Lowest Energy Path Research Articles

Construction of Continuous Collective Energy Landscapes for Large Amplitude Nuclear Many-Body Problems.

Several protocols are proposed to build continuous energy surfaces of many-body quantum systems, regarding both energy and states. The standard variational principle is augmented with constraints on state overlap, ensuring arbitrary precision on continuity. As an illustration, the lowest energy and excited state paths relevant for the ^{240}Pu asymmetric fission are studied. The scission is clearly signed, with a neutron excess in the neck, the ultimate glue before its rupture. Our approach can potentially connect any couple of Hilbert space states, which opens up new horizons for various applications.

Modeling dynamic crack growth in quasicrystals: Unraveling the role of phonon–phason coupling

In this work, we employed the phase-field fracture (PFF) model for dynamic brittle fracture in quasicrystals (QCs). The dynamic PFF formulation is derived using both elastodynamics and elasto-hydrodynamic theory. The temporal discretization is achieved using an implicit generalized-α method, which is unconditionally stable for a particular choice of constants. The model incorporates two distinct crack driving forces: (a) the contribution of elastic strain energy from both phonon and phason fields and (b) the contribution solely from the elastic energy associated with the phonon field. To validate the implementation of QCs, we have conducted benchmarking against recent results in the literature, particularly in the context of quasi-static loading. We addressed various paradigmatic case studies to demonstrate the dynamic crack nucleation and propagation in planar 2D decagonal QCs, with a primary emphasis on understanding the interplay between phonon and phason fields. Phason walls, representing low-energy crack paths resulting from atomic rearrangements, play a significant role in crack propagation by introducing an additional energy component. Notably, increasing the phonon–phason coupling constant expedites both crack initiation and propagation. Furthermore, variations in the phonon–phason coupling parameter result in different crack trajectories, observed in both uniaxial and biaxial loading scenarios. The developed code can be downloaded from https://github.com/Hirshikesh/Quasicrystal.git.

Topological twists of massive SQCD, Part I

We consider topological twists of four-dimensional N=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N}=2$$\\end{document} supersymmetric QCD with gauge group SU(2) and Nf≤3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_f\\le 3$$\\end{document} fundamental hypermultiplets. The twists are labelled by a choice of background fluxes for the flavour group, which provides an infinite family of topological partition functions. In this Part I, we demonstrate that in the presence of such fluxes the theories can be formulated for arbitrary gauge bundles on a compact four-manifold. Moreover, we consider arbitrary masses for the hypermultiplets, which introduce new intricacies for the evaluation of the low-energy path integral on the Coulomb branch. We develop techniques for the evaluation of these path integrals. In the forthcoming Part II, we will deal with the explicit evaluation.

Curvature-driven pathways interpolating between stationary points: the case of the pure spherical 3-spin model

This paper focuses on characterizing the energy profile along pathways connecting different regions of configuration space in the context of a prototypical glass model, the pure spherical p-spin model with p = 3. The study investigates pairs of stationary points (local minima or rank-1 saddles), analyzing the energy profile along geodesic paths and comparing them with ‘perturbed’ pathways correlated to the landscape curvature. The goal is to assess the extent to which information from the local Hessian matrices around stationary points can identify paths with lower energy barriers. Surprisingly, unlike findings in other systems, the direction of softest local curvature is not a reliable predictor of low-energy paths, except in the case in which the direction of softest curvature corresponds to an isolated mode of the Hessian. However, other information encoded in the local Hessian does allow the identification of pathways associated with lower energy barriers. We conclude commenting on implications for the system’s activated dynamics.

Tuning the Hydrogenation Selectivity of an Unsaturated Aldehyde via Single-Atom Alloy Catalysts.

