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Chemical processes taking place on ice-grain mantles are pivotal to the complex chemistry of interstellar environments. In this study, we conducted a comprehensive analysis of the catalytic effects of an amorphous solid water (ASW) surface on the reaction between ammonia (NH$_3$) and formaldehyde (H$_2$CO) to form aminomethanol (NH$_2$CH$_2$OH) using density functional theory. We identified potential catalytic sites based on the binding energy distribution of NH$_3$ and H$_2$CO reactants, on a set-of-clusters surface model composed of 22 water molecules and found a total of 14 reaction paths. Our results indicate that the catalytic sites can be categorized into four groups, depending on the interactions of the carbonyl oxygen and the amino group with the ice surface in the reactant complex. A detailed analysis of the reaction mechanism using Intrinsic Reaction Coordinate and reaction force analysis revealed three distinct chemical events for this reaction: formation of the C--N bond, breaking of the N--H bond, and formation of the O--H hydroxyl bond. Depending on the type of catalytic site, these events can occur within a single, concerted, albeit asynchronous, step, or can be isolated in a step-wise mechanism, with the lowest overall transition state energy observed at 1.3 kcal mol$^{-1}$. A key requirement for the low-energy mechanism is the presence of a pair of dangling OH bonds on the surface, found at 5\% of the potential catalytic sites on an ASW porous surface.

The past decade has seen tremendous breakthroughs in computation and there is no indication that this will slow any time soon. Machine learning, large-scale computing resources, and increased industry focus have resulted in rising investments in computer-driven solutions for data management, simulations, and model generation. However, with this growth in computation has come an even larger expansion of data and with it, complexity in data storage, sharing, and tracking. In this work, we introduce ZnTrack, a Python-driven data versioning tool. ZnTrack builds upon established version control systems to provide a user-friendly and easy-to-use interface for tracking parameters in experiments, designing workflows, and storing and sharing data. From this ability to reduce large datasets to a simple Python script emerges the concept of Data as Code, a core component of the work presented here and an undoubtedly important concept as the age of computation continues to evolve. ZnTrack offers an open-source, FAIR data compatible Python package to enable users to harness these concepts of the future., Comment: 22 pages, 10 figures, 2MB PDF

We propose a machine learning method to model molecular tensorial quantities, namely the magnetic anisotropy tensor, based on the Gaussian-moment neural-network approach. We demonstrate that the proposed methodology can achieve an accuracy of 0.3--0.4 cm$^{-1}$ and has excellent generalization capability for out-of-sample configurations. Moreover, in combination with machine-learned interatomic potential energies based on Gaussian moments, our approach can be applied to study the dynamic behavior of magnetic anisotropy tensors and provide a unique insight into spin-phonon relaxation.

Efficiently creating a concise but comprehensive data set for training machine-learned interatomic potentials (MLIPs) is an under-explored problem. Active learning (AL), which uses either biased or unbiased molecular dynamics (MD) simulations to generate candidate pools, aims to address this objective. Existing biased and unbiased MD simulations, however, are prone to miss either rare events or extrapolative regions -- areas of the configurational space where unreliable predictions are made. Simultaneously exploring both regions is necessary for developing uniformly accurate MLIPs. In this work, we demonstrate that MD simulations, when biased by the MLIP's energy uncertainty, effectively capture extrapolative regions and rare events without the need to know \textit{a priori} the system's transition temperatures and pressures. Exploiting automatic differentiation, we enhance bias-forces-driven MD simulations by introducing the concept of bias stress. We also employ calibrated ensemble-free uncertainties derived from sketched gradient features to yield MLIPs with similar or better accuracy than ensemble-based uncertainty methods at a lower computational cost. We use the proposed uncertainty-driven AL approach to develop MLIPs for two benchmark systems: alanine dipeptide and MIL-53(Al). Compared to MLIPs trained with conventional MD simulations, MLIPs trained with the proposed data-generation method more accurately represent the relevant configurational space for both atomic systems.

