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Reactive molecular dynamics (MD) simulation is a powerful tool to study the reaction mechanism of complex chemical systems. Central to the method is the potential energy surface (PES) that can describe the breaking and formation of chemical bonds. The development of both accurate and efficient PES has attracted significant effort in the past 2 decades. A recently developed deep potential (DP) model has the promise to bring ab initio accuracy to large-scale reactive MD simulations. However, for complex chemical reaction processes like pyrolysis, it remains challenging to generate reliable DP models with an optimal training data set. In this work, a data set construction scheme for such a purpose was established. The employment of a concurrent learning algorithm allows us to maximize the exploration of the chemical space while minimizing the redundancy of the data set. This greatly reduces the cost of computational resources required for ab initio calculations. Based on this method, we constructed a data set for the pyrolysis of n-dodecane, which contains 35 496 structures. The reactive MD simulation with the DP model trained based on this data set revealed the pyrolysis mechanism of n-dodecane in detail, and the simulation results are in good agreement with the experimental measurements. In addition, this data set shows excellent transferability to different long-chain alkanes. These results demonstrate the advantages of the proposed method for constructing training data sets for similar systems.

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... Machine learning potentials offer a potential mechanism to improve the accuracy and efficiency of QM/MM simulations, and they have had considerable impact in the development of methods to study chemical reactions. [15][16][17][18][19][20][21] Herein we develop an approach whereby we employ a recently described deep-potential range correction (DPRc) model 22 to enhance the accuracy of a fast, approximate base QM/MM model to reproduce the energies and forces of a much more computationally costly target QM/MM model. The new model parametrizes the DPRc potential using a machine learning neural network training procedure 22 to correct the 2nd-order density-functional tight-binding (DFTB2) semiempirical method [23][24][25] to reproduce the PBE0/6-31G* energies and forces in explicit solvent QM/MM calculations. ...

... Whereas the mean absolute error (MAE) for activation and reaction free energies for DFTB2 with respect to PBE0/6-31G* reference values are 3.4 and 9.4 kcal/mol, re- · · · · · · · · · · · · PBE0/6-31G* -1.62 -0. 21 ...

We present a fast, accurate, and robust approach for determination of free energy profiles and kinetic isotope effects for RNA 2'-O-transphosphorylation reactions with inclusion of nuclear quantum effects. We apply a deep potential range correction (DPRc) for combined quantum mechanical/molecular mechanical (QM/MM) simulations of reactions in the condensed phase. The method uses the second-order density-functional tight-binding method (DFTB2) as a fast, approximate base QM model. The DPRc model modifies the DFTB2 QM interactions and applies short-range corrections to the QM/MM interactions to reproduce ab initio DFT (PBE0/6-31G*) QM/MM energies and forces. The DPRc thus enables both QM and QM/MM interactions to be tuned to high accuracy, and the QM/MM corrections are designed to smoothly vanish at a specified cutoff boundary (6 Å in the present work). The computational speed-up afforded by the QM/MM+DPRc model enables free energy profiles to be calculated that include rigorous long-range QM/MM interactions under periodic boundary conditions and nuclear quantum effects through a path integral approach using a new interface between the AMBER and i-PI software. The approach is demonstrated through the calculation of free energy profiles of a native RNA cleavage model reaction and reactions involving thio-substitutions, which are important experimental probes of the mechanism. The DFTB2+DPRc QM/MM free energy surfaces agree very closely with the PBE0/6-31G* QM/MM results, and it is vastly superior to the DFTB2 QM/MM surfaces with and without weighted thermodynamic perturbation corrections. 18O and 34S primary kinetic isotope effects are compared, and the influence of nuclear quantum effects on the free energy profiles is examined.

... In the past three years, DPs have been applied in a number of systems in materials science including (1) elemental bulk systems, (2) multi-element bulk systems, (3) aqueous systems, (4) molecular systems and clusters, and (5) surfaces and lowdimensional systems. Table 2 shows a list of the material systems to which DPs have been applied (as of the writing of [188,189] Molecular systems and clusters Organic molecules [99,[190][191][192][193][194][195] Metal and alloy clusters [119,196] Surfaces and low-dimensional systems Metal and alloy surfaces [103,119,129] Graphane [125,197] Monolayer In 2 Se 3 [198] 2D Co-Fe-B [199] this paper). We choose several examples from each category to briefly discuss the corresponding DP application and how DP aids materials science research. ...

... Jiang et al [190] developed DPs for sulfuric acid-sulfuric acid, dimethylamine-dimethylamine, and sulfuric aciddimethylamine organic molecular systems to investigate the atmospheric aerosol nucleation process. Zeng et al [191] trained a DP based on a dataset for the pyrolysis of n-dodecane and performed a reactive DP MD simulation to reveal the detailed pyrolysis mechanism, in good agreement with experiment. Chen et al [192] used a DP to accurately represent the ground-and excited-state PES of CN 2 NH. ...

To fill the gap between accurate (and expensive) ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials, a new class of descriptions of atomic interactions has emerged and been widely applied; i.e., machine learning potentials (MLPs). One recently developed type of MLP is the Deep Potential (DP) method. In this review, we provide an introduction to DP methods in computational materials science. The theory underlying the DP method is presented along with a step-by-step introduction to their development and use. We also review materials applications of DPs in a wide range of materials systems. The DP Library provides a platform for the development of DPs and a database of extant DPs. We discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials.

... Recently, elementary reactions in the gas phase and on the surface have been studied using NNPES (32)(33)(34)(35)(36)(37)(38)(39). In our previous work, nanosecond-scale reactive MD simulations with NNPES were performed to explore detailed reaction network for methane combustion and pyrolysis of linear alkanes (40,41). ...

... These clusters were first classified according to the bond-type of the center atom and then the k-means clustering algorithm was used to remove the redundancy. Details of relevant methods can be found in our previous study (40,41). Finally, an initial dataset containing 1000 molecular clusters was obtained. ...

Soot is formed resulting from incomplete combustion processes of fossil fuels and is one of the most abundant specie in the space. The early stages of soot formation are central to many ongoing studies in combustion research, but its inception and growth are still elusive and highly debated. Herein, molecular dynamic simulations with ab initio based neural network potentials were carried out to simulate the reaction process leading to the growth of PAHs and soot inception from small hydrocarbon reactants. The in silico simulation provided detailed information of reaction paths that revealed critical steps leading to the formation and growth of large PAHs. And the simulation results clearly showed that the formation and growth of possible soot inceptions are achieved through a series of reactions with small PAH radicals, particularly the two-ring PAH radicals rather than by direct combination of large polynuclear hydrocarbons.

... See [103] for details. [177,178] Aqueous Systems water [96,[179][180][181][182][183][184][185][186][187][188][189][190] zinc ion in water [191] water-vapor interface [192,193] water-TiO2 interface [194] ice [195,196] Molecular Systems and Clusters organic molecules [101,[197][198][199][200][201][202] metal and alloy clusters [126,203] Surfaces and Low-dimensional Systems metal and alloy surfaces [105,126,136] graphane [132,204] monolayer In2Se3 ...

... Jiang, et al. [197] developed DPs for sulfuric acid-sulfuric acid, dimethylaminedimethylamine, and sulfuric aciddimethylamine organic molecular systems to investigate the atmospheric aerosol nucleation process. Zeng, et al. [198] trained a DP based on a dataset for the pyrolysis of n-dodecane and performed a reactive DP MD simulation to reveal the detailed pyrolysis mechanism, in good agreement with experiment. Chen, et al. [199] used a DP to accurately represent the ground-and excitedstate PES of CN 2 NH. ...

