arXiv subjects

David J. Wales

Publications and source records attributed to David J. Wales.

At least 19 recordsLinked to original sources

arXiv2025

Orbital Hybridization-Driven Stabilization and Reactivity on an Asymmetrically Reconstructed Polar CeO2(100) Surface

Understanding and controlling the atomic structure of polar oxide surfaces is essential for unraveling surface reactivilty and designing advanced catalytic materials. Among these, the polar CeO2(100) surface is a prototypical and industrially important system in heterogeneous catalysis. However, due to the vast complexity of the surface configurations, its reconstruction behavior remains an open question. Here, we report a previously unidentified asymmetric (1x2) reconstructed structure on the CeO2(100) surface, discovered through an integrated approach that combines global structure search algorithms, machine learning-based atomic potential models, density functional theory (DFT) calculations, and in situ scanning transmission electron microscopy (STEM). The reconstructed surface is both thermodynamically and kinetically stable, characterized by an alternating arrangement of Ce3+ and Ce4+ ions, increased interlayer spacing, and reconfigured surface oxygen atoms. Importantly, the formation of localized Ce3+ polarons introduces occupied 4f states that strongly hybridize with surface O 2p orbitals, resulting in new occupied electronic states below the Fermi level. This orbital hybridization activates the O 2p states, enhances their electron-donating capacity, and facilitates the dissociation of adsorbed molecules such as H2O. These findings reveal a fundamental orbital-mediated mechanism by which surface reconstruction governs electronic structure and reactivity, offering critical insights and a new design strategy for tuning catalytic performance on polar oxide surfaces.

cond-mat.mtrl-sci↗

arXiv2025

A note on the minimal pairwise distance in optimal Lennard-Jones $N$-body clusters

Good a-priori bounds on the smallest pairwise distance $r_{\rm{min}}(\mbox{LJ}_N^{\rm{gmin}})$ for a three-dimensional (3D) Lennard-Jones $N$-body cluster of globally minimal energy can significantly reduce the computational search space in the NP-hard problem to find this configuration. In this contribution the virial theorem is exploited for this purpose. We prove that if a configuration ${C}^{(N)}$ is a member of $\mbox{LJ}_N^{\rm{equ}}$ (the stationary points), then $r_{\rm{min}}({C}^{(N)}) \leq r_{\rm{min}}(\mbox{LJ}_2^{\rm{gmin}})$. It is also shown that if ${C}^{(N)}\in$ LJ$_N^{\rm{gmin}}\subset$ LJ$_N^{\rm{equ}}$, equality holds if and only if $N\in\{2,3,4\}$. We conjecture that $r_{\rm{min}}(\mbox{LJ}_N^{\rm{gmin}}) >1$ in units for which $r_{\rm{min}}(\mbox{LJ}_2^{\rm{gmin}})= 2^\frac16 \approx 1.122462048$. This conjectured lower bound, if correct, would improve the best lower bound currently known, $r_{\rm{min}}(\mbox{LJ}_N^{\rm{gmin}})\geq 0.767764$, by about 25$\%$. In these units the smallest minimal pair distance found through numerical searches for LJ$_N^{\rm{gmin}}$ with $N\leq 1000$ is $r_{\rm{min}}(\mbox{LJ}_{923}^{\rm{gmin}}) \approx 1.01361$, so the conjectured lower bound would presumably be close to optimal. From the virial theorem we obtain an identity for any ${C}^{(N)}\in \mbox{LJ}_N^{\rm{equ}}$, which expresses $r_{\rm{min}}({C}^{(N)})$ in terms of the distribution of relative distances in ${C}^{(N)}$. This result reveals interesting connections with the Erdős distance, and related problems.

physics.atm-clus↗

arXiv2025

Encoding molecular structures in quantum machine learning

Quantum machine learning (QML) has great potential for the analysis of chemical datasets. However, conventional quantum data-encoding schemes, such as fingerprint encoding, are generally unfeasible for the accurate representation of chemical moieties in such datasets. In this contribution, we introduce the quantum molecular structure encoding (QMSE) scheme, which encodes the molecular bond orders and interatomic couplings expressed as a hybrid Coulomb-adjacency matrix, directly as one- and two-qubit rotations within parameterised circuits. We show that this strategy provides an efficient and interpretable method in improving state separability between encoded molecules compared to other fingerprint encoding methods, which is especially crucial for the success in preparing feature maps in QML workflows. To benchmark our method, we train a parameterised ansatz on molecular datasets to perform classification of state phases and regression on boiling points, demonstrating the competitive trainability and generalisation capabilities of QMSE. We further prove a fidelity-preserving chain-contraction theorem that reuses common substructures to cut qubit counts, with an application to long-chain fatty acids. We expect this scalable and interpretable encoding framework to greatly pave the way for practical QML applications of molecular datasets.