Selective hydrogenation of α,β-unsaturated aldehydes to produce unsaturated alcohols remains a challenge in catalysis. Here, we explore, on the basis of first-principles simulations, single-atom alloy (SAA) catalysts on copper as a class of catalytic materials to enhance the selectivity for C═O bond hydrogenation in unsaturated aldehydes by controlling the binding strength of the C═C and C═O bonds. We show that on SAA of early transition metals such as Ti, Zr, and Hf, the C═O binding mode of acrolein is favored but the strong binding renders subsequent hydrogenation and desorption impossible. On SAA of late-transition metals, on the other hand, the C═C binding mode is favored and C═C bond hydrogenation follows, resulting in the production of undesired saturated aldehydes. Mid-transition metals (Cr and Mn) in Cu(111) appear as the optimal systems, since they favor acrolein adsorption via the C═O bond but with a moderate binding strength, compatible with catalysis. Additionally, acrolein migration from the C═O to the C═C binding mode, which would open the low energy path for C═C bond hydrogenation, is prevented by a large barrier for this process. SAA of Cr in Cu appears as an optimal candidate, and kinetic simulations show that the selectivity for propenol formation is controlled by preventing the acrolein migration from the more stable C═O to the less stable C═C binding mode and subsequent H-migration and by the formation of the O-H bond from the monohydrogenated intermediate. Dilute alloy catalysts therefore enable tuning the binding strength of intermediates and transition states, opening control of catalytic activity and selectivity.

Temperature-Dependent Investigation of ORR Kinetics on Non-Precious Metal-Free Catalysts in Alkaline Media - Doping Effect on Electrocatalysis

The kinetic analysis of oxygen reduction reaction (ORR) on non-precious catalysts is cumbersome due to the formation of more than one major products ( and ). In the present study, ORR is investigated on Vulcan XC-72 (C) and a metal-free nitrogen-doped (~≤ 1%) carbon (N/C-900) catalysts in 0.1 M KOH [1]. The experiments are conducted in the temperature range of 293–323 K using a rotating ring disk electrode (RRDE) assembly to quantify the product distribution, viz., and . The measured kinetic current () is partitioned into and on the basis of the potential-dependent product distribution ( and ) .and is used in the estimation of kinetic parameters [2]. The α values are derived from Butler-Volmer (B-V) theory, Tafel equation at high overpotentials (η), and from the derivative of the change in Gibbs free energy of activation () with respect to η. The α values obtained from all the three methods are different. Therefore, the origin of the difference in the α values is the subject of the present investigation. The seemingly unreasonable values of (> 1.0)on N/C-900 may be due to the alternative lower energy path for the formation of activated complex along with the change in the free energy of the reactant [3,4]. On C, it does not provide any alternative pathway for the formation of activated complex and perhaps η influences only the energy state of the reactant. Therefore, the free energy of activation for the formation of activated complex is a stronger function of η on N/C-900 and an indication of strong electrocatalysis. References B. Bera, T. Kar, A. Chakraborty, M. Neergat, J. Electroanal. Chem., 805, 184–192 (2017).R. Das, D. Choudhury, R. Maurya, S. Sharma, M. Neergat, Langmuir,39 (12), 4351–4361 (2023).U. Stimming, J. Wang, A. Bund, ChemPhysChem, 20 (22), 3004–3009 (2019).R. Maurya, R. Das, A. K. Tripathi, M. Neergat, Phys. Chem. Chem. Phys., 25, 700–707 (2023). *Corresponding author: Tel.: +91 22 2576 7893; Fax: +91 22 2576 4890E-mail: nmanoj@iitb.ac.in (M. Neergat)

Time-dependent clay gels: Stepdown shear rate behavior, microstructure, ageing, and phase state ambiguity

To study the time-dependent properties of clay gels in the structural rejuvenation mode, a combination of the stepdown shear rate method and an ageing test is advocated. In this mode, the structural development process at two different initial equilibrium states during the low stepdown shear rate and the rest period of the ageing test were followed. The roles played by the electric double layer (EDL) repulsive force in this structural development process with and without shear, for platelet sodium montmorillonite or NaMnt, hectorite and Laponite gels, and fibrous sepiolite gels were assessed. The response of the stepdown shear stress and ageing yield stress reflects the action of these forces on the structural rejuvenation kinetics and the type of structure formed. The platelet clay gels with their strong EDL repulsive particle interaction commenced the structural development process immediately and formed an open network structure. This process is short in shear and takes years when without. The fibrous sepiolite gel with its weak EDL repulsive interaction did not display structural rejuvenation in shear and only showed a significant yield stress increase after the first few hours of ageing. An additional issue concerning the stability of the isotropic liquid (IL) phase state of dilute Laponite dispersions was addressed. These dispersions aged for >9 years, displaying that yield stress and network structure confirmed that the IL phase is unstable. A low energy path available for Laponite particles to aggregate was discussed. A new method for determining the flocculate phase state was also presented.