To fill the gap between accurate (and expensive) ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials, a new class of descriptions of atomic interactions has emerged and been widely applied; i.e., machine learning potentials (MLPs). One recently developed type of MLP is the Deep Potential (DP) method. In this review, we provide an introduction to DP methods in computational materials science. The theory underlying the DP method is presented along with a step-by-step introduction to their development and use. We also review materials applications of DPs in a wide range of materials systems. The DP Library provides a platform for the development of DPs and a database of extant DPs. We discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials.

... To improve the accuracy and transferability of the DeepPot-SE models, the Deep Potential GENerator (DP-GEN) scheme 39,40 uses an active-learning algorithm to generate models in a way that minimizes human intervention and reduces the computational cost for data generation and model training. The DP-GEN scheme has been successful in modeling metallic systems, 39,40 chemical reactions at the interface of water and TiO 2 , 41 transition from molecular to ionic ice at high pressure, 42 gas-phase reactive systems, 43 etc. These methods have evolved into an open-source software platform (DeePMD-kit 44 and DP-GEN 40 ), and have been enhanced with GPU acceleration and applied to simulations of 100 million atoms. ...

... These values were chosen to be consistent with previous works using the Deep Potential model. 38,43 In addition, we consider different initial data used in the ML potential training. Specifically, we consider: 1) "MD@298", traditional MD at 298K, 2) "TREMD@298,(315),(330)", enhanced sampling with TREMD at 298K, and 3) "TREMD@298,315,330", TREMD using data at 298K in addition to data from elevated temperatures 315K and 330K. ...

We develop a new Deep Potential - Range Correction (DPRc) machine learning potential for combined quantum mechanical/molecular mechanical (QM/MM) simulations of chemical reactions in the condensed phase. The new range correction enables short-ranged QM/MM interactions to be tuned for higher accuracy, and the correction smoothly vanishes within a specified cutoff. We further develop an active learning procedure for robust neural network training. We test the DPRc model and training procedure against a series of 6 non-enzymatic phosphoryl transfer reactions in solution that are important in mechanistic studies of RNA-cleaving enzymes. Specifically, we apply DPRc corrections to a base QM model and test its ability to reproduce free energy profiles generated from a target QM model. We perform comparisons using the MNDO/d and DFTB2 semiempirical models because they produce free energy profiles which differ significantly from each other, thereby providing us a rigorous stress test for the DPRc model and training procedure. The comparisons show that accurate reproduction of the free energy profiles requires correction of the QM/MM interactions out to 6 Å. We further find that the model's initial training benefits from generating data from temperature replica exchange simulations and including high-temperature configurations into the fitting procedure so the resulting models are trained to properly avoid high-energy regions. A single DPRc model was trained to reproduce 4 different reactions and yielded good agreement with the free energy profiles made from the target QM/MM simulations. The DPRc model was further demonstrated to be transferable to 2D free energy surfaces and 1D free energy profiles that were not explicitly considered in the training. Examination of the computational performance of the DPRc model showed that it was fairly slow when run on CPUs, but was sped up almost 100-fold when using an NVIDIA V100 GPUs, resulting in almost negligible overhead. The new DPRc model and training procedure provide a potentially powerful new tool for the creation of next-generation QM/MM potentials for a wide spectrum of free energy applications ranging from drug discovery to enzyme design.

Machine learning potentials (MLPs) capable of accurately describing complex ab initio potential energy surfaces (PES) have revolutionized the field of multiscale atomistic modeling. In this work, using an extensive density functional theory (DFT) dataset (denoted as Si-ZEO22) consisting of 187 unique silica topologies found in the International Zeolite Association (IZA) database, we have trained a DeePMD-kit MLP to model the dynamics of silica frameworks. The performance of our model is evaluated by calculating various properties that probe the accuracy of the energy and force predictions. This MLP demonstrates impressive agreement with DFT for predicting zeolite structural properties, energy-volume trends, and phonon density of states. Furthermore, our model achieves reasonable predictions for stress-strain relationships without including DFT stress data during training. These results highlight the ability of MLPs to capture the flexibility of zeolite frameworks and motivates further MLP development for nanoporous materials with near-ab initio accuracy.

Recently, artificial neural network-based methods for the construction of potential energy surfaces and molecular dynamics (MD) simulations based on them have been increasingly used in the field of theoretical chemistry. The neural network potentials (NNP) strike a good balance between accuracy and computational efficiency relative to quantum chemical calculations and MD simulations based on classical force fields. Thus, NNP is becoming a powerful tool for studying the structure and function of molecules. In this chapter, we introduce the basic theory of NNP. The construction steps and the usage of NNP are also introduced in detail with the MD simulation of methane combustion as an example. We hope that this chapter can help those readers who are new but interested in entering this field.

The Fischer-Tropsch synthetic paraffin residue are mainly treated by combustion or landfill. In this study, an innovative process has been developed for the grading utilization of the Fischer-Tropsch synthetic paraffin residue by extraction and pyrolysis. Firstly, the Fischer-Tropsch synthetic paraffin residue was respectively extracted by n-pentane, n-hexane, n-heptane, cyclohexane and dichloromethane. The yield of extracted paraffin was related to solvent molecular weight and polarity, light alkanes were extracted more easily in non-polar solvents with relatively larger molecular weight. N-heptane showed the highest extraction yield of 57.86%, the extracted paraffin was similar to the paraffin product from Fischer-Tropsch and had more light components, less alkenes and oxygenated components. Afterwards, the solid residues after extraction were pyrolyzed at optimum conditions with 10 ℃/min and 500 ℃. The maximum yield of paraffin was up to 61.75% with the solvent of n-heptane in the grading utilization process, which accounted for 94.33% of the organic components in the Fischer-Tropsch synthetic paraffin residue. The recovered paraffin had higher saturation and less impurity than the Fischer-Tropsch paraffin. The solid product after pyrolysis had high specific surface area and could be processed into adsorbent and catalyst carrier. The grading technology could provide a rationalizing industrial scheme for handling the Fischer-Tropsch synthetic paraffin residue from the Shanxi Lu′an group corporation coal to oil plant of 1.0 million tons/a, 1852.5 tons of high-quality paraffin can be recovered each year.

We report a new deep learning message passing network that takes inspiration from Newton's equations of motion to learn interatomic potentials and forces. With the advantage of directional information from trainable force vectors, and physics-infused operators that are inspired by Newtonian physics, the entire model remains rotationally equivariant, and many-body interactions are inferred by more interpretable physical features. We test NewtonNet on the prediction of several reactive and non-reactive high quality ab initio data sets including single small molecules, a large set of chemically diverse molecules, and methane and hydrogen combustion reactions, achieving state-of-the-art test performance on energies and forces with far greater data and computational efficiency than other deep learning models.

Combustion is a complex chemical system which involves thousands of chemical reactions and generates hundreds of molecular species and radicals during the process. In this work, a neural network-based molecular dynamics (MD) simulation is carried out to simulate the benchmark combustion of methane. During MD simulation, detailed reaction processes leading to the creation of specific molecular species including various intermediate radicals and the products are intimately revealed and characterized. Overall, a total of 798 different chemical reactions were recorded and some new chemical reaction pathways were discovered. We believe that the present work heralds the dawn of a new era in which neural network-based reactive MD simulation can be practically applied to simulating important complex reaction systems at ab initio level, which provides atomic-level understanding of chemical reaction processes as well as discovery of new reaction pathways at an unprecedented level of detail beyond what laboratory experiments could accomplish.

We propose a numerically simple and straightforward, yet accurate and efficient neural networks-based fitting strategy to construct coupled potential energy surfaces (PESs) in a quasi-diabatic representation. The fundamental invariants are incorporated to account for the complete nuclear permutation inversion symmetry. Instead of derivative couplings or interstate couplings, a so-called modified derivative coupling term is fitted by neural networks, resulting in accurate description of near degeneracy points, such as the conical intersections. The adiabatic energies, energy gradients, and derivative couplings are well reproduced, and the vanish of derivative couplings as well as the isotropic topograph of adiabatic and diabatic energies in asymptotic regions are automatically satisfied. All of these features of the coupled global PESs are requisite for accurate dynamics simulations. Our approach is expected to be very useful in developing highly accurate coupled PESs in a quasi-diabatic representation in an efficient machine learning-based way.

