Energy Surface Research Articles

2D-Generating Surfaces in a Quartic Hamiltonian System with Three Degrees of Freedom – II

In earlier research, we developed two techniques designed to expand the construction of a periodic orbit dividing surface for Hamiltonian systems with three or more degrees of freedom. Our methodology involved transforming a periodic orbit into a torus or cylinder, thereby elevating it to a higher-dimensional structure within the energy surface (refer to [Katsanikas & Wiggins, 2021a, 2021b, 2023a, 2023b]). Recently, we introduced two new methods for creating dividing surfaces, which do not rely on periodic orbits. Instead, we used 2D surfaces (geometric entities) or 3D surfaces in a Hamiltonian system with three degrees of freedom (see [Katsanikas & Wiggins, 2024a, 2024b, 2024c]). In these studies, we applied these surfaces within a quadratic normal-form Hamiltonian system with three degrees of freedom. This series of two papers (this paper and [Katsanikas et al., 2024]) extends our results to 2D-generating surfaces for quartic Hamiltonian systems with three degrees of freedom. This paper focuses on presenting the second method of constructing 2D-generating surfaces.

Quantum Chemical Molecular Dynamics Simulations for Methane‐Water Cages

ABSTRACTThe dynamic stability of various methane‐water clathrate‐like cages (CH4@(H2O)n, n = 16, 18, 20, 22), has been analyzed explicitly considering thermal effects by means of ab initio M06‐2X/6–31+G*/PCM calculations, which make use of Gaussian basis functions. Starting from the equilibrium filled cage structures, classical, dynamic reaction coordinate (DRC) on the Born–Oppenheimer surface, and semiclassical, Born–Oppenheimer plus harmonic zero‐point energy surface (BOMD), molecular dynamics have been carried out. Water molecules have a high tendency to orient covalent O–H bonds tangentially to the hydrophobic surface, thus clathrate‐like arrangements are an acceptable model to fully hydrate methane. If the cage size is such as to minimize core repulsion, due to electron cloud overlap, and to maximize host–guest van der Waals attractions, the clathrate‐like structures have a life‐time of two picoseconds in classical DRC simulations. The inclusion of quantum kinetic energy in BOMD simulations results in less structured cages with a reduced amount of hydrogen bond network. The preferential tangential orientation of the O‐H bonds is largely maintained, although few of them point toward the methane for a very short time in BOMD simulations. The reduced configurational space of water molecules hydrating hydrophobic moiety is highlighted, thus any satisfactory molecular modeling has to account for it.

2D Generating Surfaces in a Quartic Hamiltonian System with Three Degrees of Freedom – I

In previous studies, we developed two techniques aimed at expanding the scope of constructing a periodic orbit dividing surface within a Hamiltonian system with three or more degrees of freedom. Our approach involved extending a periodic orbit into a torus or cylinder, thereby elevating it into a higher-dimensional entity within the energy surface (see [Katsanikas & Wiggins, 2021a, 2021b, 2023a, 2023b]). Recently, we introduced two alternative methods for creating dividing surfaces, distinct from the utilization of periodic orbits, by employing 2D surfaces (geometric entities) or 3D surfaces within a Hamiltonian system with three degrees of freedom (refer to [Katsanikas & Wiggins, 2024a, 2024b, 2024c]). In these studies, we applied these surfaces in a quadratic normal form Hamiltonian system with three degrees of freedom. In this series of two papers, we extend our results to 2D generating surfaces for quartic Hamiltonian systems with three degrees of freedom. This paper presents the first method of constructing 2D generating surfaces.

Predicting Selectivity with a Bifurcating Surface: Inaccurate Model or Inaccurate Statistics of Dynamics?