quant-ph↗

arXiv2025

Global properties of the energy landscape: a testing and training arena for machine learned potentials

Machine learning interatomic potentials (MLIPs) have achieved remarkable accuracy on standard benchmarks, yet their ability to reproduce molecular kinetics -- critical for reaction rate calculations -- remains largely unexplored. We introduce Landscape17, a dataset of complete kinetic transition networks (KTNs) for the molecules of the MD17 dataset, computed using hybrid-level density functional theory. Each KTN contains minima, transition states, and approximate steepest-descent paths, along with energies, forces, and Hessian eigenspectra at stationary points. We develop a comprehensive test suite to evaluate the MLIP ability to reproduce these reference landscapes and apply it to a number of state-of-the-art architectures. Our results reveal limitations in current MLIPs: all the models considered miss over half of the DFT transition states and generate stable unphysical structures throughout the potential energy surface. Data augmentation with pathway configurations improves reproduction of DFT potential energy surfaces, resulting in significant improvement in the global kinetics. However, these models still produce many spurious stable structures, indicating that current MLIP architectures face underlying challenges in capturing the topology of molecular potential energy surfaces. The Landscape17 benchmark provides a straightforward but demanding test of MLIPs for kinetic applications, requiring only up to a few hours of compute time. We propose this test for validation of next-generation MLIPs targeting reaction discovery and rate prediction.

physics.chem-ph↗

arXiv2024

Efficient Composite Infrared Spectroscopy: Combining the Doubly-Harmonic Approximation with Machine Learning Potentials

Vibrational spectroscopy is a cornerstone technique for molecular characterization and offers an ideal target for the computational investigation of molecular materials. Building on previous comprehensive assessments of efficient methods for infrared (IR) spectroscopy, this study investigates the predictive accuracy and computational efficiency of gas-phase IR spectra calculations, accessible through a combination of modern semiempirical quantum mechanical and transferable machine learning potentials. A composite approach for IR spectra prediction based on the doubly-harmonic approximation, utilizing harmonic vibrational frequencies in combination squared derivatives of the molecular dipole moment, is employed. This approach allows for methodical flexibility in the calculation of IR intensities from molecular dipoles and the corresponding vibrational modes. Various methods are systematically tested to suggest a suitable protocol with an emphasis on computational efficiency. Among these methods, semiempirical extended tight-binding (xTB) models, classical charge equilibrium models, and machine learning potentials trained for dipole moment prediction are assessed across a diverse dataset of organic molecules. We particularly focus on the recently reported machine learning potential MACE-OFF23 to address the accuracy limitations of conventional low-cost quantum mechanical and force-field methods. This study aims to establish a standard for the efficient computational prediction of IR spectra, facilitating the rapid and reliable identification of unknown compounds and advancing automated analytical workflows in chemistry.

physics.chem-ph↗

arXiv2024

Going for Gold(-Standard): Attaining Coupled Cluster Accuracy in Oxide-Supported Nanoclusters

The structure of oxide-supported metal nanoclusters plays an essential role in their sharply enhanced catalytic activity over bulk metals. Simulations provide the atomic-scale resolution needed to understand these systems. However, the sensitive mix of metal-metal and metal-support interactions which govern their structure puts stringent requirements on the method used, requiring going beyond standard density functional theory (DFT). The method of choice is coupled cluster theory [specifically CCSD(T)], but its computational cost has so far prevented applications. In this work, we showcase two approaches to make CCSD(T) accuracy readily achievable in oxide-supported nanoclusters. First, we leverage the SKZCAM protocol to provide the first benchmarks of oxide-supported nanoclusters, revealing that it is specifically metal-metal interactions that are challenging to capture with DFT. Second, we propose a CCSD(T) correction ($Δ$CC) to the metal-metal interaction errors in DFT, reaching comparable accuracy to the SKZCAM protocol at significantly lower cost. This forges a path towards studying larger systems at reliable accuracy, which we highlight by identifying a ground state structure in agreement with experiments for Au$_{20}$ on MgO; a challenging system where DFT models have yielded conflicting predictions.