Excited-state dynamics simulations are a powerful tool to investigate photo-induced reactions of molecules and materials and provide complementary information to experiments. Since the applicability of these simulation techniques is limited by the costs of the underlying electronic structure calculations, we develop and assess different machine learning models for this task. The machine learning models are trained on ab initio calculations for excited electronic states, using the methylenimmonium cation (CH 2 NH 2 + ) as a model system. Two distinct strategies for modeling excited state properties are tested in this work. The first strategy is to treat each state separately in a kernel ridge regression model and all states together in a multiclass neural network. The second strategy is to instead encode the state as input into the model, which is tested with both models. Numerical evidence suggests that using the state as input yields the best performance. An important goal for excited-state machine learning models is their use in dynamics simulations, which needs not only state-specific information but also couplings, i.e. properties involving pairs of states. Accordingly, we investigate how well machine learning models can predict the couplings. Furthermore, we explore how combining all properties in a single neural network affects the accuracy. Finally, machine learning predicted energies, forces, and couplings are used to carry out excited-state dynamics simulations. Results demonstrate the scopes and possibilities of machine learning to model excited-state properties.

TiO2 is a widely used photocatalyst in science and technology and its interface with water is important in fields ranging from geochemistry to biomedicine. Yet, it is still unclear whether wateradsorbs in molecular or dissociated form on TiO2 even for the case of well-defined crystalline surfaces. To address this issue, we simulated the TiO2 -water interface using molecular dynamics with an ab initio-based deep neural network potential. Our simulations show a dynamical equilibrium of molecular and dissociative adsorption of water on TiO2 . Water dissociates through a solvent-assisted concerted proton transfer to form a pair of short-lived hydroxyl groups on the TiO2 surface. Molecular adsorption of water is ∆F = 7.5 ± 0.9 kJ/mol lower in free energy than the dissociative adsorption, giving rise to a 6 ± 0.5% equilibrium water dissociation fraction at room temperature. Due to the relevance of surface hydroxyl groups to the surface chemistry of TiO2, our model might be key to understanding phenomena ranging from surface functionalization to photocatalytic mechanisms.

Atomic neural networks (ANNs) constitute a class of machine learning methods for predicting potential energy surfaces and physico-chemical properties of molecules and materials. Despite many successes, developing interpretable ANN architectures and implementing existing ones efficiently are still challenging. This calls for reliable, general-purpose and open-source codes. Here, we present a python library named PiNN as a solution toward this goal. In PiNN, we designed a new interpretable and high-performing graph convolutional neural network variant, PiNet, as well as implemented the established Behler-Parrinello high-dimensional neural network. These implementations were tested using datasets of isolated small molecules, crystalline materials, liquid water and an aqueous alkaline electrolyte. PiNN comes with a visualizer called PiNNBoard to extract chemical insight ``learned'' by ANNs, provides analytical stress tensor calculations and interfaces to both the Atomic Simulation Environment and a development version of the Amsterdam Modeling Suite. Moreover, PiNN is highly modularized which makes it useful not only as a standalone package but also as a chain of tools to develop and to implement novel ANNs. The code is distributed under a permissive BSD license and is freely accessible at \href{https://github.com/Teoroo-CMC/PiNN/}{https://github.com/Teoroo-CMC/PiNN/} with full documentation and tutorials.

Glucose pyrolysis, a model system in biomass utilization, is renowned for its great complexity, deep in reaction network hierarchy and rich in reaction patterns. The selectivity in glucose pyrolysis, e.g., the high yield of 5-hydroxymethylfurfural (HMF), a value-added platform product, remains an intriguing puzzle even after 60 years of experimental study. Here we resolve the whole reaction network of glucose pyrolysis using a global-to-global technique for reaction pathway sampling. This is achieved by establishing the first organic chemistry reaction database via stochastic surface walking (SSW) global optimization, building the global neural network (G-NN) potential via machine learning and extensively exploring the reaction network of glucose pyrolysis. In total, 6407 elementary reactions, screened out from more than 150 000 reaction pairs in glucose pyrolysis, are collected in our reaction database. The established reaction network from SSW-NN, further validated by first-principles calculations, reveals that for glucose to HMF, the lowest energy reaction pathway involves fructose and 3-deoxyglucos-2-ene (3-DGE) as key intermediates and a site-selective reaction type, retro-Michael-addition, for three consecutive dehydration steps. The overall barrier is determined to be 1.91 eV, being at least 0.19 eV lower than all previously proposed mechanisms, which assumes direct β-H elimination dehydration. The lowest pathways to the other two major products, furfural (FF) and hydroxyacetaldehyde (HAA), are also discovered with a similar barrier 1.95 eV, which exhibit a competing nature by sharing the same key intermediate, 3-ketohexose. Since chemical reactions occurring in fast glucose pyrolysis are generally present in biomass chemistry, containing essentially all reaction patterns of C-H-O elements, the methodology designed and the results presented would help to advance reaction design and mechanistic modeling in renewable fuels from biomass.

Modern research on heterogeneous catalysis calls for new techniques and methods to resolve the active site structure and reaction intermediates at the atomic scale. Here, we overview our recent progress on large-scale atomistic simulation via potential energy surface (PES) global optimization based on neural network (NN) potential, focusing on methodology details and recent applications on catalysis. The combination of stochastic surface walking (SSW) global optimization and the NN method provides a convenient and automated way to generate the transferable and robust NN potential for global PES, which can be utilized to reveal new chemistry from the unknown region of PES with an affordable computational cost. The predictive power of SSW-NN is demonstrated in several examples, where the method is applied to explore the material crystal phases, to follow the surface structure evolution under high pressure hydrogen and to determine the ternary oxide phase diagram. The limitations and future directions to develop the SSW-NN method are also discussed.

Photo-induced processes are fundamental in nature but accurate simulations are seriously limited by the cost of the underlying quantum chemical calculations, hampering their application for long time scales. Here we introduce a method based on machine learning to overcome this bottleneck and enable accurate photodynamics on nanosecond time scales, which are otherwise out of reach with contemporary approaches. Instead of expensive quantum chemistry during molecular dynamics simulations, we use deep neural networks to learn the relationship between a molecular geometry and its high-dimensional electronic properties. As an example, the time evolution of the methylenimmonium cation for one nanosecond is used to demonstrate that machine learning algorithms can outperform standard excited-state molecular dynamics approaches in their computational efficiency while delivering the same accuracy.

Metal oxide alloys (for example AxByOz) exhibit dramatically different catalytic properties in response to small changes in composition (the A:B ratio). Here, we show that for the ternary zinc–chromium oxide (ZnCrO) catalysts the activity and selectivity during syngas (CO/H2) conversion strongly depend on the Zn:Cr ratio. By using a global neural network potential, stochastic surface walking global optimization and first principles validation, we constructed a thermodynamics phase diagram for Zn–Cr–O that reveals the presence of a small stable composition island, that is, Zn:Cr:O = 6:6:16 to 3:8:16, where the oxide alloy crystallizes into a spinel phase. By changing the Zn:Cr ratio from 1:2 to 1:1, the ability to form oxygen vacancies increases appreciably and extends from the surface to the subsurface, in agreement with previous experiments. This leads to the critical presence of a four-coordinated planar Cr²⁺ cation that markedly affects the syngas conversion activity and selectivity to methanol, as further proved by microkinetics simulations.