Pathways of hydrogen atom diffusion at fcc Cu: Σ9 and Σ5 grain boundaries vs single crystal

The diffusion of H-atoms is relevant for innumerous physical–chemical processes in metals. A detailed understanding of diffusion in a polycrystalline material requires the knowledge of the activation energies (ΔEa’s) for diffusion at different defects. Here, we report a study of the diffusion of H-atoms at the Σ9 and Σ5 grain boundaries (GBs) of fcc Cu that are relevant for practical applications of the material. The complete set of possible diffusion pathways was determined for each GB and we compared the ΔEa at bulk fcc Cu with the landscape of ΔEa’s at these defects. We found that while a number of diffusion pathways at the GBs have high tortuosity, there are also many paths with very low tortuosity because of specific structural features of the interstitial GB sites. These data show that the diffusion of H-atoms at these GBs is highly directional but can be fast because at certain paths the ΔEa can be as low as 0.05 eV. The lowest energy paths for diffusion of H-atoms through the whole GB models are ΔEa = 0.05 eV for the Σ9 and ΔEa = 0.20 eV at Σ5 which compare with ΔEa = 0.42 eV for the bulk fcc crystal. This shows that H-atoms will be able to diffuse very fast at these defects. With the Laguerre–Voronoi tessellation method, we studied how the local atomic structure of the interstitial sites of the GBs leads to different ΔEa’s for diffusion of H-atoms. We found that the volume expansions and the coordination numbers alone cannot account for the magnitude of the ΔEa’s. Hence, we developed a symmetry quantifying parameter that measures the deviation of symmetry of the GB sites from that of the bulk octahedral site and hence accounts for the distortion at the GB site. Only when this parameter is introduced together with the volume expansions and the coordination numbers, it is possible to correlate the local structure with the ΔEa’s and to obtain descriptors of diffusion. The complete set of data shows that the extrapolation of diffusion data for H-atoms between different types of GBs is non-trivial and should be done with care.

Darcy's law of yield stress fluids on a treelike network.

Understanding the flow of yield stress fluids in porous media is a major challenge. In particular, experiments and extensive numerical simulations report a nonlinear Darcy law as a function of the pressure gradient. In this letter we consider a treelike porous structure for which the problem of the flow can be resolved exactly due to a mapping with the directed polymer (DP) with disordered bond energies on the Cayley tree. Our results confirm the nonlinear behavior of the flow and expresses its full pressure dependence via the density of low-energy paths of DP restricted to vanishing overlap. These universal predictions are confirmed by extensive numerical simulations.

Defect properties of a body-centered cubic equiatomic TiVZrTa high-entropy alloy from atomistic simulations

TiVZrTa high-entropy alloys (HEAs) have been experimentally proven to exhibit excellent irradiation tolerance. In this work, defect energies and evolution were studied to reveal the underlying mechanisms of the excellent irradiation tolerance in TiVZrTa HEA via molecular statics calculations and molecular dynamics simulations. The atomic size mismatch of TiVZrTa is ∼6%, suggesting a larger lattice distortion compared to most face-centered cubic and body-centered cubic M/HEAs. Compared to pure Ta and V, smaller vacancy formation and migration energies with large energy spreads lead to higher equilibrium vacancy concentration and faster vacancy diffusion via low-energy migration paths. Vacancies in TiVZrTa have weaker abilities to form large vacancy clusters and prefer to form small clusters, indicating excellent resistance to radiation swelling. The formation energies of different types of dumbbells in TiVZrTa show significant differences and have large energy spreads. The binding abilities of interstitials in TiVZrTa are weaker compared to that in pure Ta and V. In TiVZrTa, fast vacancy diffusion and slow interstitial diffusion result in closer mobilities of vacancies and interstitials, significantly promoting point defect recombination. We further studied the effects of short-range ordered structures (SROs) on defect diffusion and evolution. SROs in TiVZrTa can effectively lead to higher fractions of defect recombination and fewer surviving defects. Our findings provide a comprehensive understanding of the underlying mechanisms of the high irradiation tolerance in body-centered cubic HEAs with large lattice distortion and suggest SROs are beneficial microstructures for enhancing irradiation tolerance.

