Global Potential Energy Surface Research Articles

Resolving the Temperature and Composition Dependence of Ion Conductivity for Yttria-Stabilized Zirconia from Machine Learning Simulation

The temperature and composition dependence of the ion conductivity for yttria-stabilized zirconia (YSZ) have been hotly studied over the past 50 years. Due to the sluggish oxygen anion diffusion and the low doping of oxide, the computation of ion conductivity traditionally has to be performed with empirical force field potentials in order to achieve the required long timescale, which, however, fails to reproduce some critical observations in experiment, e.g., the conductivity maximum achieved at 8 mol % YSZ at the operating temperatures. Here by using our recently developed Y–Zr–O global neural network (G-NN) potential, we are able to carry out a series of long-time molecular dynamics simulations for YSZ at 6.7, 8, 10, and 14.3 mol % over a wide temperature range (800–2000 K). This finally quantitatively resolves the effects of temperature and composition on the ion conductivity. We confirm the key experimental findings that (i) 8 mol % YSZ has the highest ion conductivity, 0.16–0.51 S/cm, at 1200–1600 K, agreeing with 0.16–0.55 S/cm in experiment, and the maximum conductivity shifts to the higher Y composition above 1600 K and (ii) over the wide temperature range (800–2000 K) the ion conductivity of 8YSZ exhibits the non-Arrhenius behaviors with two different activation energies. The physical origin for these peculiar phenomena is revealed at the atomic level by analyzing the MD pathways. The presence of monoclinic phase and the aggregation of oxygen vacancy along ⟨112⟩ are two key factors to retard oxygen diffusion. For 8 mol % YSZ, the oxygen movement is dominated by local vibrations below 1000 K but becomes delocalized above 1000 K, which results in the gradual aggregation of oxygen vacancy along a new ⟨112⟩ direction. Our results demonstrate that the G-NN potential from unbiased machine learning of the global potential energy surface can meet the high standard in both accuracy and speed required for material simulation.

Accurate Global Potential Energy Surfaces for the H + CH3OH Reaction by Neural Network Fitting with Permutation Invariance.

The H + CH3OH reaction, which plays an important role in combustion and the interstellar medium, presents a prototypical system with multi channels and tight transition states. However, no globally reliable potential energy surface (PES) has been available to date. Here we develop global analytical PESs for this system using the permutation-invariant polynomial neural network (PIP-NN) and the high-dimensional neural network (HD-NN) methods based on a large number of data points calculated at the level of the explicitly correlated unrestricted coupled cluster single, double, and perturbative triple level with the augmented correlation corrected valence triple-ζ basis set (UCCSD(T)-F12a/AVTZ). We demonstrate that both machine learning PESs are able to accurately describe all dynamically relevant reaction channels. At a collision energy of 20 kcal/mol, quasi-classical trajectory calculations reveal that the dominant channel is the hydrogen abstraction from the methyl site, yielding H2 + CH2OH. The reaction of this major channel takes place mainly via the direct rebound mechanism. Both the vibrational and rotational states of the H2 product are relatively cold, and large portions of the available energy are converted into the product translational motion.

How Do Local Reactivity Descriptors Shape the Potential Energy Surface Associated with Chemical Reactions? The Valence Bond Delocalization Perspective.

How do local reactivity descriptors, such as the Fukui function and the local spin density distribution, shape the potential energy surface (PES) associated with chemical reactions and thus govern reactivity trends and regioselective preferences? This is the question that is addressed here through a qualitative valence bond (VB) analysis. We demonstrate that common density functional theory (DFT)-based local reactivity descriptors can essentially be regarded—in one way or another—as indirect measures of delocalization, i.e., resonance stabilization, of the reactants within VB theory. The inherent connection between (spatial) delocalization and (energetic) resonance stabilization embedded in VB theory provides a natural and elegant framework for analyzing and comprehending the impact of individual local reactivity descriptors on the global PES. Our analysis provides new insights into the role played by local reactivity descriptors and illustrates under which conditions they can sometimes fail to predict reactivity trends and regioselective preferences, e.g., in the case of ambident reactivity. This treatment constitutes a first step toward a unification of VB theory and conceptual DFT.

