Gaussian Potential Research Articles

Impact of hydrogenation on the stability and mechanical properties of amorphous boron nitride

Interconnect materials with ultralow dielectric constant, and good thermal and mechanical properties are crucial for the further miniaturization of electronic devices. Recently, it has been demonstrated that ultrathin amorphous boron nitride (aBN) films have a very low dielectric constant, high density (above 2.1 g cm−3), high thermal stability, and mechanical properties. The excellent properties of aBN derive from the nature and degree of disorder, which can be controlled at fabrication, allowing tuning of the physical properties for desired applications. Here, we report an improvement in the stability and mechanical properties of aBN upon hydrogen doping. With the introduction of a Gaussian approximation potential for atomistic simulations, we investigate the changing morphology of aBN with varying H doping concentrations. We found that for 8 at% of H doping, the concentration of sp 3-hybridized atoms reaches to a maximum which leads to an improvement of thermal stability and mechanical properties by 20%. These results will be a guideline for experimentalists and process engineers to tune the growth conditions of aBN films for numerous applications.

Hydrostatic pressure and temperature effects on nonlinear optical properties in harmonic-Gaussian asymmetric double quantum wells

The paper examines the linear and non-linear optical characteristics of an electron in harmonic Gaussian asymmetrical double quantum wells, taking into account thermodynamic variables such as temperature and hydrostatic pressure. Numerical calculations by considering the effective mass and parabolic band approximation are performed. The electron contained within an asymmetric double well generated by the sum of a parabolic and Gaussian potential has its eigenvalues and eigenfunctions determined using the diagonalization approach. For nonlinear optical coefficients, the density matrix expansion is used. Wavefunctions and energy levels vary as an effect of the applied fields. In harmonic Gaussian asymmetrical double quantum wells, the total optical absorption coefficient (TOAC), the relative refractive index changes (RRIC), and second harmonic generation (SHG) have all been theoretically investigated. The magnitude and position of the resonant peaks are significantly influenced by the hydrostatic pressure and temperature effects. With controllable coupling and externally applied hydrostatic pressure and temperature, the potential model presented in this study can be used to simulate and manipulate the optical and electronic properties of the asymmetric double-quantum heterostructures, such as double quantum dots and wells.

Gaussian entropy and decoherence of qubit in hydrogenic impurity-center semiconductor quantum dot by confined spherical Gaussian potential

Gaussian entropy and decoherence of qubit in hydrogenic impurity-center semiconductor quantum dot by confined spherical Gaussian potential

Feynman–Kac formula for parabolic Anderson model in Gaussian potential and fractional white noise

In this paper, we establish a Feynman–Kac formula for the stochastic parabolic Anderson model with Gaussian potential in space and fractional white noise in time with Hurst parameter H > 1/2. We obtain the necesscary and suffcient condition for the integrability of the Gaussian potential and the exponential integrability of the solution which is defined by Feynman–Kac formula. By the smoothing of the fractional white noise and techniques from Malliavin calculus, we prove that the Feynman–Kac representation is a mild solution of the stochastic parabolic Anderson equation.

Non-integrability and chaos for natural Hamiltonian systems with a random potential

Consider the ensemble of Gaussian random potentials {VL(q)}L=1∞ on the d-dimensional torus where, essentially, VL(q) is a real-valued trigonometric polynomial of degree L whose coefficients are independent standard normal variables. Our main result ensures that, with a probability tending to 1 as L→∞, the dynamical system associated with the natural Hamiltonian function defined by this random potential, HL:=12|p|2+VL(q), exhibits a number of chaotic regions which coexist with a positive-volume set of invariant tori. In particular, these systems are typically neither integrable with non-degenerate first integrals nor ergodic. An analogous result for random natural Hamiltonian systems defined on the cotangent bundle of an arbitrary compact Riemannian manifold is presented too.

External field-driven property localization in liquids of responsive macromolecules.