Foreword to the special issue on new developments in structural stability.

Foreword to the special issue on new developments in structural stability.

Benchmark Structures and Conformational Landscapes of Amino Acids in the Gas Phase: A Joint Venture of Machine Learning, Quantum Chemistry, and Rotational Spectroscopy.

The accurate characterization of prototypical bricks of life can strongly benefit from the integration of high resolution spectroscopy and quantum mechanical computations. We have selected a number of representative amino acids (glycine, alanine, serine, cysteine, threonine, aspartic acid and asparagine) to validate a new computational setup rooted in quantum-chemical computations of increasing accuracy guided by machine learning tools. Together with low-lying energy minima, the barriers ruling their interconversion are evaluated in order to unravel possible fast relaxation paths. Vibrational and thermal effects are also included in order to estimate relative free energies at the temperature of interest in the experiment. The spectroscopic parameters of all the most stable conformers predicted by this computational strategy, which do not have low-energy relaxation paths available, closely match those of the species detected in microwave experiments. Together with their intrinsic interest, these accurate results represent ideal benchmarks for more approximate methods.

Effect of valence state on electrochemical nitrate reduction to ammonia in molybdenum catalysts

Intended to investigate the alternative to the traditional Haber−Bosch process for generating ammonia, electrocatalytic nitrate reduction reaction (NRA) ensures a lower energy path and decentralized manner. Inspired by the nitrate reductase, we propose two Mo-based electrocatalysts with different Mo valences: MoO2-C nanoball-flower (MoO2-C NBF) with Mo (IV) sites and MoO3-C nanoball-flower (MoO3-C NBF) with Mo (Ⅵ) sites. The theoretical prediction reveals that the Mo (IV) sites have an enhanced catalytic activity and selectivity to ammonia rather the Mo (Ⅵ) sites. Similarly, the experimental results show that the MoO2-C NBF exhibits a superior NH3 yield (109.28 µmol h−1 cm−2) and Faraday Efficiency (99.05 %). This work sheds light on the structure–activity relationship between valence state with NRA activity and paves the way for design and mechanism study of the Mo-based NRA electrocatalyst for the further development of sustainable NH3 synthesis.

Na2Mn(CO3)2: A carbonate based prototype cathode material for Na-ion batteries with high rate capability — An ab-initio study

Considering the mounting demand for energy storage systems and the issues associated with the current cathode materials, it is necessary that the search space for novel cathode materials for rechargeable batteries should be widened. In this regard, we have presented the structural, lattice dynamical, electrochemical, and electronic structure studies of a carbonate-based prototype cathode material for Na-ion batteries, using first-principles calculations. The existence of a carbon-containing Mn compound Na2Mn(CO3)2 is predicted using first-principles calculations and the compound is expected to crystallize in trigonal crystal structure with R3̄ space group. The electrochemical analyses reveal that this cathode material could deliver a theoretical capacity of 243mAh/g and a theoretical average voltage of 3.6 V. The desodiation process is modeled via finding the stable crystal structure of intermediate compositions for different Na/vacancy concentrations. The electronic structure and charge density analysis of these intermediate compositions reveal that Mn, O, and a small contribution from C involve in the desodiation process. Even though the involvement of O in the redox is high, we have found that the oxygen evolution during desodiation is not favored thermodynamically, indicating a possible enhancement in the specific capacity. The chemical bonding analyses indicate that the Mn-O bonding interaction is iono-covalent, whereas the C-O bond exhibits a more covalent character with small ionicity. The activation energy of the diffusion barrier for the Na diffusion through the lower energy path in Na2Mn(CO3)2 is estimated to be 0.22 eV using nudged elastic band method. We postulate high ionic conductivity and thereby high rate capability for Na2Mn(CO3)2 as the Na diffusion coefficient is relatively higher compared with that of Li in cathodes used for commercial Li-ion batteries.