Dynamics Studies of O2 Collision on Pt(111) Using a Global Potential Energy Surface

The dynamics of O2 collision on Pt(111) has been studied by molecular dynamics simulations using a global potential energy surface (PES), which was developed by fitting ∼4800 plane-wave density functional theory points using the permutation invariant polynomial-neural network method. The simulations were performed for the normal and off-normal incidences at a wide range of incident energies and surface temperatures. A generalized Langevin oscillator model was used to incorporate the molecule–surface coupling that plays an important role in this collision process. The trapping probability, final energy distribution, scattering angle distributions of scattered molecules, and the energy transfer to surface distribution were determined and analyzed. The PES shows an activated path to the chemisorption states, as the trapping probability directly increases with incident energy (larger than 0.1 eV) to reach a maximum and then decreases at high incident energy. The trapping probability obviously reduces by raising surface temperature at low incident energy because the initial kinetic energy of molecule is more likely to be dissipated into surface motions than molecular internal ro-vibrational modes. Additional parallel momentum of off-normal incidence leads to a strong suppression of the trapping probability, caused by the energetic corrugation of the lateral barrier heights. The scattering angular distributions are found to be quasispecular and the final translational energy slightly increases with scattering angle deviating significantly from the hard-cube model, indicating the nonconservation of parallel momentum during the collision on the corrugate PES.

Automatically growing global reactive neural network potential energy surfaces: A trajectory-free active learning strategy.

An efficient and trajectory-free active learning method is proposed to automatically sample data points for constructing globally accurate reactive potential energy surfaces (PESs) using neural networks (NNs). Although NNs do not provide the predictive variance as the Gaussian process regression does, we can alternatively minimize the negative of the squared difference surface (NSDS) given by two different NN models to actively locate the point where the PES is least confident. A batch of points in the minima of this NSDS can be iteratively added into the training set to improve the PES. The configuration space is gradually and globally covered without the need to run classical trajectory (or equivalently molecular dynamics) simulations. Through refitting the available analytical PESs of H3 and OH3 reactive systems, we demonstrate the efficiency and robustness of this new strategy, which enables fast convergence of the reactive PESs with respect to the number of points in terms of quantum scattering probabilities.

A Global Full-Dimensional Potential Energy Surface for the K2Rb2 Complex and Its Lifetime.

A full-dimensional global potential energy surface for the KRb + KRb → K2 + Rb2 reaction is developed from 20 759 ab initio points calculated using a coupled cluster singles, doubles, and perturbative triples (CCSD(T)) method with effective core potentials, extrapolated to the complete basis set limit. The ab initio points are represented with high fidelity (root-mean-square error of 1.86 cm-1) using the permutation-invariant polynomial-neural network method, which enforces the permutation invariance of the potential with respect to exchange of identical nuclei. The potential energy surface features two D2h minima and one Cs minimum connected by the isomerization saddle points. The Rice-Ramsperger-Kassel-Marcus lifetime of the K2Rb2 reaction intermediate estimated using the potential energy surface is 227 ns, in reasonable agreement with the latest experimental measurement.

Data-Driven Many-Body Models for Molecular Fluids: CO2/H2O Mixtures as a Case Study.

