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The application of machine learning methodologies for predicting properties within materials science has garnered significant attention. Among recent advancements, Kolmogorov-Arnold Networks (KANs) have emerged as a promising alternative to traditional Multi-Layer Perceptrons (MLPs). This study evaluates the impact of substituting MLPs with KANs within three established machine learning frameworks: Allegro, Neural Equivariant Interatomic Potentials (NequIP), and the Edge-Based Tensor Prediction Graph Neural Network (ETGNN). Our results demonstrate that the integration of KANs generally yields enhanced prediction accuracies. Specifically, replacing MLPs with KANs in the output blocks leads to notable improvements in accuracy and, in certain scenarios, also results in reduced training times. Furthermore, employing KANs exclusively in the output block facilitates faster inference and improved computational efficiency relative to utilizing KANs throughout the entire model. The selection of an optimal basis function for KANs is found to be contingent upon the particular problem at hand. Our results demonstrate the strong potential of KANs in enhancing machine learning potentials and material property predictions.

Akin to the traditional quasi-classical trajectory method for investigating the dynamics on a single adiabatic potential energy surface for an elementary chemical reaction, we carry out the dynamics on a 2-state ab initio potential energy surface including nonadiabatic coupling terms as friction terms for D+ + H2 collisions. It is shown that the resulting dynamics correctly accounts for nonreactive charge transfer, reactive non charge transfer and reactive charge transfer processes. In addition, it leads to the formation of triatomic DH2+ species as well., Comment: 31 pages, 7 figures

Recently, machine learning potentials (MLP) largely enhances the reliability of molecular dynamics, but its accuracy is limited by the underlying $\textit{ab initio}$ methods. A viable approach to overcome this limitation is to refine the potential by learning from experimental data, which now can be done efficiently using modern automatic differentiation technique. However, potential refinement is mostly performed using thermodynamic properties, leaving the most accessible and informative dynamical data (like spectroscopy) unexploited. In this work, through a comprehensive application of adjoint and gradient truncation methods, we show that both memory and gradient explosion issues can be circumvented in many situations, so the dynamical property differentiation is well-behaved. Consequently, both transport coefficients and spectroscopic data can be used to improve the density functional theory based MLP towards higher accuracy. Essentially, this work contributes to the solution of the inverse problem of spectroscopy by extracting microscopic interactions from vibrational spectroscopic data.

In this work we analyze the bifurcation of dividing surfaces that occurs as a result of two period-doubling bifurcations in a 2D caldera-type potential. We study the structure, the range, the minimum and maximum extents of the periodic orbit dividing surfaces before and after a subcritical period-doubling bifurcation of the family of the central minimum of the potential energy surface. Furthermore, we repeat the same study for the case of a supercritical perioddoubling bifurcation of the family of the central minimum of the potential energy surface. We will discuss and compare the results for the two cases of bifurcations of dividing surfaces., Comment: 15 pages. arXiv admin note: text overlap with arXiv:2107.09623

Temperature dependence of the thermal rate constants and kinetic isotope effects (KIE) of the CN + C2H6 gas-phase hydrogen abstraction reaction was theoretically determined within the 25-1000 K temperature range, i.e., from ultra-low to high-temperature regimes. Based on a recently developed full-dimensional analytical potential energy surface fitted to highly accurate explicitly correlated ab initio calculations, three different kinetic theories were used: canonical variational transition state theory (CVT), quasiclassical trajectory theory (QCT), and ring polymer molecular dynamics (RPMD) method for the computation of rate constants. We found that the thermal rate constants obtained with the three theories show a V-shaped temperature dependence, with a pronounced minimum near 200 K, qualitatively reproducing the experimental measurements. Among the three methods used in this work, the QCT and RPMD methods have the best agreement with the experiment at low and high temperatures, respectively. The significant increase in the rate constant at ultra-low temperatures in this very exothermic and practically barrierless reaction can be attributed to the large value of the impact parameter, ruling out the role of the tunneling effect and the intermediate complexes in the entrance channel. The theoretical H/D KIE depicted a normal behaviour, i.e., values greater than unity, emulating the experimental measurements and previous theoretical results. Finally, the discrepancies between theory and experiments were analysed as a function of several factors, such as limitations of the kinetics theories and the potential energy surface, as well as the uncertainties in the experimental measurements.