Reactions on post-transition-state bifurcation (PTSB) energy surfaces are an important class of reaction in which classical rate theories, such as the transition state theory, fail to account for the selectivity. Quasiclassical trajectory molecular dynamic (QCT-MD) simulation is an important computational approach to understanding reactions mechanisms, especially for reactions that cannot be predicted from conventional rate theories. However, the applicability of direct dynamic simulations is hampered by huge computational costs for collecting a statistically meaningful set of trajectories, making it difficult to compare simulation results with theoretical or physical insights-based predictions (non-MD predictions). In this work, we examine the PTSB of Schmidt-Aubé reactions studied by Tantillo and co-workers. With machine-learning using kernel-ridge regression (KRR) to predict atomic forces, statistical reliability was enhanced by significantly increasing the number of trajectories. With KRR, the bottleneck of simulating dynamics (atomic forces in QCT-MD with density functional theory) was accelerated more than 100-fold. We found that this KRR-aided QCT-MD approach is successful in predicting branching ratios with a much larger number of trajectories. With our approach, statistical errors are greatly reduced, and hypothetical non-MD models for predicting selectivity are tested with much higher confidence. By comparison with non-MD models, dynamical properties that affect branching ratios become more clearly described.

Development of biodegradable bioadhesive nanocomposites reinforced with quantum dots and functionalized carbon nanotubes

A series of photoluminescent nanocomposite polyurethane adhesives were elaborated from a chemoenzymatic prepared diol of caprolactone (PCL-diol) and ethylene glycol with an excess of two different isocyanates: i) hexamethylene (HDI) and (ii) isophorone (IPDI)) diisocyanates. Adhesive formulations were filled with functionalized poly(amido-amine) (PAMAM) carbon nanotubes (f-MWNTs) and carbon quantum dots (CQDTs). Dry swine gut was used as substrate and mechanical tests were performed to explore the performance of the adhesives. The obtained materials were characterized by infrared spectroscopy (FT-IR), energy surface by contact angle, differential scanning calorimetry (DSC), hydrolytic degradation, and mechanical testing under tension, lap shear, T-peel, wound closure, and burst pressure. Among the main results were the formation of covalent bonds between the substrate and the adhesive, and the fact that the mechanical strength of the nanocomposite adhesives was superior to that of the unfilled adhesives. Compatibility of nanocomposites with the substrate was achieved by increasing wettability by the incorporation of both nanofillers. Also, adhesives filled with only CQDTs and with MWNTs-CDQTs combined showed photoluminescence activity under ultraviolet light.

The Cambridge Structural Database and structural dynamics.

With the availability of the computer readable information in the Cambridge Structural Database (CSD), wide ranging, largely automated comparisons of fragment, molecular, and crystal structures have become possible. They show that the distributions of interatomic distances, angles, and torsion angles for a given structural fragment occurring in different environments are highly correlated among themselves and with other observables such as spectroscopic signals, reaction and activation energies. The correlations often extend continuously over large ranges of parameter values. They are reminiscent of bond breaking and forming reactions, polyhedral rearrangements, and conformational changes. They map-qualitatively-the regions of the structural parameter space in which molecular dynamics take place, namely, the low energy regions of the respective (free) energy surfaces. The extension and continuous nature of the correlations provides an organizing principle of large groups of structural data and suggests a reconsideration of traditional definitions and descriptions of bonds, "nonbonded" and "noncovalent" interactions in terms of Lewis acids interacting with Lewis bases. These aspects are illustrated with selected examples of historic importance and with some later developments. It seems that the amount of information in the CSD (and other structural databases) and the knowledge on the nature of, and the correlations within, this body of information should allow one-in the near future-to make credible interpolations and possibly predictions of structures and their properties with machine learning methods.

Local Structures in Proteins from Microsecond Molecular Dynamics Simulations: A Symmetry-Based Perspective.

We report on a new method for the characterization of local structures in proteins based on extensive molecular dynamics (MD) simulations, here, 1 μs in length. The N-H bond of the Rho GTPase binding domain of plexin-B1 (RBD) serves as a probe and the potential, u(MD), which restricts its internal motion, as a qualifier of the local dynamic structure. u(MD) is derived from the MD trajectory as a function of the polar angles, (θ, φ), which specify the N-H orientation in the protein. u(MD) is statistical in character yielding empirical descriptions. To establish more insightful methodical descriptions, we develop a comprehensive method which approximates u(MD) by combinations of analytical Wigner functions that belong to the D2h point group. These combinations, called u(simulated), make it possible to gain a new perspective of local dynamic structures in proteins based on explicit potentials/free energy surfaces and associated probability densities, entropy, and ordering. A simpler method was developed previously using 100 ns MD simulations. In that case, the traditional "perpendicular N-H ordering" setting centered at Cα-Cα with (θ, φ) = (90, 90) and generally, featuring positive φ, prevailed. u(MD) derived from 1 μs MD simulations is considerably more complex requiring substantial model enhancement. The enhanced method applies to the well-structured sections of the RBD. It only applies partly to its loops where u(MD) extends into the negative-φ region where we detect nonperpendicular N-H ordering. This arrangement requires devising new reference structures and making substantial algorithmic changes, to be performed in future work. Here, we focus on developing the comprehensive method and using it to investigate perpendicular ordering settings. We find that secondary structures (loops) exhibit varying (virtually invariant) potentials with Ag, B2u, and B1u (Ag and B2u) D2h symmetry. Application to RBD dimerization and RBD binding to the GTPase Rac1 is described in the subsequent article. Applications to other probes, proteins, and biological functions, based on explicit local potentials, probability densities, entropy, and ordering, are possible.