We explore theoretically the effects of external potentials on the spatial distribution of particle properties in a liquid of explicitly responsive macromolecules. In particular, we focus on the bistable particle size as a coarse-grained internal degree of freedom (DoF, or "property"), σ, that moves in a bimodal energy landscape, in order to model the response of a state-switching (big-to-small) macromolecular liquid to external stimuli. We employ a mean-field density functional theory (DFT) that provides the full inhomogeneous equilibrium distributions of a one-component model system of responsive colloids (RCs) interacting with a Gaussian pair potential. For systems confined between two parallel hard walls, we observe and rationalize a significant localization of the big particle state close to the walls, with pressures described by an exact RC wall theorem. Application of more complex external potentials, such as linear (gravitational), osmotic, and Hamaker potentials, promotes even stronger particle size segregation, in which macromolecules of different size are localized in different spatial regions. Importantly, we demonstrate how the degree of responsiveness of the particle size and its coupling to the external potential tune the position-dependent size distribution. The DFT predictions are corroborated by Brownian dynamics simulations. Our study highlights the fact that particle responsiveness can be used to localize liquid properties and therefore helps to control the property- and position-dependent function of macromolecules, e.g., in biomedical applications.

Thermal conductivity of GeTe crystals based on machine learning potentials

GeTe has attracted extensive research interest for thermoelectric applications. In this paper, we first train a neuro-evolution potential (NEP) based on a dataset constructed by ab initio molecular dynamics, with the Gaussian approximation potential (GAP) as a reference. The phonon density of states is then calculated by two machine learning potentials and compared with density functional theory results, with the GAP potential having higher accuracy. Next, the thermal conductivity of a GeTe crystal at 300 K is calculated by the equilibrium molecular dynamics method using both machine learning potentials, and both of them are in good agreement with the experimental results; however, the calculation speed when using the NEP potential is about 500 times faster than when using the GAP potential. Finally, the lattice thermal conductivity in the range of 300 K–600 K is calculated using the NEP potential. The lattice thermal conductivity decreases as the temperature increases due to the phonon anharmonic effect. This study provides a theoretical tool for the study of the thermal conductivity of GeTe.

Exploring the phase change and structure of carbon using a deep learning interatomic potential.

Small-scale systems based on periodic boundary conditions often cannot accurately describe real-world situations, especially when conducting molecular dynamics simulations to study phase transitions, where it is very necessary to use large-scale systems. However, studying phase transitions in large-scale systems is an important and difficult task. Though ab initio molecular dynamics (AIMD), based on density functional theory (DFT), provides advantages in terms of accuracy, it is very difficult to study phase transitions in large-scale systems due to the considerable computational time required. In addition, although traditional empirical potentials are faster, their lower calculation accuracy makes it difficult to use them for phase transition studies. It is crucial to devise a method that has enabled a promising fusion of computational efficiency and precision to effectively investigate phase transitions in large-scale systems. In this work, the obtained machine learning potential function of carbon through deep neural networks not only demonstrates strong scalability but also effectively enables the study of the formation mechanisms of amorphous diamond and polycrystalline diamond using C60 crystals and graphene as precursors under high-pressure high-temperature conditions (HPHT). Furthermore, the structure search software (AIRSS) was used to generate numerous initial structures which were optimized using the machine learning potential, a process which led to finding new structural clusters of carbon. Interestingly, the predictive capabilities of the machine learning potential for symmetric and asymmetric carbon clusters aligned well with the Gaussian approximation potential (GAP), yet the former demonstrated higher computational efficiency, making it more suitable for carbon material research. The results of this work signify significant progress in the field of carbon transition study, opening up new possibilities for exploring and understanding carbon materials with improved computational efficacy.