Structural optimization has been a crucial component in computational materials research, and structure predictions have relied heavily on this technique in particular. In this study, we introduce a novel method that enhances the efficiency of local optimization by integrating an extra fingerprint space into the optimization process. Our approach utilizes a mixed energy concept in the hyper potential energy surface (PES), combining real energy and a newly introduced fingerprint energy derived from the symmetry of local atomic environment. This method strategically guides the optimization process toward high-symmetry, low-energy structures by leveraging the intrinsic symmetry of atomic configurations. The effectiveness of our approach was demonstrated through structural optimizations of silicon, silicon carbide, and Lennard-Jones cluster systems. Our results show that the fingerprint space biasing technique significantly enhances the performance and probability of discovering energetically favorable, high-symmetry structures, as compared to conventional optimizations. The proposed method is anticipated to streamline the search for new materials and facilitate the discovery of novel, energetically favorable configurations., Comment: 16 pages, 4 figures

Machine learned chemical potentials have shown great promise as alternatives to conventional computational chemistry methods to represent the potential energy of a given atomic or molecular system as a function of its geometry. However, such potentials are only as good as the data they are trained on, and building a comprehensive training set can be a costly process. Therefore, it is important to extract as much information from training data as possible without further increasing the computational cost. One way to accomplish this is by training on molecular forces in addition to energies. This allows for three additional labels per atom within the molecule. Here we develop a neural network potential energy surface for studying a hydrogen transfer reaction between two conformers of C5H5. We show that, for a much smaller training set, force training can greatly improve the accuracy of the model compared to only training to energies. We also demonstrate the importance of choosing the proper force to energy weight ratio for the loss function to minimize the model test error.

The remote sensing of abundance and properties of HCl -- the main atmospheric reservoir of Cl atoms which directly participate in ozone depletion -- are important for monitoring the partitioning of chlorine between "ozone-depleting" and "reservoir" species. Such remote studies require knowledge of the shapes of molecular resonances of HCl, which are perturbed by collisions with the molecules of the surrounding air. In this work, we report the first fully quantum calculations of collisional perturbations of the shape of a pure rotational line in H$^{35}$Cl perturbed by an air-relevant molecule (as the first model system we choose the R(0) line in HCl perturbed by O$_2$). The calculations are performed on our new highly-accurate HCl($X^1\Sigma^+$)-O$_2$($X^3\Sigma^-_g$) potential energy surface. In addition to pressure broadening and shift, we determine also their speed dependencies and the complex Dicke parameter. This gives important input to the community discussion on the physical meaning of the complex Dicke parameter and its relevance for atmospheric spectra (previously, the complex Dicke parameter for such systems was mainly determined from phenomenological fits to experimental spectra and the physical meaning of its value in that context is questionable). We also calculate the temperature dependence of the line-shape parameters and obtain agreement with the available experimental data. We estimate the total combined uncertainties of our calculations at 2% relative RMSE residuals in the simulated line shape at 296~K. This result constitutes an important step towards computational population of spectroscopic databases with accurate ab initio line-shape parameters for molecular systems of terrestrial atmospheric importance., Comment: 15 pages, 7 figures, The following article has been accepted by The Journal of Chemical Physics. After it is published, it will be found at https://pubs.aip.org/aip/jcp

How does an electrochemical interface respond to changes in the electrode potential? How does the response affect the key properties of the system - energetics, excess charge, capacitance? Essential questions key to ab-initio simulations of electrochemical systems, which we address in this work on the basis of a rigorous mathematical evaluation of the interfacial energetics at constant applied potential. By explicitly taking into account the configurational and electronic degrees of freedom we derive important statements about stationary points in the electronically grand canonical ensemble. We analyze their geometric response to changes in electrode potential and show that it can be mapped identically onto an additional contribution to the system's capacitance. We draw similar conclusions for the constant charge ensemble which equally allows to assess the respective stationary points. Our analysis of the relation between the canonical and grand canonical energetics reveals, however, one key difference between both ensembles. While the constant potential ensemble yields in general positive capacitances at local minima, the capacitance of local minima in the constant charge ensemble might become negative. We trace back this feature to the possibility of character switching of stationary points when switching between the ensembles causing the differences in the response to perturbations. Our systematical analysis not only provides a detailed qualitative and quantitative understanding of the interplay between electronic and configurational degrees of freedom and their contributions to the energetics of electrified interfaces but also highlights the similarities and subtle dissimilarities between the canonical and grand canonical description of the electronic degrees of freedom, which is crucial for a better understanding of theoretical calculations with and without potentiostat., Comment: 33 pages, 0 figures, 2 tables