The accuracy of the training data limits the accuracy of bulk properties from machine-learned potentials. For example, hybrid functionals or wave-function-based quantum chemical methods are readily available for cluster data but effectively out-of-scope for periodic structures. We show that local, atom-centred descriptors for machine-learned potentials enable the prediction of bulk properties from cluster model training data, agreeing reasonably well with predictions from bulk training data. We demonstrate such transferability by studying structural and dynamical properties of bulk liquid water with density functional theory and have found an excellent agreement with experimental as well as theoretical counterparts.

Hydroxylamine, NH2OH, is one of the already detected interstellar molecules with the highest prebiotic potential. Yet, the abundance of this molecule found by astronomical observations is rather low for a relatively simple molecule, $\sim$ 10$^{-10}$ relative to H2. This seemingly low abundance can be rationalized by destruction routes operating on interstellar dust grains. In this work, we tested the viability of this hypothesis under several prisms, finding that the origin of a lower abundance of \ce{NH2OH} can be explained by two chemical processes, one operating at low temperature (10 K) and the other at intermediate temperature (20 K). At low temperatures, enabling the hydrogen abstraction reaction HNO + H -> NO + H2, even in small amounts, partially inhibits the formation of NH2OH through successive hydrogenation of NO, and reduces its abundance on the grains. We found that enabling a 15--30 % of binding sites for this reaction results in reductions of \ce{NH2OH} abundance of $\sim$ 1-2 orders of magnitude. At warmer temperatures (20 K, in our study), the reaction NH2OH + H -> HNOH + H2, which was found to be fast (k$\sim$10$^{6}$ s$^{-1}$) in this work, followed by further abstractions by adsorbates that are immobile at 10 K (O, N) are the main route of \ce{NH2OH} destruction. Our results shed light on the abundance of hydroxylamine in space and pave the way to constraining the subsequent chemistry experienced by this molecule and its derivatives in the interstellar prebiotic chemistry canvas., Comment: Accepted for publication in MNRAS

Energy redistribution after a chemical reaction is one of the few mechanisms to explain the diffusion and desorption of molecules which require more energy than the thermal energy available in quiescent molecular clouds (10 K). This energy distribution can be important in phosphorous hydrides, elusive yet fundamental molecules for interstellar prebiotic chemistry. We studied the reaction dynamics of the \ce{P + H -> PH} reaction on amorphous solid water, a reaction of astrophysical interest, using \emph{ab-initio} molecular dynamics with atomic forces evaluated by a neural network interatomic potential. We found that the exact nature of the initial phosphorous binding sites is less relevant for the energy dissipation process because the nascent PH molecule rapidly migrates to sites with higher binding energy after the reaction. Non-thermal diffusion and desorption-after-reaction were observed and occurred early in the dynamics, essentially decoupled from the dissipation of the chemical reaction energy. From an extensive sampling of reactions on sites, we constrained the average dissipated reaction energy within the simulation time (50 ps) to be between 50 and 70 %. Most importantly, the fraction of translational energy acquired by the formed molecule was found to be mostly between 1 and 5 %. Including these values, specifically for the test cases of 2% and 5% of translational energy conversion, in astrochemical models, reveals very low gas-phase abundances of PH$_{x}$ molecules and reflects that considering binding energy distributions is paramount for correctly merging microscopic and macroscopic modelling of non-thermal surface astrochemical processes. Finally, we found that PD molecules dissipate more of the reaction energy. This effect can be relevant for the deuterium fractionation and preferential distillation of molecules in the interstellar medium., Comment: Accepted for publication in Astronomy and Astrophysics

Developing machine learning-based interatomic potentials from ab-initio electronic structure methods remains a challenging task for computational chemistry and materials science. This work studies the capability of transfer learning, in particular discriminative fine-tuning, for efficiently generating chemically accurate interatomic neural network potentials on organic molecules from the MD17 and ANI data sets. We show that pre-training the network parameters on data obtained from density functional calculations considerably improves the sample efficiency of models trained on more accurate ab-initio data. Additionally, we show that fine-tuning with energy labels alone can suffice to obtain accurate atomic forces and run large-scale atomistic simulations, provided a well-designed fine-tuning data set. We also investigate possible limitations of transfer learning, especially regarding the design and size of the pre-training and fine-tuning data sets. Finally, we provide GM-NN potentials pre-trained and fine-tuned on the ANI-1x and ANI-1ccx data sets, which can easily be fine-tuned on and applied to organic molecules.