cond-mat.mtrl-sci↗

arXiv2024

Energy Landscapes for the Quantum Approximate Optimisation Algorithm

Variational quantum algorithms (VQAs) have demonstrated considerable potential in solving NP-hard combinatorial problems in the contemporary near intermediate-scale quantum (NISQ) era. The quantum approximate optimisation algorithm (QAOA) is one such algorithm, used in solving the maximum cut (Max-Cut) problem for a given graph by successive implementation of $L$ quantum circuit layers within a corresponding Trotterised ansatz. The challenge of exploring the cost function of VQAs arising from an exponential proliferation of local minima with increasing circuit depth has been well-documented. However, fewer studies have investigated the impact of circuit depth on QAOA performance in finding the correct Max-Cut solution. Here, we employ basin-hopping global optimisation methods to navigate the energy landscapes for QAOA ansätze for various graphs, and analyse QAOA performance in finding the correct Max-Cut solution. The structure of the solution space is also investigated using discrete path sampling to build databases of local minima and the transition states that connect them, providing insightful visualisations using disconnectivity graphs. We find that the corresponding landscapes generally have a single funnel organisation, which makes it relatively straightforward to locate low-lying minima with good Max-Cut solution probabilities. In some cases below the adiabatic limit the second lowest local minimum may even yield a higher solution probability than the global minimum. This important observation has motivated us to develop broader metrics in evaluating QAOA performance, based on collections of minima obtained from basin-hopping global optimisation. Hence we establish expectation thresholds in elucidating useful solution probabilities from local minima, an approach that may provide significant gains in elucidating reasonable solution probabilities from local minima.

quant-ph↗

arXiv2023

On the global minimum of the classical potential energy for clusters bound by many-body forces

This note establishes, first of all, the monotonic increase with $N$ of the average $K$-body energy of classical $N$-body ground state configurations with $N\geq K$ monomers that interact solely through a permutation-symmetric $K$-body potential, for any fixed integer $K\geq 2$. For the special case $K=2$ this result had previously been proved, and used successfully as a test criterion for optimality of computer-generated lists of putative ground states of $N$-body clusters for various types of pairwise interactions. Second, related monotonicity results are established for $N$-monomer ground state configurations whose monomers interact through additive mixtures of certain types of $k$-meric potentials, $k\in\{1,...,K\}$, with $K\geq 2$ fixed and $N\geq K$. All the monotonicity results furnish simple necessary conditions for optimality that any pertinent list of computer-generated putative global minimum energies for $N$-monomer clusters has to satisfy. As an application, databases of $N$-body cluster energies computed with an additive mix of the dimeric Lennard-Jones and trimeric Axilrod--Teller interactions are inspected. We also address how many local minima satisfy the upper bound inferred from the monotonicity conditions, both from a theoretical and from an empirical perspective.

physics.atm-clus↗

arXiv2023

On the mechanism of polaritonic rate suppression from quantum transition paths

Polariton chemistry holds promise for facilitating mode-selective chemical reactions, but the underlying mechanism behind the rate modifications observed under vibrational strong coupling is not well understood. Using the recently developed quantum transition path theory, we have uncovered a mechanism of resonant suppression of a thermal reaction rate in a simple model polaritonic system, consisting of a reactive mode in a bath confined to a lossless microcavity with a single photon mode. This mechanism was uncovered by resolving the quantum dynamical reactive pathways and identifying their rate limiting transitions. Upon inspecting the wavefunctions associated with the rate limiting transition, we observed the formation of a polariton and identified the concomitant rate suppression as due to hybridization between the reactive mode and the cavity mode, which inhibits bath-mediated tunneling during the reaction. The transition probabilities that define the quantum master equation can be directly translated into a visualisation of the corresponding polariton energy landscape. This landscape exhibits a double funnel structure, with a large barrier between the initial and final states. This mechanism of resonant rate suppression is found to be robust to model parameters and computational details, and thus expected to be general.

physics.chem-ph↗

arXiv2023

Evolution of $K$-means solution landscapes with the addition of dataset outliers and a robust clustering comparison measure for their analysis