We train an equivariant machine learning model to predict energies and forces for a real-world study of hydrogen combustion under conditions of finite temperature and pressure. This challenging case for reactive chemistry illustrates that ML learned potential energy surfaces (PESs) are always incomplete as they are overly reliant on chemical intuition of what data is important for training, i.e. stable or metastable energy states. Instead we show here that a negative design data acquisition strategy is necessary to create a more complete ML model of the PES, since it must also learn avoidance of unforeseen high energy intermediates or even unphysical energy configurations. Because this type of data is unintuitive to create, we introduce an active learning workflow based on metadynamics that samples a lower dimensional manifold within collective variables that efficiently creates highly variable energy configurations for further ML training. This strategy more rapidly completes the ML PES such that deviations among query by committee ML models helps to now signal occasional calls to the external ab initio data source to further molecular dynamics in time without need for retraining the ML model. With the hybrid ML-physics model we predict the change in transition state and/or reaction mechanism at finite temperature and pressure for hydrogen combustion, thereby delivering on the promise of real application work using ML trained models of an ab initio PES with two orders of magnitude reduction in cost.

Two actinide isotopes, $^{241}$Am and $^{244}$Cm, produced and chemically purified by the HFIR/REDC complex at ORNL are candidates for target materials of heavy-ion fusion reaction experiments for the synthesis of new superheavy elements (SHEs) with $Z>118$. In the framework of the dinuclear system model with a dynamical potential energy surface (DNS-DyPES model), we systematically study the $^{48}$Ca-induced reactions that have been applied to synthesize SHEs with $Z=112$--118, as well as the hot-fusion reactions with $^{241}$Am and $^{244}$Cm as targets which are promising for synthesizing new SHEs with $Z=119$--122. Detailed results including the maximal evaporation residue cross section and the optimal incident energy for each reaction are presented and discussed.

Globally accurate full-dimensional ground state potential energy surface (PES) for the Cl($^2$P) + XCl $\to$ HCl + Cl($^2$P) reaction, a prototypical heavy-light-heavy abstract reaction, is developed using permutation invariant polynomial neural network (PIP-NN) method and embedded atom neural network (EANN) method, with the corresponding total root mean square error (RMSE) being only 0.043 and 0.056 kcal/mol, respectively. The saddle point of this reaction system is found to be nonlinear. A full-dimensional approximate quantum mechanical method, ring-polymer molecular dynamics (RPMD) with Cayley propagator, is employed to calculate the thermal rate coefficients and kinetic isotopic effects of title reactions Cl($^2$P) + XCl $\to$ XCl + Cl($^2$P) (X = H, D, Mu) on both new PESs. The results reproduce the experimental results at high temperatures perfectly, but with moderate accuracy at lower temperatures. The similar kinetic behavior is supported by quantum dynamics using wave packet calculations as well., Comment: 23 pages,5 figures