In this study, we extend the scope of the many-body TTM-nrg and MB-nrg potential energy functions (PEFs), originally introduced for halide ion-water and alkali-metal ion-water interactions, to the modeling of carbon dioxide (CO2) and water (H2O) mixtures as prototypical examples of molecular fluids. Both TTM-nrg and MB-nrg PEFs are derived entirely from electronic structure data obtained at the coupled cluster level of theory and are, by construction, compatible with MB-pol, a many-body PEF that has been shown to accurately reproduce the properties of water. Although both TTM-nrg and MB-nrg PEFs adopt the same functional forms for describing permanent electrostatics, polarization, and dispersion, they differ in the representation of short-range contributions, with the TTM-nrg PEFs relying on conventional Born-Mayer expressions and the MB-nrg PEFs employing multidimensional permutationally invariant polynomials. By providing a physically correct description of many-body effects at both short and long ranges, the MB-nrg PEFs are shown to quantitatively represent the global potential energy surfaces of the CO2-CO2 and CO2-H2O dimers and the energetics of small clusters, as well as to correctly reproduce various properties in both gas and liquid phases. Building upon previous studies of aqueous systems, our analysis provides further evidence for the accuracy and efficiency of the MB-nrg framework in representing molecular interactions in fluid mixtures at different temperature and pressure conditions.

Stability and anion diffusion kinetics of Yttria-stabilized zirconia resolved from machine learning global potential energy surface exploration.

Yttria-stabilized zirconia (YSZ) is an important material with wide industrial applications particularly for its good conductivity in oxygen anion transportation. The conductivity is known to be sensitive to Y concentration: 8 mol. % YSZ (8YSZ) achieves the best performance, which, however, degrades remarkably under ∼1000 °C working conditions. Here, using the recently developed SSW-NN method, stochastic surface walking global optimization based on global neural network potential (G-NN), we establish the first ternary Y-Zr-O G-NN potential by fitting 28 803 first principles dataset screened from more than 107 global potential energy surface (PES) data and explore exhaustively the global PES of YSZ at different Y concentrations. Rich information on the thermodynamics and the anion diffusion kinetics of YSZ is, thus, gleaned, which helps resolve the long-standing puzzles on the stability and conductivity of the 8YSZ. We demonstrate that (i) 8YSZ is the cubic phase YSZ with the lowest possible Y concentrations. It is thermodynamically unstable, tending to segregate into the monoclinic phase of 6.7YSZ and the cubic phase of 20YSZ. (ii) The O anion diffusion in YSZ is mediated by O vacancy sites and moves along the ⟨100⟩ direction. In 8YSZ and 10YSZ, despite different Y concentrations, their anion diffusion barriers are similar, ∼ 1 eV, but in 8YSZ, the O diffusion distance is much longer due to the lack of O vacancy aggregation along the ⟨112⟩ direction. Our results illustrate the power of G-NN potential in solving challenging problems in material science, especially those requiring a deep knowledge on the complex PES.

Time-dependent wave packet studies of the abstraction and exchange channels of the H + NaH+ reaction

The abstraction reaction H + NaH+ (v0 = 0, j0 = 0) → Na+ + H2 and exchange reaction H′ + NaH+ (v0 = 0, j0 = 0) → NaH′+ + H were studied using the time-dependent wave packet method with second order split operator in the collision energy range from 0.01 to 1.0 eV. A new global potential energy surface (PES), which was reported by Yuan and co-workers (2018 Chem. Phys. Lett. 700 122), was used in the present dynamics calculation. The dynamics properties such as reaction probability, integral cross section, differential cross section, and the distribution of the product were presented in the present work. The results show that direct abstraction mechanism is dominated in abstraction reaction whereas the ‘rebound’ mechanism plays a dominant role in exchange reaction.

Interpolation and Extrapolation of Global Potential Energy Surfaces for Polyatomic Systems by Gaussian Processes with Composite Kernels.

Gaussian process (GP) regression has recently emerged as a powerful, system-agnostic tool for building global potential energy surfaces (PES) of polyatomic molecules. While the accuracy of GP models of PES increases with the number of potential energy points, so does the numerical difficulty of training and evaluating GP models. Here, we demonstrate an approach to improve the accuracy of global PES without increasing the number of energy points. We show that GP models of PES trained by a small number of energy points can be significantly improved by iteratively increasing the complexity of GP kernels. The composite kernels thus obtained maximize the accuracy of GP models for a given distribution of potential energy points. The accuracy can then be further improved by varying the training point distributions. We also show that GP models with composite kernels can be used for physical extrapolation of PES. We illustrate the approach by constructing the six-dimensional PES for H3O+. For the interpolation problem, we show that this algorithm produces a global six-dimensional PES in the energy range between 0 and 21 000 cm-1 with the root-mean-square error 65.8 cm-1 using only 500 randomly selected ab initio points as input. To illustrate extrapolation, we produce the PES at high energies using the energy points at low energies. We show that one can obtain an accurate global fit of the PES extending to 21 000 cm-1 based on 1500 potential energy points at energies below 10 000 cm-1.