In recent years, machine learning (ML) methods have become increasingly popular in computational chemistry. After being trained on appropriate ab initio reference data, these methods allow to accurately predict the properties of chemical systems, circumventing the need for explicitly solving the electronic Schrödinger equation. Because of their computational efficiency and scalability to large datasets, deep neural networks (DNNs) are a particularly promising ML algorithm for chemical applications. This work introduces PhysNet, a DNN architecture designed for predicting energies, forces and dipole moments of chemical systems. PhysNet achieves state-of-the-art performance on the QM9, MD17 and ISO17 benchmarks. Further, two new datasets are generated in order to probe the performance of ML models for describing chemical reactions, long-range interactions, and condensed phase systems. It is shown that explicitly including electrostatics in energy predictions is crucial for a qualitatively correct description of the asymptotic regions of a potential energy surface (PES). PhysNet models trained on a systematically constructed set of small peptide fragments (at most eight heavy atoms) are able to generalize to considerably larger proteins like deca-alanine (Ala10): The optimized geometry of helical Ala10 predicted by PhysNet is virtually identical to ab initio results (RMSD = 0.21 Å). By running unbiased molecular dynamics (MD) simulations of Ala10 on the PhysNet-PES in gas phase, it is found that instead of a helical structure, Ala10 folds into a "wreath-shaped" configuration, which is more stable than the helical form by 0.46 kcal mol⁻¹ according to the reference ab initio calculations.

An active learning procedure called deep potential generator (DP-GEN) is proposed for the construction of accurate and transferable machine learning-based models of the potential energy surface (PES) for the molecular modeling of materials. This procedure consists of three main components: exploration, generation of accurate reference data, and training. Application to the sample systems of Al, Mg, and Al-Mg alloys demonstrates that DP-GEN can produce uniformly accurate PES models with a minimal number of reference data.

Deep learning has led to a paradigm shift in artificial intelligence, including web, text, and image search, speech recognition, as well as bioinformatics, with growing impact in chemical physics. Machine learning, in general, and deep learning, in particular, are ideally suitable for representing quantum-mechanical interactions, enabling us to model nonlinear potential-energy surfaces or enhancing the exploration of chemical compound space. Here we present the deep learning architecture SchNet that is specifically designed to model atomistic systems by making use of continuous-filter convolutional layers. We demonstrate the capabilities of SchNet by accurately predicting a range of properties across chemical space for molecules and materials, where our model learns chemically plausible embeddings of atom types across the periodic table. Finally, we employ SchNet to predict potential-energy surfaces and energy-conserving force fields for molecular dynamics simulations of small molecules and perform an exemplary study on the quantum-mechanical properties of C20-fullerene that would have been infeasible with regular ab initio molecular dynamics.

We discuss a theoretical approach that employs machine learning potential energy surfaces (ML-PESs) in the nonadiabatic dynamics simulation of polyatomic systems by taking 6-aminopyrimidine as a typical example. The Zhu-Nakamura theory is employed in the surface hopping dynamics, which does not require the calculation of the nonadiabatic coupling vectors. The kernel ridge regression is used in the construction of the adiabatic PESs. In the nonadiabatic dynamics simulation, we use ML-PESs for most geometries and switch back to the electronic structure calculations for a few geometries either near the S1/S0 conical intersections or in the out-of-confidence regions. The dynamics results based on ML-PESs are consistent with those based on CASSCF PESs. The ML-PESs are further used to achieve the highly efficient massive dynamics simulations with a large number of trajectories. This work displays the powerful role of ML methods in the nonadiabatic dynamics simulation of polyatomic systems.

Recent developments in many-body potential energy representation via deep learning have brought new hopes to addressing the accuracy-versus-efficiency dilemma in molecular simulations. Here we describe DeePMD-kit, a package written in Python/C++ that has been designed to minimize the effort required to build deep learning based representation of potential energy and force field and to perform molecular dynamics. Potential applications of DeePMD-kit span from finite molecules to extended systems and from metallic systems to chemically bonded systems. DeePMD-kit is interfaced with TensorFlow, one of the most popular deep learning frameworks, making the training process highly automatic and efficient. On the other end, DeePMD-kit is interfaced with high-performance classical molecular dynamics and quantum (path-integral) molecular dynamics packages, i.e., LAMMPS and the i-PI, respectively. Thus, upon training, the potential energy and force field models can be used to perform efficient molecular simulations for different purposes. As an example of the many potential applications of the package, we use DeePMD-kit to learn the interatomic potential energy and forces of a water model using data obtained from density functional theory. We demonstrate that the resulted molecular dynamics model reproduces accurately the structural information contained in the original model.

The use of machine learning methods for accelerating the design of crystalline materials usually requires manually constructed feature vectors or complex transformation of atom coordinates to input the crystal structure, which either constrains the model to certain crystal types or makes it difficult to provide chemical insights. Here, we develop a crystal graph convolutional neural networks (CGCNN) framework to directly learn material properties from the connection of atoms in the crystal, providing a universal and interpretable representation of the crystals structure. Our method achieves the same accuracy as DFT for 8 different properties of crystals with various structure types and compositions after trained with $10^4$ data points. Further, our framework is interpretable because one can extract the contributions from local chemical environments to global properties. Using an example of perovskites, we show how this information can be utilized to discover empirical rules for materials design.

We introduce a new scheme for molecular simulations, based on a many-body potential and interatomic forces generated by a deep neural network trained with ab initio data. We show that the proposed scheme, which we call Deep Potential Molecular Dynamics (DeePMD), provides an efficient and accurate protocol in a variety of systems, including bulk materials and molecules. In all these cases, DeePMD gives results that are essentially indistinguishable from the original data, at a cost that scales linearly with system size. Moreover, in a few test cases, DeePMD shows good structural transferability to thermodynamic conditions not included in the original training data.

Deep learning is revolutionizing many areas of science and technology, especially image, text and speech recognition. In this paper, we demonstrate how a deep neural network (NN) trained on quantum mechanical (QM) DFT calculations can learn an accurate and fully transferable potential for organic molecules. We introduce ANAKIN-ME (Accurate NeurAl networK engINe for Molecular Energies) or ANI in short. ANI is a new method and procedure for training neural network potentials that utilizes a highly modified version of the Behler and Parrinello symmetry functions to build single-atom atomic environment vectors as a molecular representation. We utilize ANI to build a potential called ANI-1, which was trained on a subset of the GDB databases with up to 8 heavy atoms to predict total energies for organic molecules containing four atom types: H, C, N, and O. To obtain an accelerated but physically relevant sampling of molecular potential surfaces, we also propose a Normal Mode Sampling (NMS) method for generating molecular configurations. Through a series of case studies, we show that ANI-1 is chemically accurate compared to reference DFT calculations on much larger molecular systems (up to 54 atoms) than those included in the training data set, with root mean square errors as low as 0.56 kcal/mol.

Kohn-Sham density functionals are widely used; however, no currently available exchange-correlation functional can predict all chemical properties with chemical accuracy. Here we report a new functional, called MN15, that has broader accuracy than any previously available one. The properties considered in the parameterization include bond energies, atomization energies, ionization potentials, electron affinities, proton affinities, reaction barrier heights, noncovalent interactions, hydrocarbon thermochemistry, isomerization energies, electronic excitation energies, absolute atomic energies, and molecular structures. When compared with 82 other density functionals that have been defined in the literature, MN15 gives the second smallest mean unsigned error (MUE) for 54 data on inherently multiconfigurational systems, the smallest MUE for 313 single-reference chemical data, and the smallest MUE on 87 noncovalent data, with MUEs for these three categories of 4.75, 1.85, and 0.25 kcal/mol, respectively, as compared to the average MUEs of the other 82 functionals of 14.0, 4.63, and 1.98 kcal/mol. The MUE for 17 absolute atomic energies is 7.4 kcal/mol as compared to an average MUE of the other 82 functionals of 34.6 kcal/mol. We further tested MN15 for 10 transition-metal coordination energies, the entire S66x8 database of noncovalent interactions, 21 transition metal reaction barrier heights, 69 electronic excitation energies of organic molecules, 31 semiconductor band gaps, seven transition metal dimer bond lengths, and 193 bond lengths of 47 organic molecules. The MN15 functional not only performs very well for our training set, which has 481 pieces of data, but also performs very well for our test set, which has 823 data that are not in our training set. The test set includes both ground-state properties and molecular excitation energies. For the latter MN15 achieves simultaneous accuracy for both valence and Rydberg electronic excitations when used with linear-response time-dependent density functional theory, with an MUE of less than 0.3 eV for both types of excitations.