In the framework of density functional theory (DFT) simulations of molecules and materials, anharmonic terms of the potential energy surface are commonly computed numerically, with an associated cost that rapidly increases with the size of the system. Recently, an efficient approach to calculate cubic and quartic interatomic force constants in the basis of normal modes [Theor. Chem. Acc., 120, 23 (2008)] was implemented in the Crystal program [J. Chem. Theory Comput., 15, 3755-3765 (2019)]. By applying group theory, we are able to further reduce the associated computational cost, as the exploitation of point symmetry can significantly reduce the number of distinct atomically displaced nuclear configurations to be explicitly explored for energy and forces calculations. Our strategy stems from Wigner's theorem and the fact that normal modes are bases of the irreducible representations (irreps) of the point group. The proposed group theoretical approach is implemented in the Crystal program and its efficiency assessed on six test case systems: four molecules (methane, CH4; tetrahedrane, C4H4; cyclo-exasulfur, S6; cubane, C8H8), and two three-dimensional crystals (Magnesium oxide, MgO; and a prototypical Zinc-imidazolate framework, ZIF-8). The speedup imparted by this approach is consistently very large in all high-symmetry molecular and periodic systems, peaking at 76% for MgO.

We have calculated the three-dimensional potential energy surface (PES) for the fission of compound nucleus $^{236}$U using the covariant density functional theory with constraints on the axial quadrupole and octupole deformations $(\beta_2, \beta_3)$ as well as the nucleon number in the neck $q_N$. By considering the additonal degree of freedom $q_N$, coexistence of the elongated and compact fission modes is predicted for $0.9\lesssim \beta_3 \lesssim 1.3$. Remarkably, the PES becomes very shallow across a large range of quadrupole and octupole deformations for small $q_N$, and consequently, the scission line in $(\beta_2, \beta_3)$ plane will extend to a shallow band, which leads to a fluctuation for the estimated total kinetic energies by several to ten MeV and for the fragment masses by several to about ten nucleons.

A full six-dimensional Born-Oppenheimer singlet potential energy surface is constructed for the reaction CaF + CaF $\rightarrow$ CaF$_2$ + Ca using a multireference configuration interaction (MRCI) electronic structure calculation. The {\it ab initio} data thus calculated are interpolated by Gaussian process (GP) regression. The four-body potential energy surface features one $D_{2h}$ global minimum and one $C_s$ local minimum, connected by a barrierless transition state that lends insight to the reaction mechanism. This surface is intended to be of use in understanding ultracold chemistry of CaF molecules., Comment: Submitted to Phys. Rev. A

The process of design and discovery of new materials can be significantly expedited and simplified if we can learn effectively from available data. Deep learning (DL) approaches have recently received a lot of interest for their ability to speed up the design of novel materials by predicting material properties with precision close to experiments and ab-initio calculations. The application of deep learning to predict materials properties measured by experiments are valuable yet challenging due to the limited amount of experimental data. Most of the existing approaches to predict properties from computational data have also been directed towards specific material properties. In this work, we extend this approach, by proposing Landscape Crystal Graph Convolution Network(LCGCN), an accurate and transferable deep learning framework based on graph convolutional networks. LCGCN directly learns the potential energy surface (PES) from atomic configurations. This approach can enable transferable models that can predict different material properties. We apply this framework to bulk crystals (i.e. Al2O3), and test it by calculating potential energy surfaces at different temperatures and across different phases of crystal.

In this work we characterize an initial van der Waals adduct in the potential energy surface of reaction between cyanoacetylene HC3N and the cyano radical. The geometry of the CN-HC3N adduct has been optimized through calculations employing ab initio methods. Results show that the energy of the adduct lays below the reactants. Additionally, a saddle point that connects the adduct to an important intermediate of the PES has been localized, with energy below the reactants. Calculations of the intermolecular potential have been performed and results show that the energy of the van der Waals adduct is higher than estimated with the ab initio methods., Comment: 13 pages, 5 figures. Preprint version submitted to LNCS (Springer) ICCSA2021

Ground state structures found in nature are in many cases of high symmetry. But structure prediction methods typically render only a small fraction of high symmetry structures. Especially for large crystalline unit cells there are many low energy defect structures. For this reason methods have been developed where either preferentially high symmetry structures are used as input or where the whole structural search is done within a certain symmetry group. In both cases it is necessary to specify the correct symmetry group beforehand. However it can in general not be predicted which symmetry group is the correct one leading to the ground state. For this reason we introduce a potential energy biasing scheme that favors symmetry and where it is not necessary to specify any symmetry group beforehand. On this biased potential energy surface, high symmetry structures will be found much faster than on an unbiased surface and independently of the symmetry group to which they belong. For our two test cases, a $C_{60}$ fullerene and bulk silicon carbide, we get a speedups of 25 and 63. In our data we also find a clear correlation between the similarity of the atomic environments and the energy. In low energy structures all the atoms of a species tend to have similar environments., Comment: 8 pages, 4 figures, 1 table