Atomistic study on effects of solute atoms on energy profile of edge dislocation mobility in FCC-Cu alloys

Solid-solution strengthening is an effective method to increase the mechanical strength of metal alloys. Revealing the solid-solution strengthening mechanism based on the energy profile of the dislocation motion is vital for the non-empirical development of high-strength metal alloys. This study provides detailed energy profiles (i.e., energy surfaces) of the edge dislocation gliding motion under the effect of solute atoms, as well as the atomic-scale origin of solute strengthening in face-centered cubic (FCC) Cu alloys. The maximum shear stress (τmax) required for the dislocation to leave the solute atoms (Ni, Co, and Mo, all with different sizes and stacking fault effects) was qualitatively evaluated by finite temperature molecular dynamics simulations. By the nudged elastic band (NEB) analysis, we determined the atomistic origin of the energy barrier for the edge dislocation motion and the maximum force required to overcome the solute pinning effect (i.e., depinning force, FNEB) in binary Cu alloys. By linking FNEB to the size misfit, a theoretical prediction model based on size effects and the volumetric strain field was used and can qualitatively explain the increment in the maximum shear stress (Δτmax) by the solute atoms. These results provide an atomistic basis for the prediction of the solute-strengthening effect correlated with the edge dislocation motion in wide FCC systems.

2D Generating Surfaces and Dividing Surfaces in Hamiltonian Systems with Three Degrees of Freedom

In our previous work, we developed two methods for generalizing the construction of a periodic orbit dividing surface for a Hamiltonian system with three or more degrees of freedom. Starting with a periodic orbit, we extend it to form a torus or cylinder, which then becomes a higher-dimensional object within the energy surface (see [Katsanikas & Wiggins, 2021a, 2021b, 2023a, 2023b]). In this paper, we present two methods to construct dividing surfaces not from periodic orbits but by using 2D surfaces (2D geometrical objects) in a Hamiltonian system with three degrees of freedom. To illustrate the algorithm for this construction, we provide benchmark examples of three-degree-of-freedom Hamiltonian systems. Specifically, we employ the uncoupled and coupled cases of the quadratic normal form of a Hamiltonian system with three degrees of freedom.

Roles of functional group and intramolecular hydrogen bond in the S1/S0 energy Landscape: Hydrazone versus Schiff base

We investigated the S1/S0 energy surfaces and energy-minimized conical intersections (MECIs) of Schiff bases and their hydrazone analogues. Time-dependent density functional theory revealed that proton transfers on the S1 surface involve minimal barriers, or are barrier-less. In the phenolic form, the MECIs of the Schiff bases are more sloped than their hydrazone counterparts, and the MECIs of the proton-transferred species are more sloped. The hydrogen bonds result in lower-energy vertical excitations and higher-energy MECIs. The MECIs of hydrazone featuring carbonyl-furan group have the largest dot products of the energy gradient of S1 and the g and h vectors.

Unveiling Metastable Ensembles of GRB2 and the Relevance of Interdomain Communication during Folding.