The reactive force-field (ReaxFF) interatomic potential is a powerful computational tool for exploring, developing and optimizing material properties. Methods based on the principles of quantum mechanics (QM), while offering valuable theoretical guidance at the electronic level, are often too computationally intense for simulations that consider the full dynamic evolution of a system. Alternatively, empirical interatomic potentials that are based on classical principles require significantly fewer computational resources, which enables simulations to better describe dynamic processes over longer timeframes and on larger scales. Such methods, however, typically require a predefined connectivity between atoms, precluding simulations that involve reactive events. The ReaxFF method was developed to help bridge this gap. Approaching the gap from the classical side, ReaxFF casts the empirical interatomic potential within a bond-order formalism, thus implicitly describing chemical bonding without expensive QM calculations. This article provides an overview of the development, application, and future directions of the ReaxFF method.

Nose has modified Newtonian dynamics so as to reproduce both the canonical and the isothermal-isobaric probability densities in the phase space of an N-body system. He did this by scaling time (with s) and distance (with VÂ¹D/ in D dimensions) through Lagrangian equations of motion. The dynamical equations describe the evolution of these two scaling variables and their two conjugate momenta p/sub s/ and p/sub v/. Here we develop a slightly different set of equations, free of time scaling. We find the dynamical steady-state probability density in an extended phase space with variables x, p/sub x/, V, epsilon-dot, and zeta, where the x are reduced distances and the two variables epsilon-dot and zeta act as thermodynamic friction coefficients. We find that these friction coefficients have Gaussian distributions. From the distributions the extent of small-system non-Newtonian behavior can be estimated. We illustrate the dynamical equations by considering their application to the simplest possible case, a one-dimensional classical harmonic oscillator.

A global potential energy surface for the H2 + OH ↔ H2O + H reaction has been constructed using the neural networks method based on ∼17 000 ab initio energies calculated at UCCSD(T)-F12a/AVTZ level of theory. Time-dependent wave packet calculations showed that the new potential energy surface is very well converged with respect to the number of ab initio data points, as well as to the fitting process. Various tests revealed that the new surface is considerably more smooth and accurate than the existing YZCL2 and XXZ surfaces, representing the best available potential energy surface for the benchmark four-atom system. Equally importantly, the number of ab initio energies required to obtain the well converged potential energy surface is rather limited, indicating the neural network fitting is a powerful method to construct accurate potential energy surfaces for polyatomic reactions.

We present the GPU version of DeePMD-kit, which, upon training a deep neural network model using ab initio data, can drive extremely large-scale molecular dynamics (MD) simulation with ab initio accuracy. Our tests show that for a water system of 12,582,912 atoms, the GPU version can be 7 times faster than the CPU version under the same power consumption. The code can scale up to the entire Summit supercomputer. For a copper system of 113,246,208 atoms, the code can perform one nanosecond MD simulation per day, reaching a peak performance of 86 PFLOPS (43% of the peak). Such unprecedented ability to perform MD simulation with ab initio accuracy opens up the possibility of studying many important issues in materials and molecules, such as heterogeneous catalysis, electrochemical cells, irradiation damage, crack propagation, and biochemical reactions.
Program summary
Program Title: DeePMD-kit
CPC Library link to program files: https://doi.org/10.17632/phyn4kgsfx.1
Developer’s repository link: https://doi.org/10.5281/zenodo.3961106
Licensing provisions: LGPL
Programming language: C++/Python/CUDA
Journal reference of previous version: Comput. Phys. Commun. 228 (2018), 178–184.
Does the new version supersede the previous version?: Yes.
Reasons for the new version: Parallelize and optimize the DeePMD-kit for modern high performance computers.
Summary of revisions: The optimized DeePMD-kit is capable of computing 100 million atoms molecular dynamics with ab initio accuracy, achieving 86 PFLOPS in double precision.
Nature of problem: Modeling the many-body atomic interactions by deep neural network models. Running molecular dynamics simulations with the models.
Solution method: The Deep Potential for Molecular Dynamics (DeePMD) method is implemented based on the deep learning framework TensorFlow. Standard and customized TensorFlow operators are optimized for GPU. Massively parallel molecular dynamics simulations with DeePMD models on high performance computers are supported in the new version.

We introduce a deep neural network to model in a symmetry preserving way the environmental dependence of the centers of the electronic charge. The model learns from ab initio density functional theory, wherein the electronic centers are uniquely assigned by the maximally localized Wannier functions. When combined with the deep potential model of the atomic potential energy surface, the scheme predicts the dielectric response of insulators for trajectories inaccessible to direct ab initio simulation. The scheme is nonperturbative and can capture the response of a mutating chemical environment. We demonstrate the approach by calculating the infrared spectra of liquid water at standard conditions, and of ice under extreme pressure, when it transforms from a molecular to an ionic crystal.

A thorough understanding of the kinetics and dynamics of combusting mixtures is of considerable interest, especially in regimes beyond the reach of current experimental validation. The ReaxFF reactive force field method has provided a way to simulate large-scale systems of hydrogen combustion via a parameterized potential that can simulate bond breaking. This modeling approach has been applied to hydrogen combustion, as well as myriad other reactive chemical systems. In this work, we benchmark the performance of several common parameterizations of this potential against higher-level quantum mechanical (QM) approaches. We demonstrate instances where these parameterizations of the ReaxFF potential fail both quantitatively and qualitatively to describe reactive events relevant for hydrogen combustion systems.

The recombination dynamics of 3P oxygen atoms on cold amorphous solid water to form triplet and singlet molecular oxygen (O2) is investigated under conditions representative of cold clouds. Reactive molecular dynamics simulations including Landau-Zener-based hopping to account for nonadiabatic transitions find that both ground-state (X3Σ
g
-) O2 and molecular oxygen in the two lowest singlet states (a1Δ
g
and b1Σ
g
+) can be formed and the molecular species stabilize through vibrational relaxation. The relative populations of the species are approximately 1:1:1. These results also agree qualitatively with a kinetic model based on simplified wavepacket simulations. The presence and stabilization of higher electronic states of O2 are expected to modify the chemical evolution of cold interstellar (T ∼ 10-50 K) and warmer noctilucent (T ∼ 100 K) clouds.

In recent years, promising deep learning based interatomic potential energy surface (PES) models have been proposed that can potentially allow us to perform molecular dynamics simulations for large scale systems with quantum accuracy. However, making these models truly reliable and practically useful is still a very non-trivial task. A key component in this task is the generation of datasets used in model training. In this paper, we introduce the Deep Potential GENerator (DP-GEN), an open-source software platform that implements the recently proposed ”on-the-fly” learning procedure (Zhang et al. 2019) and is capable of generating uniformly accurate deep learning based PES models in a way that minimizes human intervention and the computational cost for data generation and model training. DP-GEN automatically and iteratively performs three steps: exploration, labeling, and training. It supports various popular packages for these three steps: LAMMPS for exploration, Quantum Espresso, VASP, CP2K, etc. for labeling, and DeePMD-kit for training. It also allows automatic job submission and result collection on different types of machines, such as high performance clusters and cloud machines, and is adaptive to different job management tools, including Slurm, PBS, and LSF. As a concrete example, we illustrate the details of the process for generating a general-purpose PES model for Cu using DP-GEN.
Program summary
Program Title: DP-GEN
Program Files doi: http://dx.doi.org/10.17632/sxybkgc5xc.1
Licensing provisions: LGPL
Programming language: Python
Nature of problem: Generating reliable deep learning based potential energy models with minimal human intervention and computational cost.
Solution method: The concurrent learning scheme is implemented. Supports for sampling configuration space with LAMMPS, generating ab initio data with Quantum Espresso, VASP, CP2K and training potential models with DeePMD-kit are provided. Supports for different machines including workstations, high performance clusters and cloud machines are provided. Supports for job management tools including Slurm, PBS, LSF are provided.