The automated development of a new ab initio full-dimensional potential energy surface (PES) is reported for the CH$_4\cdot$F$^-$ complex using the ROBOSURFER program package. The new potential provides a near-spectroscopic quality description over a broad configuration range including the methane-ion dissociation, as well as isolated methane vibrations. In particular, it improves upon the earlier [Czak\'o, Braams, Bowman (2008)] PES over intermediate methane-fluoride distances. Full-dimensional (12D) variational vibrational computations using the new PES and the GENIUSH-Smolyak algorithm show that tunneling splittings larger than 0.1 cm$^{-1}$ appear below the top of the interconversion barrier of the four equivalent minima of the complex.

Modeling molecular potential energy surface is of pivotal importance in science. Graph Neural Networks have shown great success in this field. However, their message passing schemes need special designs to capture geometric information and fulfill symmetry requirement like rotation equivariance, leading to complicated architectures. To avoid these designs, we introduce a novel local frame method to molecule representation learning and analyze its expressivity. Projected onto a frame, equivariant features like 3D coordinates are converted to invariant features, so that we can capture geometric information with these projections and decouple the symmetry requirement from GNN design. Theoretically, we prove that given non-degenerate frames, even ordinary GNNs can encode molecules injectively and reach maximum expressivity with coordinate projection and frame-frame projection. In experiments, our model uses a simple ordinary GNN architecture yet achieves state-of-the-art accuracy. The simpler architecture also leads to higher scalability. Our model only takes about 30% inference time and 10% GPU memory compared to the most efficient baselines., Comment: Learning on Graphs (LoG) 2022

Within the framework of Skyrme energy-density functional theory, the nucleus-nucleus potential is calculated and potential energy surface is obtained with different effective forces for accurately estimating the formation cross sections of superheavy nuclei in massive fusion reactions. The width and height of the potential pocket are influenced by the Skyrme effective forces SkM, SkM$^{\ast}$, SkP, SIII, Ska and SLy4, which correspond to the different equation of state for the isospin symmetry nuclear matter. It is found that the nucleus-nucleus potential is associated with the collision orientation and Skyrme parameters. More repulsive nuclear potential is pronounced with increasing the incompressible modulus of nuclear matter. The available data in the fusion-evaporation reaction of $^{48}$Ca+$^{238}$U are nicely reproduced with the SkM$^{\ast}$ parameter by implementing into the dinuclear system model., Comment: 9 pages, 6 figures, 1 table

We used for the first time the method of periodic orbit dividing surfaces in a non-integrable Hamiltonian system with three degrees of freedom. We have studied the structure of these four dimensional objects in the five dimensional phase space. This method enabled us to detect the reactive and non-reactive trajectories in a three dimensional Caldera potential energy surface. We distinguished four distinct types of trajectory behavior. Two of the types of trajectories could only occur in a three dimensional Caldera potential energy surface and not in a two dimensional surface, and we have shown that this is a result of homoclinic intersections. These homoclinic intersections were analyzed with the method of Lagrangian descriptors. Finally, we were able to detect and describe the phenomenon of dynamical matching in the three dimensional Caldera potential energy surface, which is an important mechanism for understanding the reaction dynamics of organic molecules., Comment: 18 pages, 13 figures, it was accepted for publication in Physica D

Recently, it has been shown that neural networks not only approximate the ground-state wave functions of a single molecular system well but can also generalize to multiple geometries. While such generalization significantly speeds up training, each energy evaluation still requires Monte Carlo integration which limits the evaluation to a few geometries. In this work, we address the inference shortcomings by proposing the Potential learning from ab-initio Networks (PlaNet) framework, in which we simultaneously train a surrogate model in addition to the neural wave function. At inference time, the surrogate avoids expensive Monte-Carlo integration by directly estimating the energy, accelerating the process from hours to milliseconds. In this way, we can accurately model high-resolution multi-dimensional energy surfaces for larger systems that previously were unobtainable via neural wave functions. Finally, we explore an additional inductive bias by introducing physically-motivated restricted neural wave function models. We implement such a function with several additional improvements in the new PESNet++ model. In our experimental evaluation, PlaNet accelerates inference by 7 orders of magnitude for larger molecules like ethanol while preserving accuracy. Compared to previous energy surface networks, PESNet++ reduces energy errors by up to 74%., Comment: Published as a conference paper at ICLR 2023