The folding process of multidomain proteins is a highly intricate phenomenon involving the assembly of distinct domains into a functional three-dimensional structure. During this process, each domain may fold independently while interacting with others. The folding of multidomain proteins can be influenced by various factors, including their composition, the structure of each domain, or the presence of disordered regions, as well as the surrounding environment. Misfolding of multidomain proteins can lead to the formation of nonfunctional structures associated with a range of diseases, including cancers or neurodegenerative disorders. Understanding this process is an important step for many biophysical analyses such as stability, interaction, malfunctioning, and rational drug design. One such multidomain protein is growth factor receptor-bound protein 2 (GRB2), an adaptor protein that is essential in regulating cell survival. GRB2 consists of one central Src homology 2 (SH2) domain flanked by two Src homology 3 (SH3) domains. The SH2 domain interacts with phosphotyrosine regions in other proteins, while the SH3 domains recognize proline-rich regions on protein partners during cell signaling. Here, we combined computational and experimental techniques to investigate the folding process of GRB2. Through computational simulations, we sampled the conformational space and mapped the mechanisms involved by the free energy profiles, which may indicate possible intermediate states. From the molecular dynamics trajectories, we used the energy landscape visualization method (ELViM), which allowed us to visualize a three-dimensional (3D) representation of the overall energy surface. We identified two possible parallel folding routes that cannot be seen in a one-dimensional analysis, with one occurring more frequently during folding. Supporting these results, we used differential scanning calorimetry (DSC) and fluorescence spectroscopy techniques to confirm these intermediate states in vitro. Finally, we analyzed the deletion of domains to compare our model outputs to previously published results, supporting the presence of interdomain modulation. Overall, our study highlights the significance of interdomain communication within the GRB2 protein and its impact on the formation, stability, and structural plasticity of the protein, which are crucial for its interaction with other proteins in key signaling pathways.

Wetting Behavior of CO2 Droplets on Smooth Solid Surface: Molecular Simulation Perspective

The wettability of droplets on solid surfaces is important for accurately revealing the microscopic mechanisms of gas condensation nucleation and droplet growth. During the contact condensation of CO2 gas on the heat exchanger surface in the pressurized liquefied natural gas technology, the wettability of CO2 droplets on the heat exchanger surface directly affects the heat transfer thermal resistance of the heat exchanger, which then affects the heat transfer efficiency of methane and ethane in the heat exchanger. Therefore, molecular dynamics simulations were used to study the spreading process and wetting patterns of nanoscale CO2 droplets on different energy surfaces. The results show that as the potential well depth ε of the wall atoms increases, the intensity of the solid-liquid interaction increases and the corresponding surface energy increases accordingly, showing different droplet spreading rates and wetting characteristics. Unlike the interfacial characteristics of macroscopic droplets, there are significant fluctuations at the gas-liquid interface of droplets on the molecular scale, but microdroplets can still form a specific contact angle after spreading on different energy surfaces in a statistical sense, and this contact angle decreases with increasing intensity of solid-liquid interaction. The low-energy surface at potential well depths ε less than 266 J·mol-1 exhibits a CO2-phobicity, and the surface becomes CO2-philic as the potential well depth continues to increase. The trend of the contact angle of CO2 droplets affected by temperature is the same as that of the center-of-mass height, which characterizes the spreading morphology of CO2 droplets. As the temperature increases, the contact angle decreases due to the further spreading and wetting of droplets on different energy surfaces. As the CO2-philicity of the surface gets higher, the contact angle decreases to a greater extent.

RNA tertiary structure modeling with BRiQ potential in CASP15.

We describe the modeling method for RNA tertiary structures employed by team AIchemy_RNA2 in the 15th Critical Assessment of Structure Prediction (CASP15). The method consists of the following steps. Firstly, secondary structure information was derived from various manually-verified sources. With this information, the full length RNA was fragmented into structural modules. The structures of each module were predicted and then assembled into the full structure. To reduce the searching conformational space, an RNA structure was organized into an optimal base folding tree. And to further improve the sampling efficiency, the energy surface was smoothed at high temperatures during the Monte Carlo sampling to make it easier to move across the energy barrier. The statistical potential energy function BRiQ was employed during Monte Carlo energy optimization.