A Tour of Soft Atomic Motions: Chemical Pressure Quadrupoles Across Transition Metal–Main Group 1:2 Structure Types

The rational design of materials requires an understanding of the relationships between structure and properties. In some fields, advances in computational tools and modeling have mapped out many of these connections. In the realm of intermetallics, however, principles for such relationships are still needed. Recently, we illustrated how the DFT–Chemical Pressure (CP) analysis can link geometrical motifs within crystalline arrangements to the phonon band structures of intermetallics and thus the physical properties related to vibrations and atomic motion. The key indicators here are quadrupolar CP features─distributions in which positive and negative interatomic pressures are oriented perpendicular to one another. These quadrupoles then create low energy paths of motion for the atoms that can be linked to various structural phenomena, such as anisotropic vibrations and incommensurate modulations. In this article, we survey the presence of CP quadrupoles in a collection of TE2 structures (T = transition metal and E = main group element) and the roles they play in the behavior observed for these compounds. We begin by developing a metric for CP quadrupolar character, which can be calculated from the output of CP analysis. After compiling these metrics for 17 TE2 structure types, we delve deeper into four systems detected as exhibiting atomic sites with quadrupolar character: (1) the Co–Sn binary system, where the quadrupoles on the Co atoms in CuAl2-type CoSn2 direct the features of its superstructure in CoSn3; (2) arsenopyrite-type CoSb2, in which the highly quadrupolar CP distributions on the Sb atoms correlate with the motions followed during the phase transition to its high-temperature marcasite-type form; (3) the CrSi2 structure, in which the expansion of the lattice is predicted to open a helical path of potential soft motion analogous to that underlying the Nowotny Chimney Ladder series; and (4) the CdAs2 type, whose CP features anticipate the ability to incorporate Li atoms as guests. Together, these case studies highlight the potential for CP quadrupoles to link local atomic arrangements with a variety of emergent properties in intermetallic phases.

Evolution of the conceptualization of hydrogen through knowledge maps, energy return on investment (EROI) and national policy strategies

In order to address Climate Change and energy dependency challenges, hydrogen (H2) is emerging as a promising energy carrier. Studies related to its production have conceptualized it as green (GH2), clean, renewable (RH2), ecological, and sustainable (SH2). The aim of this research is to deepen the understanding of the GH2 concept and to state boundaries between different terms. To reach this objective, a bibliometric analysis of publications indexed in SCOPUS is launched. Also, in order to assess the potential of renewable energy sources (RES) for GH2 production, a review of the meta-analysis literature on the Energy Return on Energy Invested (EROI) ratio as regards these RES is performed. Additionally, an analysis of main national strategies on GH2 is launched. Results indicate that the GH2 concept is gaining remarkable relevance, while the keyword maps show no significant differences between SH2, RH2 and GH2. EROI reveals low average values for the different biomass energy production processes. For their part, GH2 national strategies focus mainly on solar and wind technologies, albeit leaving the door open to biomass, where EROI could become an adequate metric to guide these strategies towards a low carbon energy path. Although the role of biomass may become fundamental in this energy transition process, given its low EROI values and considering that it is not a totally clean RES, it should be indexed as RH2, but not always as GH2. Finally, a proposal that guides a more appropriate use of the term GH2 is made.Graphical abstract

Dipole Switching by Intramolecular Electron Transfer in Single-Molecule Magnetic Complex [Mn12O12(O2CR)16(H2O)4

We study intramolecular electron transfer in the single-molecule magnetic complex [Mn12O12(O2CR)16 (H2O)4] for R = -H, -CH3, -CHCl2, -C6H5, and -C6H4F ligands as a mechanism for switching of the molecular dipole moment. Energetics is obtained using the density functional theory (DFT) with onsite Coulomb energy correction (DFT + U). Lattice distortions are found to be critical for localizing an extra electron on one of the easy sites on the outer ring in which localized states can be stabilized. We find that the lowest-energy path for charge transfer is for the electron to go through the center via superexchange-mediated tunneling. The energy barrier for such a path ranges from 0.4 to 54 meV depending on the ligands and the isomeric form of the complex. The electric field strength needed to move the charge from one end to the other, thus reversing the dipole moment, is 0.01-0.04 V/Å.