Full configuration interaction quantum Monte Carlo (FCIQMC) is a state-of-the-art stochastic electronic structure method, providing a methodology to compute FCI-level state energies of molecular systems within a quantum chemical basis. However, especially to probe {\em dynamics} at the FCIQMC level, it is necessary to devise more efficient schemes to produce nuclear forces and potential energy surfaces (PES) from FCIQMC. In this work, we derive the general formula for nuclear force from FCIQMC, and clarify different contributions of the total force. This method to obtain FCIQMC forces eliminates previous restrictions, and can be used with frozen core approximation and free selection of orbitals, making it promising for more efficient nuclear force calculations. After numerical check of this procedure on the binding curve of N$_2$ molecule, we use the FCIQMC energy and force to obtain the full-dimensional ground state PES of water molecule via Gaussian processes regression. The new water FCIQMC PES can be used as the basis for H$_2$O ground state nuclear dynamics, structure optimization, and rotation-vibrational spectrum calculation.

In this paper we study an asymmetric valley-ridge inflection point (VRI) potential, whose energy surface (PES) features two sequential index-1 saddles (the upper and the lower), with one saddle having higher energy than the other and two potential wells separated by the lower index-1 saddle. We show how the depth and the flatness of our potential changes as we modify the parameter that controls the asymmetry as well as how the branching ratio (ratio of the trajectories that enter each well) is changing as we modify the same parameter and its correlation with the area of the lobes as they have formulated by the stable and unstable manifolds that have been extracted from the gradient of the LD scalar fields.

With gates of a quantum computer designed to encode multi-dimensional vectors, projections of quantum computer states onto specific qubit states can produce kernels of reproducing kernel Hilbert spaces. We show that quantum kernels obtained with a fixed ansatz implementable on current quantum computers can be used for accurate regression models of global potential energy surfaces (PES) for polyatomic molecules. To obtain accurate regression models, we apply Bayesian optimization to maximize marginal likelihood by varying the parameters of the quantum gates. This yields Gaussian process models with quantum kernels. We illustrate the effect of qubit entanglement in the quantum kernels and explore the generalization performance of quantum Gaussian processes by extrapolating global six-dimensional PES in the energy domain.

The construction of the potential energy surface (PES) of even a medium-sized molecule employing correlated theory, such as CCSD(T), is an arduous task due to the high computational cost. In this Letter, we report the possibility of efficient construction of such a PES employing the molecular tailoring approach (MTA) on off-the-shelf hardware. The full calculation (FC) as well as MTA energies at CCSD(T)/aug-cc-pVTZ level for three test molecules, viz. acetylacetone, N-methyacetamide, and tropolone are reported. All the MTA energies are in excellent agreement with their FC counterparts (typical error being sub-millihartree) with a time advantage factor of 3 to 5. The energy barrier from the ground- to transition-state is accurately captured. Further, the accuracy and efficiency of the MTA method for estimating energy gradients at CCSD(T) level are demonstrated. This work brings out the possibility of the construction of PES for large molecules using MTA with the computational economy at a high level of theory and/or basis set.

In this work, we continue the study of the bifurcations of the critical points in a symmetric Caldera potential energy surface. In particular, we study the influence of the depth of the potential on the trajectory behavior before and after the bifurcations of the critical points. We observe two different types of trajectory behavior: dynamical matching and the non-existence of dynamical matching. Dynamical matching is a phenomenon that limits the way in which a trajectory can exit the Caldera based solely on how it enters the Caldera. Furthermore, we discuss two different types of symmetric Caldera potential energy surface and the transition from the one type to the other through the bifurcations of the critical points.