause of rich local hysteresis, it is a challenge to determine the global minimum surface energy and consequently, the true apparent contact angle of a liquid droplet on chemically-heterogeneous, rough surfaces. Meanwhile, a specific type of wetting phenomena strongly dominated by the hydrodynamic process is expected to be resulted by the chemically-heterogeneous micro-structures, yet not well studied. SimulationsA series of micropatterned hybrid substrates, which have the same pillar dimensions but different pillar spacings, have been studied using continuum simulations. The hybrid feature of the micropatterns presented here has two defining facets: the pillar top-surface is highly hydrophilic (SiO2-based), while the pillar side-surface and substrate bottom surface are hydrophobic (Teflon). Different initializations of a 0.4 µL water droplet have been simulated to mimic the experimental measurements, i.e., releasing a stationary droplet near the substrate, impacting the droplet at various speeds, and setting an initial apparent contact angle of 90°. FindingsThe simulated contact angles agree with the experiments in the literature. Moreover, this study vividly depicts the hydrodynamics-dominated wetting processes, and captures multiple metastable Cassie-Baxter states. This research is applicable to the design of new hybrid superhydrophobic surfaces with special functionality, such as high controllability at varied hydrodynamic conditions.

(5E/Z,7E,9)-Decatrien-2-ones, Pineapple-like Flavors from Fomitopsis betulina-Structure Elucidation and Sensorial Properties.

During the cultivation of the edible mushroom Fomitopsis betulina on agro-industrial side streams, a pleasant flavor strongly reminiscent of pineapple was perceived. Aroma extract dilution analyses identified two flavor components with a distinct pineapple odor. On the basis of mass spectrometric data, a Wittig reaction of (E)-penta-2,4-dien-1-yltriphosphonium bromide with ethyl levulinate was conducted. The resulting (5E/Z,7E,9)-decatrien-2-ones were identical to the compounds isolated from the fungal culture. Some structurally related methyl ketones were synthesized, confirmed by nuclear magnetic resonance and mass spectrometry, and their odor was characterized. The lowest odor threshold and most characteristic pineapple-like odor was found for (5Z,7E,9)-decatrien-2-one. Global minimum energy calculation of the methyl ketones and the comparison to (1,3E,5Z)-undecatriene, a character impact compound of fresh pineapple, showed that a chain length of at least 10 carbon atoms and a terminal double bond embedded in a "L"-shaped conformation were common to compounds imparting an intense pineapple-like odor. Both (5E/Z,7E,9)-decatrien-2-ones have not been described as natural flavor compounds.

Discrete Mutation Hopfield Neural Network in Propositional Satisfiability

The dynamic behaviours of an artificial neural network (ANN) system are strongly dependent on its network structure. Thus, the output of ANNs has long suffered from a lack of interpretability and variation. This has severely limited the practical usability of the logical rule in the ANN. The work presents an integrated representation of k-satisfiability (kSAT) in a mutation hopfield neural network (MHNN). Neuron states of the hopfield neural network converge to minimum energy, but the solution produced is confined to the limited number of solution spaces. The MHNN is incorporated with the global search capability of the estimation of distribution algorithms (EDAs), which typically explore various solution spaces. The main purpose is to estimate other possible neuron states that lead to global minimum energy through available output measurements. Furthermore, it is shown that the MHNN can retrieve various neuron states with the lowest minimum energy. Subsequent simulations performed on the MHNN reveal that the approach yields a result that surpasses the conventional hybrid HNN. Furthermore, this study provides a new paradigm in the field of neural networks by overcoming the overfitting issue.

Exploring the Binding Mechanism and Dynamics of EndoMS/NucS to Mismatched dsDNA.

The well-known mismatch repair (MMR) machinery, MutS/MutL, is absent in numerous Archaea and some Bacteria. Recent studies have shown that EndoMS/NucS has the ability to cleave double-stranded DNA (dsDNA) containing a mismatched base pair, which suggests a novel mismatch repair process. However, the recognition mechanism and the binding process of EndoMS/NucS in the MMR pathway remain unclear. In this study, we investigate the binding dynamics of EndoMS/NucS to mismatched dsDNA and its energy as a function of the angle between the two C-terminal domains of EndoMS/NucS, through molecular docking and extensive molecular dynamics (MD) simulations. It is found that there exists a half-open transition state corresponding to an energy barrier (at an activation angle of approximately 80) between the open state and the closed state, according to the energy curve. When the angle is larger than the activation angle, the C-terminal domains can move freely and tend to change to the open state (local energy minimum). Otherwise, the C-terminal domains will interact with the mismatched dsDNA directly and converge to the closed state at the global energy minimum. As such, this two-state system enables the exposed N-terminal domains of EndoMS/NucS to recognize mismatched dsDNA during the open state and then stabilize the binding of the C-terminal domains of EndoMS/NucS to the mismatched dsDNA during the closed state. We also investigate how the EndoMS/NucS recognizes and binds to mismatched dsDNA, as well as the effects of K ions. The results provide insights into the recognition and binding mechanisms of EndoMS/NucS to mismatched dsDNA in the MMR pathway.

Coil-Globule Transition Thermodynamics of Poly(N-isopropylacrylamide).

Thermosensitive polymers such as poly(N-isopropylacrylamide) (PNIPAM) undergo a phase transition in aqueous solution from a random-coil structural ensemble to a globule structural ensemble at the lower critical solution temperature (LCST). Above this temperature, PNIPAM agglomerates and becomes insoluble, whereas it is soluble below the temperature. Thus, thermosensitive polymers represent essential targets for several applications, e.g., in drug delivery. Although their ability to change structure in response to a temperature alteration is highly relevant for industrial processes, their thermodynamic properties are mostly qualitatively understood, and the quantitative thermodynamic picture is still elusive. In this study, we used a combined atomistic molecular dynamics and well-tempered metadynamics simulation approach to estimate coil-globule transition thermodynamics. An isotactic 30-mer of PNIPAM was investigated over a broad temperature range between 200 and 360 K. The transition from the globule to the random-coil structure was observed with well-tempered metadynamics. For the first time, the free energy surface of PNIPAM was estimated and it is shown that the simulation results are in line with the experimentally observed thermosensitive behavior. Below the LCST, the random-coil ensemble represents the global energy minimum and is thermodynamically favored by 21 ± 9 kJ/mol compared to the globule ensemble; both are separated by a barrier of 49 ± 14 kJ/mol. In contrast, above the LCST, the globule ensemble is thermodynamically favored by 21 ± 8 kJ/mol over the random-coil ensemble. The barrier from random-coil to globule is 17 ± 10 kJ/mol.