Invisible energy policy and schools: how energy issues feature in the policies and documents of a UK secondary school

There is a growing research literature focused on ‘invisible energy policy’ that explores the complex links between policies in non-energy sectors and energy demand. Invisible energy policies are those that do not include energy as a visible policy objective but still pose implications for energy demand that are largely unrecognised in non-energy organisational settings. Within this innovative area of analysis, to date, little attention has been paid to how ‘energy’ features in the discourse of non-energy contexts. This paper makes a distinctive contribution by examining how energy issues, such as energy demand, travel, and energy skills, do or do not feature in the policy and wider strategy of a non-energy policy setting. The research focuses on the content of policies and other documents in the non-energy policy context of UK secondary schooling, using a case study approach. It aimed to identify how energy surfaces and/or remains absent in different types of documentary evidence at the school. The textual analysis shows how openings for energy to surface as a concern at the school are often heavily bounded in specific policy areas, such as sustainability and education. It also foregrounds the lack of recognition in the sample for how school operations and strategy can produce demand for energy more fundamentally. It argues that these openings for energy to surface can provide points of negotiation to discuss the more fundamental energy impacts of policy. The paper concludes by reflecting on the analysis’ implications for research on ‘invisible energy policies’ and low-carbon transitions.

Lyapunov center theorem on rotating periodic orbits for Hamiltonian systems

We introduce the Q(s)-index ind Γ for a symplectic orthogonal group Q(s) and Q(s) invariant subset Γ of R2n and prove that indS2n−1=n. Using this fact, we study multiple rotating periodic orbits of Hamiltonian systems. For an orthogonal matrix Q, a Q-rotating periodic solution z(t) has the form z(t+T)=Qz(t) for all t∈R and some constant T>0. According to the structure of Q, it can be periodic, anti-periodic, subharmonic, or just a quasi-periodic one. Under a non-resonant condition, we prove that on each energy surface near the equilibrium, the Hamiltonian system admits at least n Q-rotating periodic orbits, which can be regarded as a Lyapunov type theorem on rotating periodic orbits.

Phase field modeling of shearing processes of a dual-lobed γ″|γ′|γ″ coprecipitate

The Ni-based superalloy IN718 is one of the most widely used commercial alloy in the aerospace industry since its development in 1960s. The excellent mechanical properties have been attributed in a great deal to strengthening by coherent γ′ and γ″ precipitates. The deformation mechanisms of these two phases have been well studied individually. Recent experimental characterization has shown coprecipitates of these two phases in a variety of morphologies and it was argued that these coprecipitates may lead to improved strengthening as compared to their monolithic counterparts. However, the deformation mechanisms of these coprecipitates are still not well understood. In this study, we performed microscopic phase field simulations, with generalized-stacking-fault (GSF) energy surfaces from ab initio calculations as inputs, to systematically study the shearing processes of a periodical array of dual-lobed coprecipitates as well as monolithic precipitates. We found that the coupling between the γ′ and γ″ phases in the coprecipitates forces dislocations to take high energy shearing pathways in both phases that would not occur if they were in monolithic forms. The coupling also creates stacking fault configurations in the coprecipitates that require high stress to form. Thus, the presence of coprecipitates in general should increase the resistance to dislocation shearing and lead to higher strength levels. Various fault configurations observed during the shearing process are documented as a reference for future comparison with experimental observations. The link between stacking fault shearing and microtwinning is also discussed. The mechanisms analyzed in this study deepens our understanding of coprecipitation effects on alloy strength and may form a cornerstone for multi-precipitate strengthened alloy design strategies.

Integrating Protein Interaction Surface Prediction with a Fragment-Based Drug Design: Automatic Design of New Leads with Fragments on Energy Surfaces.

Protein-protein interactions (PPIs) have emerged in the past years as significant pharmacological targets in the development of new therapeutics due to their key roles in determining pathological pathways. Herein, we present fragments on energy surfaces, a simple and general design strategy that integrates the analysis of the dynamic and energetic signatures of proteins to unveil the substructures involved in PPIs, with docking, selection, and combination of drug-like fragments to generate new PPI inhibitor candidates. Specifically, structural representatives of the target protein are used as inputs for the blind physics-based prediction of potential protein interaction surfaces using the matrix of low coupling energy decomposition method. The predicted interaction surfaces are subdivided into overlapping windows that are used as templates to direct the docking and combination of fragments representative of moieties typically found in active drugs. This protocol is then applied and validated using structurally diverse, important PPI targets as test systems. We demonstrate that our approach facilitates the exploration of the molecular diversity space of potential ligands, with no requirement of prior information on the location and properties of interaction surfaces or on the structures of potential lead compounds. Importantly, the hit molecules that emerge from our ab initio design share high chemical similarity with experimentally tested active PPI inhibitors. We propose that the protocol we describe here represents a valuable means of generating initial leads against difficult targets for further development and refinement.