Interatomic force fields for zirconium based on the embedded atom method and the tabulated Gaussian Approximation Potential

The accuracy of interatomic interaction potentials – also known as force fields – is the main factor determining the physical soundness of classical molecular dynamics (MD) simulations. Here, we present a multi-objective framework to generate embedded-atom-method (EAM) force fields using ab initio data. The EAM force fields were tuned via particle swarm optimization to capture the non-linear association between atomic structures and system energies. Using this framework, 95 standard EAM force fields for zirconium were developed and 45 physical features for each developed force field were tracked. Principal component analysis (PCA) was performed to provide insights into the compromises that must be made when generating EAM force fields. Of note, by assigning large fitting weights to generalized stacking fault energy (GSFE) surfaces, there exist EAM force fields with properly positioned minima on prismatic GSFE surfaces and containing no spurious minima in basal GSFE surfaces. However, while standard EAM force fields achieved this without explicitly taking the angular dependence of atomic interactions into account, they led to a severe mismatch between other important physical properties and benchmarks. Hence, we also constructed two machine-learned tabulated Gaussian approximation potentials (tabGAP) with an additional three-body term, which successfully tackled the aforementioned issue and exhibit acceptable prediction accuracy across many physical properties (lattice parameters, elastic properties, dimer potential energies, melting temperatures, phase stability, point defect formation energies, point defect migration energies, and free surface energies) of Zr. Remarkably, its computational efficiency is only 6 times slower than standard EAM force fields.

Topological belief space planning for active SLAM with pairwise Gaussian potentials and performance guarantees

Determining a globally optimal solution of belief space planning (BSP) in high-dimensional state spaces directly is computationally expensive, as it involves belief propagation and objective function evaluation for each candidate action. However, many problems of interest, such as active SLAM, exhibit structure that can be harnessed to expedite planning. Also, in order to choose an optimal action, an exact value of the objective function is not required as long as the actions can be sorted in the same way. In this paper we leverage these two key aspects and present the topological belief space planning (t-bsp) concept that uses topological signatures to perform this ranking for information-theoretic cost functions, considering only topologies of factor graphs that correspond to future posterior beliefs. In particular, we propose a highly efficient topological signature based on the von Neumann graph entropy that is a function of graph node degrees and supports an incremental update. We analyze it in the context of active pose SLAM and derive error bounds between the proposed topological signature and the original information-theoretic cost function. These bounds are then used to provide performance guarantees for t-bsp with respect to a given solver of the original information-theoretic BSP problem. Realistic and synthetic simulations demonstrate drastic speed-up of the proposed method with respect to the state-of-the-art methods while retaining the ability to select a near-optimal solution. A proof of concept of t-bsp is given in a small-scale real-world active SLAM experiment.

Atomistic fracture in bcc iron revealed by active learning of Gaussian approximation potential

The prediction of atomistic fracture mechanisms in body-centred cubic (bcc) iron is essential for understanding its semi-brittle nature. Existing atomistic simulations of the crack-tip under mode-I loading based on empirical interatomic potentials yield contradicting predictions and artificial mechanisms. To enable fracture prediction with quantum accuracy, we develop a Gaussian approximation potential (GAP) using an active learning strategy by extending a density functional theory (DFT) database of ferromagnetic bcc iron. We apply the active learning algorithm and obtain a Fe GAP model with a converged model uncertainty over a broad range of stress intensity factors (SIFs) and for four crack systems. The learning efficiency of the approach is analysed, and the predicted critical SIFs are compared with Griffith and Rice theories. The simulations reveal that cleavage along the original crack plane is the atomistic fracture mechanism for {100} and {110} crack planes at T = 0 K, thus settling a long-standing issue. Our work also highlights the need for a multiscale approach to predicting fracture and intrinsic ductility, whereby finite temperature, finite loading rate effects and pre-existing defects (e.g., nanovoids, dislocations) should be taken explicitly into account.

Gaussian approximation potentials: Theory, software implementation and application examples.

Gaussian Approximation Potentials (GAPs) are a class of Machine Learned Interatomic Potentials routinely used to model materials and molecular systems on the atomic scale. The software implementation provides the means for both fitting models using abinitio data and using the resulting potentials in atomic simulations. Details of the GAP theory, algorithms and software are presented, together with detailed usage examples to help new and existing users. We review some recent developments to the GAP framework, including Message Passing Interface parallelisation of the fitting code enabling its use on thousands of central processing unit cores and compression of descriptors to eliminate the poor scaling with the number of different chemical elements.

Gaussian attractive potential for carboxylate/cobalt surface interactions.