Accurate Potential Energy Surface for Quartet State HN2 and Interplay of N(4S) + NH(X̃3Σ–) versus H + N2(A3Σu+) Reactions

A global potential energy surface for the lowest quartet state of HN2 is reported for the first time from accurate multireference ab initio calculations extrapolated to the complete basis set limit using the double many-body expansion method. All its stationary points are characterized, with the lowest quartet of HN2 predicted to have a bent global minimum 36 kcal mol-1 below the N(4S) + NH(X̃3Σ-) asymptote, from which it is barrierlessly achievable. The entire set of calculated ab initio points has been fitted for energies up to 1000 kcal mol-1 above the global minimum with an RMSD of 0.89 kcal mol-1, a gap comprising all identified stationary points. Special care is taken in modeling the involved long-range forces and cusps caused by crossing seams. The novel PES prompts for the calculation of rate constants for several unexplored reactions that are relevant for combustion, plasma, and atmospheric chemistry.

Accurate global adiabatic potential energy surfaces for three low-lying electronic states of AlH2 free radicals.

In order to obtain the all-round molecular properties of the AlH2 system and the corresponding dynamical characteristics of the Al + H2 (v = 0, j = 0) → H + AlH reaction, three significant global adiabatic potential energy surfaces of AlH2 (X2A1, 2B1, and 2B2) free radicals were constructed for the first time. Ab initio energies were calculated under the multi-reference configuration interaction method and the aug-cc-pV(T,Q)Z basis sets; then the ab initio energies were extrapolated to the complete basis sets limit. The three adiabatic potential energy surfaces were constructed by the many-body expansion theory. The maximum root-mean square error was just 50 cm-1, which was small enough to ensure that the potential energy surfaces were accurate. The concerned T-type insertion topographical features, dissociation schemes, C2v geometry reaction mechanisms, and minimum energy curve paths were investigated and are discussed in detail. Several differences from previous studies are also pointed out. Eventually, the integral cross-sections of Al + H2 (v = 0, j = 0) → H + AlH reaction as calculated by quasi-classical trajectory method were employed to predict the dynamical properties of AlH2, providing the most reliable theoretical reference of the dynamical characteristics known thus far for such a reaction. These new potential energy surfaces can be treated as a reliable basis for investigation of the dynamics and as a component for constructing larger aluminum-/hydrogen-containing systems.

Global accurate diabatic potential surfaces for the reaction H + Li2.

The adiabatic potential energies for the lowest three states of a Li2H system are calculated with a high level ab initio method (MCSCF/MRCI) with a large basis set (aV5Z). The accurate three dimensional B-spline fitting method is used to map the global adiabatic potential energy surfaces, using the existing adiabatic potential energies, for the lowest two adiabatic states of the title reaction system. The different vibrational states and corresponding energies are studied for the diatomic molecule of reactant and products. In order to clearly understand the nonadiabatic process, the avoided crossing area and conical intersection are carefully studied. For further study of the nonadiabatic dynamic reaction, the diabatic potential energy surfaces are deduced in the present work.

Kinetics and dynamics study of the OH + C2H6 → H2O + C2H5 reaction based on an analytical global potential energy surface.