(Invited) Mechanism of Interlayer Transport on a Growing Metal Surface: 2D vs. 3D Growth

The atomic scale transitions corresponding to diffusion and interlayer transport of metal adatoms on the low energy, close packed surfaces of several transition metals are studied using density functional theory calculations within the generalized gradient approximation. Minimum energy paths and estimates of activation energy are calculated for processes that influence whether the crystal grows layer-by-layer, i.e. 2D growth, or whether new islands nucleate on top of existing islands resulting in 3D growth. In some cases, the path of lowest activation energy for the descent of an adatom, i.e. interlayer transport, turns out to take place near, but not at, a kink site on a step. The energy barrier for the adatom to subsequently round the corner and enter the kink site is significantly higher. This near-kink-descent mechanism promotes the formation of a new row of step atoms and leads to the introduction of additional kink sites, thereby opening up new low activation energy paths for descent and promoting 2D growth. The sites adjacent and above the step edge can provide large binding energy for the adatom, and form a trough along which the adatom can migrate before descending, thereby increasing the probability that an adatom finds a kink site. These features of the energy landscape for an adatom point to the possibility of re-entrant layer-by-layer growth mode and have, for example, been found for Pt(111) and Au(111) surfaces.

Electrochemically induced amorphous-to-rock-salt phase transformation in niobium oxide electrode for Li-ion batteries.

Intercalation-type metal oxides are promising negative electrode materials for safe rechargeable lithium-ion batteries due to the reduced risk of Li plating at low voltages. Nevertheless, their lower energy and power density along with cycling instability remain bottlenecks for their implementation, especially for fast-charging applications. Here, we report a nanostructured rock-salt Nb2O5 electrode formed through an amorphous-to-crystalline transformation during repeated electrochemical cycling with Li+. This electrode can reversibly cycle three lithiums per Nb2O5, corresponding to a capacity of 269 mAh g-1 at 20 mA g-1, and retains a capacity of 191 mAh g-1 at a high rate of 1 A g-1. It exhibits superb cycling stability with a capacity of 225 mAh g-1 at 200 mA g-1 for 400 cycles, and a Coulombic efficiency of 99.93%. We attribute the enhanced performance to the cubic rock-salt framework, which promotes low-energy migration paths. Our work suggests that inducing crystallization of amorphous nanomaterials through electrochemical cycling is a promising avenue for creating unconventional high-performance metal oxide electrode materials.

Mechanism of Interlayer Transport on a Growing Au(111) Surface: 2D vs. 3D Growth

The atomic scale transitions corresponding to diffusion and interlayer transport of a Au adatom on the low energy, close packed Au(111) surface are studied using density functional theory calculations within the generalized gradient approximation. Minimum energy paths and estimates of activation energy are calculated for processes that influence whether the crystal grows layer-by-layer, i.e. 2D growth, or whether new islands tend to nucleate on top of existing islands resulting in 3D growth. Kinks on island edges turn out to provide paths for adatom descent with lower activation energy than straight steps. The energy barrier for an adatom to round the corner and enter a kink site is significantly higher. A descent mechanism that places an adatom near but not at a kink site can therefore promote the formation of a new row of step atoms and lead to the introduction of additional kink sites, thereby opening up new low activation energy paths for descent and promotion of 2D growth. The sites adjacent and above the step edge provide large binding energy for the adatom, especially at the B-type step, and form a trough along which the adatom can migrate before descending, thereby increasing the probability that an adatom finds a kink on the B-type step. These features of the energy landscape representing the interaction of a Au adatom with the surface point to the possibility of a re-entrant layer-by-layer growth mode of the low energy, close packed surface of the gold crystal.