Reactive molecular dynamics (MD) simulation makes it possible to study the reaction mechanisms of complex reaction systems at the atomic level. However, the analysis of the MD trajectories which contain thousands of species and reaction pathways has become a major obstacle to the application of reactive MD simulation in large-scale systems. Here, we report the development and application of the Reaction Network Generator (ReacNetGenerator) method. It can automatically extract the reaction network from the reaction trajectory without any predefined reaction coordinates and elementary reaction steps. Molecular species can be automatically identified from the cartesian coordinates of atoms and the hidden Markov model is used to filter the trajectory noises which makes the analysis process easier and more accurate. The ReacNetGenerator has been successfully used to analyze the reactive MD trajectories of the combustion of methane and 4-component surrogate fuel for rocket propellant 3 (RP-3), and it has great advantages in efficiency and accuracy compared to traditional manual analysis.

We propose a simple, but efficient and accurate machine learning (ML) model for developing high-dimensional potential energy surface. This so-called embedded atom neural network (EANN) approach is inspired by the well-known empirical embedded atom method (EAM) model used in condensed phase. It simply replaces the scalar embedded atom density in EAM with a Gaussian-type orbital based density vector, and represents the complex relationship between the embedded density vector and atomic energy by neural networks. We demonstrate that the EANN approach is equally accurate as several established ML models in representing both big molecular and extended periodic systems, yet with much fewer parameters and configurations. It is highly efficient as it implicitly contains the three-body information without an explicit sum of the conventional costly angular descriptors. With high accuracy and efficiency, EANN potentials can vastly accelerate molecular dynamics and spectroscopic simulations in complex systems at ab initio level.

High-temperature, reactive gas flow is inherently nonequilibrium in terms of energy and state population distributions. Modeling such conditions is challenging even for the smallest molecular systems due to the extremely large number of accessible states and transitions between them. Here, neural networks (NNs) trained on explicitly simulated data are constructed and shown to provide quantitatively realistic descriptions which can be used in mesoscale simulation approaches such as Direct Simulation Monte Carlo to model gas flow at the hypersonic regime. As an example, the state-to-state cross sections for N(⁴S) + NO(²Π) → O(³P) + N2(X1Σg+) are computed from quasiclassical trajectory (QCT) simulations. By training NNs on a sparsely sampled noisy set of state-to-state cross sections, it is demonstrated that independently generated reference data are predicted with high accuracy. State-specific and total reaction rates as a function of temperature from the NN are in quantitative agreement with explicit QCT simulations and confirm earlier simulations, and the final state distributions of the vibrational and rotational energies agree as well. Thus, NNs trained on physical reference data can provide a viable alternative to computationally demanding explicit evaluation of the microscopic information at run time. This will considerably advance the ability to realistically model nonequilibrium ensembles for network-based simulations.

In this work we show that deep learning (DL) can be used for exploring complex and highly nonlinear multi-state potential energy surfaces of polyatomic molecules and related nonadiabatic dynamics. Our DL is based on deep neural networks (DNNs), which are used as accurate representations of the CASSCF ground- and excited-state potential energy surfaces (PESs) of CH2NH. After including geometries near conical intersection in the training set, the DNN models accurately reproduce excited-state topological structures, photoisomerization paths, and, importantly, conical intersections. We have also demonstrated that the results from nonadiabatic dynamics run with the DNN models are very close to those from the dynamics run with the pure ab initio method. The present work should encourage further studies of using machine learning methods to explore excited-state potential energy surfaces and nonadiabatic dynamics of polyatomic molecules.

The C + NO collision system is of interest in the area of high-temperature combustion and atmospheric chemistry. In this work, full dimensional potential energy surfaces for the ²A′, ²A″, and ⁴A″ electronic states of the [CNO] system have been constructed following a reproducing kernel Hilbert space approach. For this purpose, more than 50 000 ab initio energies are calculated at the MRCI+Q/aug-cc-pVTZ level of theory. The dynamical simulations for the C(³P) + NO(X²Π) → O(³P) + CN(X²Σ⁺), N(²D)/N(⁴S) + CO(X¹Σ⁺) reactive collisions are carried out on the newly generated surfaces using the quasiclassical trajectory (QCT) calculation method to obtain reaction probabilities, rate coefficients, and the distribution of product states. Preliminary quantum calculations are also carried out on the surfaces to obtain the reaction probabilities and compared with QCT results. The effect of nonadiabatic transitions on the dynamics for this title reaction is explored within the Landau-Zener framework. QCT simulations have been performed to simulate molecular beam experiment for the title reaction at 0.06 and 0.23 eV of relative collision energies. Results obtained from theoretical calculations are in good agreement with the available experimental as well as theoretical data reported in the literature. Finally, the reaction is studied at temperatures that are not practically achievable in the laboratory environment to provide insight into the reaction dynamics at temperatures relevant to hypersonic flight.

The current status of reactive molecular dynamics (MD) simulations is summarized. Both, methodological aspects and applications to problems ranging from gas phase reaction dynamics to ligand‐binding in solvated proteins are discussed, focusing on extracting information from simulations that cannot easily be obtained from experiments alone. One specific example is the structural interpretation of the ligand rebinding time scales extracted from state‐of‐the art time‐resolved experiments. Atomistic simulations employing validated reactive interaction potentials are capable of providing structural information about the time scales involved. Both, merits and shortcomings of the various methods are discussed and the outlook summarizes possible future avenues such as reactive potentials based on machine learning techniques.
This article is categorized under:
• Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods
• Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics
• Molecular and Statistical Mechanics > Molecular Interactions

n-Dodecane combustion was investigated experimentally and numerically in present study. Pyrolysis experiments of n-dodecane at pressures of 0.0066, 0.039, 0.197 and 1 atm, temperatures from 750 to 1430 K were studied in a flow reactor. Mole fractions of n-dodecane, argon and pyrolysis products (including active radicals) were evaluated. A kinetic model of n-dodecane was developed by validating both present and literature reported experiments. The rate of production analysis reveals H-abstraction and C–C bond fission reactions are main consumption pathways of n-dodecane. The β-C–C scission reactions of alkyls contribute to the formation of alkenes, which are mainly consumed via the allylic C–C fission reactions. As a soot precursor, benzene is largely produced from the recombination of C3 species. Moreover, effects of carbon chain length on flow reactor pyrolysis were investigated for n-decane, n-dodecane and n-tetradecane. The decay of n-tetradecane is the fastest, followed by n-dodecane and n-decane, indicating that the pyrolysis reactivity of n-alkanes increases as the carbon chain length increases from C10 to C14 n-alkanes. Ignition delay times and laminar burning velocities (LBVs) of n-alkanes under similar conditions were also compared, the result shows that effects of the carbon chain length on ignition delay times and LBVs are slight.

Despite the ever-increasing computer power, accurate ab initio calculations for large systems (thousands to millions of atoms) remain infeasible. Instead, approximate empirical energy functions are used. Most current approaches are either transferable between different chemical systems, but not particularly accurate, or they are fine-tuned to a specific application. In this work, a data-driven method to construct a potential energy surface based on neural networks is presented. Since the total energy is decomposed into local atomic contributions, the evaluation is easily parallelizable and scales linearly with system size. With prediction errors below 0.5 kcal mol⁻¹ for both unknown molecules and configurations, the method is accurate across chemical and configurational space, which is demonstrated by applying it to datasets from nonreactive and reactive molecular dynamics simulations and a diverse database of equilibrium structures. The possibility to use small molecules as reference data to predict larger structures is also explored. Since the descriptor only uses local information, high-level ab initio methods, which are computationally too expensive for large molecules, become feasible for generating the necessary reference data used to train the neural network.