The $K$-means algorithm remains one of the most widely-used clustering methods due to its simplicity and general utility. The performance of $K$-means depends upon location of minima low in cost function, amongst a potentially vast number of solutions. Here, we use the energy landscape approach to map the change in $K$-means solution space as a result of increasing dataset outliers and show that the cost function surface becomes more funnelled. Kinetic analysis reveals that in all cases the overall funnel is composed of shallow locally-funnelled regions, each of which are separated by areas that do not support any clustering solutions. These shallow regions correspond to different types of clustering solution and their increasing number with outliers leads to longer pathways within the funnel and a reduced correlation between accuracy and cost function. Finally, we propose that the rates obtained from kinetic analysis provide a novel measure of clustering similarity that incorporates information about the paths between them. This measure is robust to outliers and we illustrate the application to datasets containing multiple outliers.

cs.LG↗

arXiv2023

Physics Inspired Approaches To Understanding Gaussian Processes

Prior beliefs about the latent function to shape inductive biases can be incorporated into a Gaussian Process (GP) via the kernel. However, beyond kernel choices, the decision-making process of GP models remains poorly understood. In this work, we contribute an analysis of the loss landscape for GP models using methods from physics. We demonstrate $ν$-continuity for Matern kernels and outline aspects of catastrophe theory at critical points in the loss landscape. By directly including $ν$ in the hyperparameter optimisation for Matern kernels, we find that typical values of $ν$ are far from optimal in terms of performance, yet prevail in the literature due to the increased computational speed. We also provide an a priori method for evaluating the effect of GP ensembles and discuss various voting approaches based on physical properties of the loss landscape. The utility of these approaches is demonstrated for various synthetic and real datasets. Our findings provide an enhanced understanding of the decision-making process behind GPs and offer practical guidance for improving their performance and interpretability in a range of applications.

cs.LG↗

arXiv2023

Archetypal solution spaces for clustering gene expression datasets in identification of cancer subtypes

Gene expression profiles are essential in identifying different cancer phenotypes. Clustering gene expression datasets can provide accurate identification of cancerous cell lines, but this task is challenging due to the small sample size and high dimensionality. Using the $K$-means clustering algorithm we determine the organisation of the solution space for a variety of gene expression datasets using energy landscape theory. The solution space landscapes allow us to understand $K$-means performance, and guide more effective use when varying common dataset properties; number of features, number of clusters, and cluster distribution. We find that the landscapes have a single-funnelled structure for the appropriate number of clusters, which is lost when the number of clusters deviates from this. We quantify this landscape structure using a frustration metric and show that it may provide a novel diagnostic tool for the appropriate number of cancer subtypes.

physics.bio-ph↗

arXiv2022

Exact electronic states with shallow quantum circuits through global optimisation

Quantum computers promise to revolutionise electronic simulations by overcoming the exponential scaling of many-electron problems. While electronic wave functions can be represented using a product of fermionic unitary operators, shallow quantum circuits for exact states have not yet been achieved. We construct universal wave functions from gate-efficient, symmetry-preserving fermionic operators by introducing an algorithm that globally optimises the wave function in the discrete ansatz design and the continuous parameter spaces. Our approach maximises the accuracy that can be obtained with near-term quantum circuits. Highly accurate numerical simulations on strongly correlated molecules, including water and molecular nitrogen, and the condensed-matter Hubbard model, demonstrate that our algorithm reliably advances the state-of-the-art, defining a new paradigm for quantum simulations featuring strong electron correlation.

quant-ph↗

arXiv2022

Nested sampling for physical scientists

We review Skilling's nested sampling (NS) algorithm for Bayesian inference and more broadly multi-dimensional integration. After recapitulating the principles of NS, we survey developments in implementing efficient NS algorithms in practice in high-dimensions, including methods for sampling from the so-called constrained prior. We outline the ways in which NS may be applied and describe the application of NS in three scientific fields in which the algorithm has proved to be useful: cosmology, gravitational-wave astronomy, and materials science. We close by making recommendations for best practice when using NS and by summarizing potential limitations and optimizations of NS.