To describe the gas-phase hydrogen abstraction reaction between the hydroxyl radical and the ethane molecule, an analytical full-dimensional potential energy surface was developed within the Born-Oppenheimer approximation. This reactive process is a ten-body system with 24 degrees of freedom, which represents a theoretical challenge. The new surface, named PES-2020, presents low barrier, 3.76 kcal mol-1, high exothermicity, -16.20 kcal mol-1, and intermediate complexes in the entrance and exit channels. To test the quality and accuracy of the analytical surface several stringent tests were performed and, in general, PES-2020 reasonably simulates the theoretical information used as input, it is a continuous and smooth potential, without spurious minima, it presents great versatility and a reasonable description of this ten-body reaction. Based on this surface, an exhaustive kinetics and dynamics study was performed with a double objective: to analyze the capacity of the new surface to simulate the experimental evidence, and to help understand the mechanism of reaction and the role of the ethyl group in the reaction. In the kinetics study, three approaches were used: variational transition-state theory with multidimensional tunnelling (VTST/MT), ring polymer molecular dynamics (RPMD) and quasi-classical trajectory (QCT) results, in the temperature range 200-2000 K. There is general agreement between the three approaches and they reasonably simulate the experimental behaviour, which gives confidence to the fitness of the new surface to describe the system. In the dynamics study, QCT calculations were performed at 298 K for a direct comparison with the only experimental result reported. We found that ethyl fragment presents a noticeable internal energy (∼20%) and so cannot be considered as a spectator. The water product vibrational energy is reasonably reproduced, though when a level-by-level distribution is analyzed the agreement is only qualitative.

Theoretical study of the O(3P) + C2H6 reaction based on a new ab initio-based global potential energy surface.

A new analytical potential energy surface was developed for the first time for the nine-body O(3P) + C2H6 hydrogen abstraction reaction, named PES-2020, which was fitted to explicitly-correlated high-level electronic structure calculations. This surface simulates the topography of the reactive system, from reactants to products, OH(v,j) + C2H5. The adiabatic energy of reaction, ΔHr(0 K) = -2.33 kcal mol-1, reproduces the experimental evidence, and the barrier height, 10.70 kcal mol-1, agrees with the ab initio calculations used as input. In addition, an intermediate complex in the exit channel is observed, which is stabilized with respect to the products of the reaction. Based on PES-2020 a dynamics study was carried out, where quasi-classical trajectory calculations were performed for collision energies in the range of 7.0-60.0 kcal mol-1, which covers high collision energy regions. The reaction cross section increases with collision energy; the largest fraction of available energy is deposited as translational energy (44-66%), and the scattering distribution evolves from backward to forward with collision energy. These findings reproduce previous theoretical calculations using electronic structure calculations of lower levels. However, where these previous studies failed, viz. in rotational and vibrational OH(v,j) distributions, PES-2020 reproduces practically quantitatively the experimental evidence, i.e., cold vibration and rotation, the rotational distribution peaking at j = 1-3 depending on the collision energy. In sum, this behaviour is typical of gas-phase hydrogen abstraction reactions with direct mechanism and high reaction barrier.

Thermodynamic rules for zeolite formation from machine learning based global optimization.

While the [TO4] tetrahedron packing rule leads to millions of likely zeolite structures, there are currently only 252 types of zeolite frameworks reported after decades of synthetic efforts. The subtle synthetic conditions, e.g. the structure-directing agents, pH and the feed ratio, were often blamed for the limited zeolite types due to the complex kinetics. Here by developing machine learning global optimization techniques, we are now able to establish the global potential energy surface of a typical zeolite system, SixAlyPzO2Hy−z with 12 T atoms (T: Si, Al and P) that is the general formula shared by CHA, ATS, ATO and ATV zeolite frameworks. After analyzing more than 106 minima data, we identify thermodynamic rules on energetics and local bonding patterns for stable zeolites. These rules provide general guidelines to classify zeolite types and correlate them with synthesis conditions. The machine learning based atomistic simulation thus paves a new way towards rational design and synthesis of stable zeolite frameworks with desirable compositions.

Automating the Development of High-Dimensional Reactive Potential Energy Surfaces with the robosurfer Program System.