Ligand-decorated metal surfaces play a pivotal role in various areas of chemistry, particularly in selective catalysis. Molecular dynamics simulations at the molecular mechanics level of theory are best adapted to gain complementary insights to experiments regarding the structure and dynamics of such organic films. However, standard force fields tend to capture only weak physisorption interactions. This is inadequate for ligands that are strongly adsorbed such as carboxylates on metal surfaces. To address this limitation, we employ the Gaussian Lennard-Jones (GLJ) potential, which incorporates an attractive Gaussian potential between the surface and ligand atoms. Here, we develop this approach for the interaction between cobalt surfaces and carboxylate ligands. The accuracy of the GLJ approach is validated through the analysis of the interaction of oxygen with two distinct cobalt surfaces. The accuracy of this method reaches a root mean square deviation (RMSD) of about 3 kcal/mol across all probed configurations, which corresponds to a percentage error of roughly 4%. Application of the GLJ force field to the dynamics of the organic layer on these surfaces reveals how the ligand concentration influences the film order, and highlights differing mobility in the x and y directions, attributable to surface corrugation on Co(112̄0). GLJ is versatile, suitable for a broad range of metal/ligand systems, and can, subsequently, be utilized to study the organic film on the adsorption/desorption of reactants and products during a catalytic process.

Global analysis of energy landscapes for materials modeling: A test case for C60.

In this contribution, we employ computational tools from the energy landscape approach to test Gaussian Approximation Potentials (GAPs) for C60. In particular, we apply basin-hopping global optimization and explore the landscape starting from the low-lying minima using discrete path sampling. We exploit existing databases of minima and transition states harvested from previous work using tight-binding potentials. We explore the energy landscape for the full range of structures and pathways spanning from the buckminsterfullerene global minimum up to buckybowls. In the initial GAP model, the fullerene part of the landscape is reproduced quite well. However, there are extensive families of C1@C59 and C2@C58 structures that lie lower in energy. We succeeded in refining the potential to remove these artifacts by simply including two minima from the C2@C58 families found by global landscape exploration. We suggest that the energy landscape approach could be used systematically to test and improve machine learning interatomic potentials.

Comparing interatomic potentials in calculating basic structural parameters and Peierls stress in tungsten-based random binary alloys

The field of machine learning-based interatomic potentials (ML-IAPs) has seen increasing development in recent years. In this work, we compare three widely used ML-IAPs–the moment tensor potential (MTP), the spectral neighbor analysis potential (SNAP), and the tabulated Gaussian approximation potential (tabGAP)with a conventional non-ML-IAP, the embedded atom method (EAM) potential. We evaluated these potentials on the basis of their accuracy and efficiency in determining basic structural parameters and Peierls stress under equivalent conditions. Three tungsten (W)-based alloys (Mo-W, Nb-W, and Ta-W) are considered, and their lattice parameter, formation energy, elastic tensor, and Peierls stress of edge dislocation are calculated. Compared with DFT results, MTP demonstrates the highest accuracy in predicting the lattice parameter and the best computational efficiency among the three ML-IAPs, while tabGAP accurately predicts two independent elastic constants, C 11 and C 12. Despite being the slowest, SNAP shows the highest accuracy in predicting the third independent elastic constant C 44 and its Peierls stress value is comparable to that based on MTP.

Estimation of the S34(0) S-factor for 3He(α, γ)7Be reaction by using distorted wave born approximation and artificial neural network

The astrophysical S-factor and total cross-section of radiative capture reaction are analyzed using the first-order distorted wave born approximation and artificial neural network. To make estimations of S34(0) at energies going to zero, we have used an artificial neural network model as a new approximation in this area. First, we obtain distorted wave born approximation results using the Gaussian and Woods-Saxon potentials. After, we evaluate artificial neural network approximation to analyze reaction observables of the system. Our results show that artificial neural network model is a powerful candidate as an extrapolation model for astrophysical energies for estimating of the S-factor observable.