Reactive force field (Reaxff) is a powerful method, which employs bond order/bond length formulism in order to describe the bond breaking and bond re-formation. In this work, a modification to the bond order formula was made and Reaxff parameters were re-optimized. The underlying idea of these modifications is to improve the energy gradient. Better agreements of the bond dissociation potential curves with the QM curves were obtained based on the aforementioned changes. Reaxff simulation was carried out to gain the understandings of the iso-octane pyrolysis. The new parameters based apparent rate constants of the iso-octane decomposition fit well with the experimental results. The simulation results are in agreement with the existing experimental results. A maximum of C2-hydrocarbons were found to have the largest percentage. And distribution of the iso-octane decomposition pathway was illustrated.

A detailed insight of key reactive events related to oxidation and pyrolysis of hydrocarbon fuels further enhances our understanding of combustion chemistry. Though comprehensive kinetic models are available for smaller hydrocarbons (typically C3 or lower), developing and validating reaction mechanisms for larger hydrocarbons is a daunting task, due to the complexity of their reaction networks. The ReaxFF method provides an attractive computational method to obtain reaction kinetics for complex fuel and fuel mixtures, providing an accuracy approaching ab-initio based methods, but with a significantly lower computational expense. The development of the first ReaxFF combustion force field by Chenoweth et al. (CHO-2008 parameter set) in 2008 has opened new avenues for researchers to investigate combustion chemistry from atomistic-level. In this manuscript, we seek to address two issues with the CHO-2008 ReaxFF description. While the CHO-2008 description has achieved significant popularity for studying large hydrocarbon combustion, it fails to accurately describe the chemistry of small hydrocarbon oxidation, especially conversion of CO2 from CO, which is highly relevant to syngas combustion. Additionally, CHO-2008 description obtained faster than expected H-abstraction by O2 from hydrocarbons, thus underestimating the oxidation initiation temperature. In this study, we seek to systemically improve CHO-2008 description and validate it for these cases. Additionally, our aim was to retain the accuracy of the 2008 description for larger hydrocarbons and provide similar quality results. Thus, we expanded the ReaxFF CHO-2008 DFT-based training set by including reactions and transition state structures relevant to the syngas and oxidation initiation pathways and re-trained the parameters. To validate the quality of our force field, we performed high temperature NVT-MD simulations to study oxidation and pyrolysis of four different hydrocarbon fuels, namely syngas, methane, JP-10 and n-butylbenzene. Results obtained from syngas and methane oxidation simulation indicated that our re-developed parameters (named as CHO-2016 parameter set) has significantly improved the C1 chemistry predicted by ReaxFF and has solved the low temperature oxidation initiation problem. Moreover, Arrhenius parameters of JP-10 decomposition and initiation mechanism pathways of n-butylbenzene pyrolysis obtained using CHO-2016 parameter set are also in good agreement with both experimental and CHO-2008 simulation results. This demonstrated the transferability of CHO-2016 description for a wide range of hydrocarbon chemistry.

A more flexible neural network (NN) method using the fundamental invariants (FIs) as the input vector is proposed in the construction of potential energy surfaces for molecular systems involving identical atoms. Mathematically, FIs finitely generate the permutation invariant polynomial (PIP) ring. In combination with NN, fundamental invariant neural network (FI-NN) can approximate any function to arbitrary accuracy. Because FI-NN minimizes the size of input permutation invariant polynomials, it can efficiently reduce the evaluation time of potential energy, in particular for polyatomic systems. In this work, we provide the FIs for all possible molecular systems up to five atoms. Potential energy surfaces for OH3 and CH4 were constructed with FI-NN, with the accuracy confirmed by full-dimensional quantum dynamic scattering and bound state calculations.

Electronic structure calculations, such as those employing Kohn–Sham density functional theory or ab initio wavefunction theories, have allowed for atomistic-level understandings of a wide variety of phenomena and properties of matter at small scales. However, the computational cost of electronic structure methods drastically increases with length and time scales, which makes these methods difficult for long time-scale molecular dynamics simulations or large-sized systems. Machine-learning techniques can provide accurate potentials that can match the quality of electronic structure calculations, provided sufficient training data. These potentials can then be used to rapidly simulate large and long time-scale phenomena at similar quality to the parent electronic structure approach. Machine-learning potentials usually take a bias-free mathematical form and can be readily developed for a wide variety of systems. Electronic structure calculations have favorable properties—namely that they are noiseless and targeted training data can be produced on-demand—that make them particularly well-suited for machine learning. This paper discusses our modular approach to atomistic machine learning through the development of the open-source Atomistic Machine-learning Package (Amp), which allows for representations of both the total and atom-centered potential energy surface, in both periodic and non-periodic systems. Potentials developed through the atom-centered approach are simultaneously applicable for systems with various sizes. Interpolation can be enhanced by introducing custom descriptors of the local environment. We demonstrate this in the current work for Gaussian-type, bispectrum, and Zernike-type descriptors. Amp has an intuitive and modular structure with an interface through the python scripting language yet has parallelizable fortran components for demanding tasks; it is designed to integrate closely with the widely used Atomic Simulation Environment (ASE), which makes it compatible with a wide variety of commercial and open-source electronic structure codes. We finally demonstrate that the neural network model inside Amp can accurately interpolate electronic structure energies as well as forces of thousands of multi-species atomic systems.

Initiator could accelerate the rate of hydrocarbon pyrolysis and reduce the required material temperatures for a hypersonic aircraft heat exchanger/reactor. Nitroalkanes were proposed as the effective initiator because of the lower CN bond dissociation energy. In order to investigate the initiation mechanism of nitroalkanes on hydrocarbon pyrolysis, the pyrolysis of n-decane, nitromethane and their binary mixture were carried out at 30, 150 and 760 Torr in a flow reactor with synchrotron vacuum ultraviolet photoionization mass spectrometry (SVUV-PIMS). The identified and quantified pyrolysis species include C1C2 alkanes, C2C10 alkenes, C3C6 dialkenes, C2C3 alkynes, nitrogen oxides such as NO and NO2, benzene, and radicals including CH3, C3H3, and C3H5, which shed light on the mechanism of n-decane and nitromethane pyrolysis, as well as the interactions of these two fuels. The experimental results indicate that the addition of nitromethane decreases the initial decomposition temperature of n-decane, and a stronger promotion effect could be obtained as the experimental pressure increases. The distributions of alkanes, alkenes, dialkenes, alkynes and benzene are also influenced by the addition of nitromethane. A detailed kinetic model with 266 species and 1648 reactions was developed and validated against the mole fraction profiles of reactants, major products and important intermediates during the pyrolysis of each fuel and their binary mixture. The satisfactory model prediction to the experimental measurements permits the analysis of the kinetic effect of nitromethane initiation on the pyrolysis of n-decane. So that, the increase of the conversion rate at a lower temperature, the selectivity of decomposition products, and reduction of benzene formation are better understood.

The current study investigates n-dodecane (n-C12H26) pyrolysis and oxidation kinetics in the temperature regime of 1000-1300 K in the Stanford Variable Pressure Flow Reactor facility. The reactor environment is vitiated and the experiments were conducted at atmospheric pressure. Species time history data were collected for n-dodecane and oxygen, as well as for 12 intermediate and product species over a span of 1-40 ms residence times using real time gas chromatography. The experimental data were compared against the predictions of four detailed kinetic models. The results showed that the fuel oxidation proceeds through an early pyrolytic stage where the fuel breaks down into smaller hydrocarbon fragments, including mostly C2-4 alkenes, and a late oxidation stage where the fragments oxidize to CO. The kinetic models were observed to diverge notably in their predictions from one another. Sensitivity and flux analysis identified the cause of the divergences to differences in the small hydrocarbon chemistry modeling. Finally, the flow reactor data were used to demonstrate how model uncertainty minimization can improve model predictions. It is shown that after uncertainty minimization against a selected set of n-dodecane combustion data, the predictions of the resulting optimized model are improved notably for all existing n-dodecane data sets tested, including those of the current flow reactor study that were not part of the optimization target list.