The construction of high-dimensional global potential energy surfaces (PESs) from ab initio data has been a major challenge for decades. Advances in computer hardware, electronic structure theory, and PES fitting methods have greatly alleviated many challenges in PES construction, but building fitting sets has remained a bottleneck so far. We present the robosurfer program system that completely automates the generation of new geometries, performs ab initio computations, and iteratively improves the PES under development. Unlike previous efforts to automate PES development, robosurfer does not require any uncertainty estimate from the PES fitting method and thus it is compatible with the permutationally invariant polynomial (PIP) method. As a demonstration we have developed five related but different global reactive PIP PESs for the CH3Br + F- system and used them to perform quasiclassical trajectory (QCT) reaction dynamics simulations over a wide range of collision energies. The automatically developed PESs show good to excellent accuracy at known stationary points without any manual sampling, and QCT results indicate the lack of unphysical minima on the fitted surfaces. We also present evidence suggesting that the breakdown of single reference electronic structure theory may contribute significantly to the fitting errors of global reactive PESs.

Globally accurate potential energy surface for PH2 + (11 A′) by using the switching function formalism

As an intermediate product of phosphorus compounds in astrophysical chemistry, has great significance in research on the systems. However, as a basis for studying its reaction mechanisms, lacks an accurate global potential energy surface (PES) and related dynamic reports. In this investigation, based on a multi-reference configuration interaction approach with Davidson correction, an accurate global many-body expansion PES for in its ground state was reported by fitting extensive ab initio energies, as calculated with the correlation-consistent basis set aug-cc-pVQZ. Meanwhile, the switching function formalism was adopted to explain and distinguish the transformation between and in one-body energy terms, which ensured the correct dissociation channel in the reaction process of . The topographical characteristics of the title system PES were meticulously contrasted with those in other literature reports, which were consistent with previous experimental and theoretical values. Subsequently, the time-dependent wave packet approach was adopted to calculate the reaction probability and integral cross-section for the reaction to verify the accuracy of the new PES. This dynamics study may help to further explain the thermochemical reactions of phosphorus-containing molecules in interstellar media.

Dynamics studies of the H + HBr reaction: Based on a new potential energy surface.

The initial state specific quantum wave packet dynamics studies of the H + HBr (v0 = 0, j0 = 0-2) reaction were performed using a new global potential energy surface (PES) of the ground state of the BrH2 system for the collision energy ranging from 0.01 to 2.0 eV. The PES was constructed using the permutation invariant polynomial neural network method based on approximately 63 000 ab initio points, which were calculated by the multireference configuration interaction method with AVTZ and AVQZ basis sets. To improve the accuracy of the PES, Davidson's correction and spin-orbit coupling effects were considered in the ab initio calculation and the basis set was extrapolated to complete basis set limit. The new PES was compared with the previous ones and also the available experimental data, which suggests that the new PES is more accurate. The state-to-state quantum wave packet dynamics was carried out using the reactant-coordinate based approach. The reaction probabilities, integral and differential cross sections, rovibrational state distributions of product and rate constants, etc., were compared with the available theoretical and experimental studies. In general, the present work is in better agreement with the available experimental data. The quantum dynamics studies suggest that the rotational excitation of HBr has little effect on the reaction.

Pyrolysis of Glyphosate and Its Toxic Products.

With health concerns developing about the use of glyphosate (phosphonomethylglycine, PMG), the world's most used herbicide, the possibility of destruction of stockpiles via incineration arises. Little is known, however, about the possible toxic products of decomposition. We have performed a quantum chemical computation of the mechanism of thermal decomposition of PMG. Two initiation channels, one producing sarcosine and the other producing N-methylaminomethylphosphonic acid, have been located. Both the initial products decompose to dimethylamine (DMA), and the mechanism of further decomposition and toxic products is explored. Global potential energy surfaces for the initial decomposition of DMA are presented together with chemical kinetic modeling wherein the rate constants employed have been calculated from the quantum chemical data. Time and temperature evolution of the expected toxic products are presented and discussed.