stat.CO↗

arXiv2021

Stochastic paths controlling speed and dissipation

Near equilibrium, thermodynamic intuition suggests that fast, irreversible processes will dissipate more energy and entropy than slow, quasistatic processes connecting the same initial and final states. Here, we test the hypothesis that this relationship between speed and dissipation holds for stochastic processes far from equilibrium. To analyze these processes on finite timescales, we derive an exact expression for the path probabilities of continuous-time Markov chains from the path summation solution of the master equation. Applying this formula to a model for nonequilibrium self-assembly, we show that more speed can lead to less dissipation when there are strong nonequilibrium currents. In the model, the relative energies of the initial and target states control the speed, and the nonequilibrium currents of a cycle situated between these states control the path-level dissipation. This model serves as a minimal prototype for designing kinetics to sculpt the nonequilibrium path space, so that faster structure-forming paths dissipate less.

cond-mat.stat-mech↗

arXiv2019

Energy landscapes and dynamics of xylo-nucleic acids

Artificial analogues of the natural nucleic acids have attracted recent interest as a diverse class of information storage molecules capable of self-replication. In the present study, we use the computational potential energy landscape framework to investigate the structural and dynamical properties of xylo- and deoxyxylo-nucleic acids (XyNA and dXyNA), which are derived from their respective RNA and DNA analogues by an inversion of configuration at a single chiral center in the sugar moiety of the nucleotide unit. The free energy landscapes of an octameric XyNA sequence and its dXyNA analogue demonstrate the existence of a facile conformational transition between a left-handed helix that is the global free energy minimum, and a closely competing ladder-type structure with approximately zero helicity. The separation of the competing conformational ensembles is better-defined for the dXyNA system, whereas the XyNA analogue is inherently more flexible. The former therefore appear more suitable candidates for a molecular switch. The landscapes differ qualitatively from those reported in previous studies for evolved biomolecules: they are significantly more frustrated, so that XyNAs provide an example of an unnatural system for which the conditions constituting the principle of minimal frustration are, as may be expected, violated.

physics.bio-ph↗

arXiv2018

Exotic Bilayer Crystals in a Strong Magnetic Field

Electron bilayers in a strong magnetic field exhibit insulating behavior for a wide range of interlayer separation $d$ for total Landau level fillings $ν\leq 1/2$, which has been interpreted in terms of a pinned crystal. We study theoretically the competition between many strongly correlated liquid and crystal states and obtain the phase diagram as a function of quantum well width and $d$ for several filling factors of interest. We predict that three crystal structures can be realized: (a) At small $d$, the Triangular Ising AntiFerromagnetic (TIAF) crystal is stabilized in which the particles overall form a single-layer like triangular crystal while satisfying the condition that no nearest-neighbor triangle has all three particles in the same layer. (b) At intermediate $d$, a Correlated Square (CS) crystal is stabilized, in which particles in each layer form a square lattice, with the particles in one layer located directly across the centers of the squares of the other. (c) At large $d$, we find a Bilayer Graphene (BG) crystal in which the A and B sites of the graphene lattice lie in different layers. All crystals that we predict are strongly correlated crystals of composite fermions; a theory incorporating only electron Hartree-Fock crystals does not find any crystals besides the `trivial' ones occurring at large interlayer separations for total filling factor $ν\leq1/3$ (when layers are uncorrelated and each layer is in the long familiar single-layer crystal phase). The TIAF, CS and BG crystals come in several varieties, with different flavors of composite fermions and different interlayer correlations. The appearance of these exotic crystal phases adds to the richness of the physics of electron bilayers in a strong magnetic field, and also provides insight into experimentally observed bilayer insulator as well as transitions within the insulating part of the phase diagram.

cond-mat.str-el↗

arXiv2018

The Loss Surface of XOR Artificial Neural Networks

Training an artificial neural network involves an optimization process over the landscape defined by the cost (loss) as a function of the network parameters. We explore these landscapes using optimisation tools developed for potential energy landscapes in molecular science. The number of local minima and transition states (saddle points of index one), as well as the ratio of transition states to minima, grow rapidly with the number of nodes in the network. There is also a strong dependence on the regularisation parameter, with the landscape becoming more convex (fewer minima) as the regularisation term increases. We demonstrate that in our formulation, stationary points for networks with $N_h$ hidden nodes, including the minimal network required to fit the XOR data, are also stationary points for networks with $N_{h} +1$ hidden nodes when all the weights involving the additional nodes are zero. Hence, smaller networks optimized to train the XOR data are embedded in the landscapes of larger networks. Our results clarify certain aspects of the classification and sensitivity (to perturbations in the input data) of minima and saddle points for this system, and may provide insight into dropout and network compression.

stat.ML↗