A short overview is presented of the density functional theory and molecular dynamics (DFT–MD) method and of a code (CPMD) based on a plane wave scheme. Its power is shown through the survey of specific applications to diverse frontier areas of chemistry and materials science that make use of parallel computing.

We present a swift walk-through of our recent work that uses machine learning to fit interatomic potentials based on quantum mechanical data. We describe our Gaussian approximation potentials (GAP) framework, discuss a variety of descriptors, how to train the model on total energies and derivatives, and the simultaneous use of multiple models of different complexity. We also show a small example using QUIP, the software sandbox implementation of GAP that is available for noncommercial use. © 2015 Wiley Periodicals, Inc.

To make practical the molecular dynamics simulation of large scale reactive chemical systems (1000s of atoms), we developed ReaxFF, a force field for reactive systems. ReaxFF uses a general relationship between bond distance and bond order on one hand and between bond order and bond energy on the other hand that leads to proper dissociation of bonds to separated atoms. Other valence terms present in the force field (angle and torsion) are defined in terms of the same bond orders so that all these terms go to zero smoothly as bonds break. In addition, ReaxFF has Coulomb and Morse (van der Waals) potentials to describe nonbond interactions between all atoms (no exclusions). These nonbond interactions are shielded at short range so that the Coulomb and van der Waals interactions become constant as R-ij --> 0. We report here the ReaxFF for hydrocarbons. The parameters were derived from quantum chemical calculations on bond dissociation and reactions of small molecules plus heat of formation and geometry data for a number of stable hydrocarbon compounds. We find that the ReaxFF provides a good description of these data. Generally, the results are of an accuracy similar or better than PM3, while ReaxFF is about 100 times faster. In turn, the PM3 is about 100 times faster than the QC calculations. Thus, with ReaxFF we hope to be able to study complex reactions in hydrocarbons.

cp2k has become a versatile open-source tool for the simulation of complex systems on the nanometer scale. It allows for sampling and exploring potential energy surfaces that can be computed using a variety of empirical and first principles models. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern and massively parallel hardware. This review briefly summarizes the main capabilities and illustrates with recent applications the science cp2k has enabled in the field of atomistic simulation. WIREs Comput Mol Sci 2014, 4:15–25. doi: 10.1002/wcms.1159 The authors have declared no conflicts of interest in relation to this article. For further resources related to this article, please visit the WIREs website.

High pressure n-decane and n-dodecane shock tube experiments were conducted to assist in the development of a Jet A surrogate kinetic model. Jet A is a kerosene based jet fuel composed of hundreds of hydrocarbons consisting of paraffins, olefins, aromatics and naphthenes. In the formulation of the surrogate mixture, n-decane or n-dodecane represent the normal paraffin class of hydrocarbons present in aviation fuels like Jet A. The experimental work on both n-alkanes was performed in a heated high pressure single pulse shock tube. The mole fractions of the stable species were determined using gas chromatography and mass spectroscopy. Experimental data on both n-decane and n-dodecane oxidation and pyrolysis were obtained for temperatures from 867 to 1739 K, pressures from 19 to 74 atm, reaction times from 1.15 to 3.47 ms, and equivalence ratios from 0.46 to 2.05, and ∞. Both n-decane and n-dodecane oxidation showed that the fuel decays through thermally driven oxygen free decomposition at the conditions studied. This observation prompted an experimental and modeling study of n-decane and n-dodecane pyrolysis using a recently submitted revised n-decane/iso-octane/toluene surrogate model. The surrogate model was extended to n-dodecane in order to facilitate the study of the species and the 1-olefin species quantified during the pyrolysis of n-dodecane and n-decane were revised with additional reactions and reaction rate constants modified with rate constants taken from literature. When compared against a recently published generalized n-alkane model and the original and revised surrogate models, the revised (based on our experimental work) and extended surrogate model showed improvements in predicting 1-olefin species profiles from pyrolytic and oxidative n-decane and n-dodecane experiments. The revised and extended model when compared to the published generalized n-alkane and surrogate models also showed improvements in predicting species profiles from flow reactor n-decane oxidation experiments, but similarly predicted n-decane and n-dodecane ignition delay times.

A simple, general, and rigorous scheme for adapting permutation symmetry in molecular systems is proposed and tested for fitting global potential energy surfaces using neural networks (NNs). The symmetry adaptation is realized by using low-order permutation invariant polynomials (PIPs) as inputs for the NNs. This so-called PIP-NN approach is applied to the H + H2 and Cl + H2 systems and the analytical potential energy surfaces for these two systems were accurately reproduced by PIP-NN. The accuracy of the NN potential energy surfaces was confirmed by quantum scattering calculations.

For pyrolysis of n-tetradecane at 450 C under elevated pressures (about 2--9 MPa) for 6--480 min, the major products in the early stage are n-alkanes in the carbon number range of C[sub 1]-C[sub 11] and 1-alkenes in the carbon number range of C[sub 2]-C[sub 14]. Formation of the olefinic product with 13 carbon atoms is very limited, but 1-C[sub 12]H[sub 24] is as abundant as the 1-alkenes in the range of C[sub 2]-C[sub 11]. As compared to the well-known gas-phase pyrolysis, the molar ratios of alkenes to alkanes are much smaller ([le]1), except the ratio for the group with 12 carbon atoms where the 1-C[sub 12]H[sub 24]/n-C[sub 12]H[sub 26] ratio can be as high as 9 in the early stage. This is because 1-C[sub 12]H[sub 24] is produced from [beta]-scission of a secondary 4-C[sub 14]H[sub 29] radical, whereas n-C[sub 12]H[sub 26] is formed from a primary 1-C[sub 14]H[sub 29] radical, whose population is much less than the secondary radical due to both higher activation energy and the competing isomerization reaction. There appeared a preferential formation of 1-C[sub 6]H[sub 12] and 1-C[sub 5]H[sub 10] among the 1-alkenes formed after 12 min. This may be attributed to the 1,5-shift and 1,4-shift isomerization of primary radicals formed during tetradecane pyrolysis. The peak of carbon number distribution shifts toward 2 for paraffinic products and toward 3 for olefinic products, and the ratios of alkenes to alkanes decrease with increasing residence time up to 60 min. The general reaction mechanism is characterized by the one-step decomposition of secondary radicals and the 1,5 and 1,4-shift isomerization of primary radicals to secondary radicals. The substrate alkane molecules are the source for hydrogen abstraction in the early stage, but in the later stages the olefinic products also undergo the H-abstraction reactions, which lead to the formation of cyclic alkenes/alkanes and alkylaromatics.

Thermal decomposition of n-decane is studied in a flow reactor heated by high-frequency induction around 810 °C (1083 K). The main products, determined by gas-phase chromatography, are hydrogen, methane, ethylene, and C3 to C9 α-olefins. A theoretical chain radical mechanism indicates that these compounds should be primary products. We estimate the importance of intramolecular isomerizations by 1,4- and 1,5-hydrogen transfer (transition states with five and six centers, including H) with respect to other elementary processes for bond breaking. Nine theoretical and independent main primary stoichiometries can be deduced from this radical mechanism. Secondary products are also formed. The main secondary products are benzene, toluene, and 1,3-butadiene. To qualitatively interpret the formation of these products (initial rate zero), elementary processes, including the main primary products, are proposed.