Temperature gradient control of frequency conversion heating for a thick-walled pipe based on energy transfer

Characterized by energy concentration, electromagnetic heating technology has a significant advantage in achieving local rapid heating of a workpiece. However, electromagnetic heating may create a great temperature gradient in the wall thickness direction for a workpiece with a thick wall that requires penetrating heating. To improve the evenness of the temperature between the internal and external surfaces, a frequency conversion heating method is proposed. An electric–magnetic–thermal coupling model for frequency conversion heating of welded pipes is established and verified by temperature measurement experiments, thereby revealing the distribution characteristics of the induced current, temperature, and magnetic flux intensity. On this basis, a new concept—the energy surface—is defined. An induction heating schedule suitable for thick-walled pipes is formulated with the energy surface transfer characteristics. The electromagnetic distribution resembles the topology of an underwater lake. There is a "demagnetization region" with a magnetic flux intensity of < 0.321 T. The field width varies with the frequency. The temperature difference along the wall thickness of the welded pipe reaches its maximum after the critical demagnetization surface manifests. By controlling the frequency conversion heating, the temperature difference can be decreased to 88.82%, thus improving the induction heating quality of the welded pipe. This study provides a measurable theoretical reference basis for investigating the change in the internal heat source caused by the change of electromagnetic characteristics to accurately control the temperature gradient.

Spin-Orbit Coupling Calculation Combined with the Reference Interaction Site Model Self-Consistent Field Explicitly Including Constrained Spatial Electron Density Distribution.

Studying the radiative and non-radiative decay processes of molecules in a solution is an important issue in the design of organic and functional molecules. Theoretical approaches have great potential for revealing this decay process through computation of various parameters, such as the energy surfaces at the excited state and spin-orbit coupling (SOC). The development of quantum chemical programs has enabled the calculation of SOC values to become popular for the gas phase. However, SOC calculations in solution have some difficulties that need to be overcome. In the present study, the authors combined the SOC calculations with the reference interaction site model self-consistent field explicitly including constrained spatial electron density distribution. To validate the reliability of our method, the decay process of dimethylaminobenzonitrile in cyclohexane and acetonitrile was studied. By computing the SOC values in both solution systems, the authors were able to investigate the decay process at the atomistic level. Furthermore, a natural transition orbital analysis and the measurement of the decomposed SOC values were found to provide a clear understanding of intersystem crossing.

Molecular Structure, Spectroscopic Elucidation (FT-IR, FT-Raman, UV-Visible and NMR) with NBO, ELF, LOL, RDG, Fukui, Drug Likeness and Molecular Docking Analysis on Dimethomorph

In the present study, 3-(4-chlorophenyl)-3-(3,4-dimethoxyphenyl)-1-morpholin-4-ylprop-2-en-1-one (dimethomorph) was characterized by spectroscopic investigations employing FT-IR, FT-Raman, UV-Vis and NMR (13 C, 1H) techniques. The optimized geometrical parameters and complete vibrational assignments of frequencies based on Potential Energy Distribution (PED) were determined by using Density Functional Theory (DFT) through the B3LYP with the level of 6-31G(d) basis set and compared with the experimental values. Besides, to gain better insight into structural features of title composite, HOMO-LUMO bandgap energy and electron excitation analysis was obtained. Molecular Electrostatic Potential (MEP) energy surface and Fukui function descriptor using natural atomic analysis charges were employed to investigate the most reactive sites of the title compound. Natural bond orbital analysis (NBO) elucidates the delocalization of charge due to intermolecular interactions. The topological studies (RDG, ELF and LOL). Molecular docking done with antifungal, antiviral and antimicrobial proteins endorses the bioactivity of molecule. Drug likeness factors were calculated to comprehend the biological assets of dimethomorph. The stability of the title compound has been investigated via molecular dynamics simulations (MDS). In-vitro analysis was done with two fungal pathogens, such as Aspergillus niger and Candida albicans.