Complex Ga2O3 polymorphs explored by accurate and general-purpose machine-learning interatomic potentials

Ga2O3 is a wide-band gap semiconductor of emergent importance for applications in electronics and optoelectronics. However, vital information of the properties of complex coexisting Ga2O3 polymorphs and low-symmetry disordered structures is missing. We develop two types of machine-learning Gaussian approximation potentials (ML-GAPs) for Ga2O3 with high accuracy for β/κ/α/δ/γ polymorphs and generality for disordered stoichiometric structures. We release two versions of interatomic potentials in parallel, namely soapGAP and tabGAP, for high accuracy and exceeding speedup, respectively. Both potentials can reproduce the structural properties of all the five polymorphs in an exceptional agreement with ab initio results, meanwhile boost the computational efficiency with 5 × 102 and 2 × 105 computing speed increases compared to density functional theory, respectively. Moreover, the Ga2O3 liquid-solid phase transition proceeds in three different stages. This experimentally unrevealed complex dynamics can be understood in terms of distinctly different mobilities of O and Ga sublattices in the interfacial layer.

Revisiting four-phonon scattering in WS2 monolayer with machine learning potential

Recently, the importance of the higher-order anharmonic effect on the thermal transport has been demonstrated in a few two-dimensional (2D) materials. As a member of 2D materials, the WS2 monolayer possesses excellent properties, but its higher-order phonon anharmonic effect is still unclear. As an emerging tool for atomistic simulations, the machine learning Gaussian approximation potential (GAP) has good computational speed and accuracy. In this work, the effect of the four-phonon scattering on the thermal transport properties of the WS2 monolayer is systematically investigated by combining a well-trained GAP with the Boltzmann transport equation. We find that the in-plane thermal conductivity of the WS2 monolayer decreases by 34.68% at 300 K compared to the results without considering the four-phonon scattering, which mainly originates from the strong low-frequency redistribution scattering process. The temperature-induced phonon renormalization in WS2 monolayer is investigated using the temperature-dependent effective potential method. The results show that phonon modes slightly soften with increasing temperature, and the temperature effect weakens the four-phonon scattering while hardly affect the three-phonon scattering. Our work reveals that previous studies considering only the three-phonon scattering and the temperature effect are insufficient, and the four-phonon interaction must be introduced to accurately describe the thermal transport properties of the WS2 monolayer.

Spectrum of a q$$ q $$‐deformed Schrödinger equation by means of the variational method

In this work, the ‐deformed Schrödinger equations defined in different form of the ‐Hamiltonian for ‐harmonic oscillator are considered with symmetric, asymmetric, and non‐polynomial potentials. The spectrum of the ‐Hamiltonian is obtained by using the Rayleigh‐Ritz variational method in which the discrete ‐Hermite I polynomials are taken as the basis. As applications, ‐harmonic, purely ‐quartic, and ‐quartic oscillators are examined in the class of symmetric polynomial potentials. Moreover, the ‐version of Gaussian potential for an example of a non‐polynomial symmetric potential and a specific example of ‐version of asymmetric double well potential are presented. Numerous results are given for these potentials for several values of . The limit relation as is discussed. The obtained results of ground‐ and excited‐state energies of the purely ‐quartic oscillator and the accuracy of the ground‐state energy levels are compared with the existing results. Also, the results are compared with the classical case appearing in the literature in the limiting case .

An Efficient Reactive Force Field without Explicit Coordination Dependence for Studying Caustic Aluminum Chemistry.

Reactive force fields (RFFs) are an expedient approach to sample chemical reaction paths in complex systems, relative to density functional theory. However, there is continued need to improve efficiencies, specifically in systems that have slow transverse degrees of freedom, as in highly viscous and superconcentrated solutions. Here, we present an RFF that is differentiated from current models (e.g., ReaxFF) by omitting explicit dependence on the atom coordination and employing a small parameter set based on Lennard-Jones, Gaussian, and Stillinger-Weber potentials. The model was parametrized from AIMD simulation data and is used to model aluminate reactivity in sodium hydroxide solutions with extensive validation against experimental radial distribution functions, computed free energy profiles for oligomerization, and formation energies. The model enables simulation of early stage Al(OH)3 nucleation which has significant relevance to industrial processing of aluminum and has a computational cost that is reduced by 1 order of magnitude relative to ReaxFF.