The isomerism of molecules in the interstellar medium and the mechanisms behind it are essential questions in the chemistry of organic molecules in space. In particular, for the simple formic and thioformic acids, the low temperatures found in molecular clouds indicate that cis-trans isomerization in the gas-phase must be impeded. Reactions happening on top of interstellar dust grains may explain the isomer interconversion at low temperatures. We studied the isomerization processes of formic and thioformic acid susceptible to happen on the surface of interstellar dust grains and initiated by H abstraction reactions. Similarly, deuterium enrichment of the acids can occur by the same mechanism. Our objective is to shed light on both topics to increase our understanding of key precursors of organic molecules in space., Comment: Accepted for publication in Astronomy and Astrophysics

The acquisition of labels for supervised learning can be expensive. To improve the sample efficiency of neural network regression, we study active learning methods that adaptively select batches of unlabeled data for labeling. We present a framework for constructing such methods out of (network-dependent) base kernels, kernel transformations, and selection methods. Our framework encompasses many existing Bayesian methods based on Gaussian process approximations of neural networks as well as non-Bayesian methods. Additionally, we propose to replace the commonly used last-layer features with sketched finite-width neural tangent kernels and to combine them with a novel clustering method. To evaluate different methods, we introduce an open-source benchmark consisting of 15 large tabular regression data sets. Our proposed method outperforms the state-of-the-art on our benchmark, scales to large data sets, and works out-of-the-box without adjusting the network architecture or training code. We provide open-source code that includes efficient implementations of all kernels, kernel transformations, and selection methods, and can be used for reproducing our results., Comment: Published at the Journal of Machine Learning Research (JMLR). Changes in v4: Improvements in writing and other minor changes. Accompanying code can be found at https://github.com/dholzmueller/bmdal_reg

Sorption of gases in micro- and mesoporous materials is typically interpreted on the basis of idealized structural models where real structure effects such as defects and disorder are absent. For covalent organic frameworks (COFs) significant discrepancies between measured and simulated adsorption isotherms are often reported but rarely traced back to their origins. This is because little is known about the real structure of COFs and its effect on the sorption properties of these materials. In the present work molecular simulations are used to obtain adsorption isotherms of argon, nitrogen, and carbon dioxide in the COF-LZU1 at various temperatures. The (perfect) model COF has a BET surface that is higher than the experimental BET surface by a factor of approximately 1.33, suggesting defects or inclusions are present in the real structure. We find that the saturation adsorption loading of small gaseous species in COF-LZU1, as determined from grand canonical Monte Carlo simulations, is also higher by approximately the same factor compared to the experimental saturation loading. The influence of interlayer slipping on the shape of the adsorption isotherm and the adsorption capacity is studied. Comparison between simulation and experiment at lower loadings suggests the layers to be shifted instead of perfectly eclipsed. The sensitivity of the adsorption isotherms in this regime towards the underlying framework topology shows that real structure effects have significant influence on the gas uptake. Accounting for layer slipping is important to applications such as catalysis, gas storage and separation.

The diffusion of atoms and radicals on interstellar dust grains is a fundamental ingredient for predicting accurate molecular abundances in astronomical environments. Quantitative values of diffusivity and diffusion barriers usually rely heavily on empirical rules. In this paper, we compute the diffusion coefficients of adsorbed nitrogen atoms by combining machine-learned interatomic potentials, metadynamics, and kinetic Monte Carlo simulations. With this approach, we obtain a diffusion coefficient of nitrogen atoms on the surface of amorphous solid water of merely $(3.5 \pm 1.1)10^{-34}$cm$^2$s$^{-1}$ at 10 K for a bare ice surface. Thus, we find that nitrogen, as a paradigmatic case for light and weakly bound adsorbates, is unable to diffuse on bare amorphous solid water at 10 K. Surface coverage has a strong effect on the diffusion coefficient by modulating its value over 9--12 orders of magnitude at 10 K and enables diffusion for specific conditions. In addition, we have found that atom tunneling has a negligible effect. Average diffusion barriers of the potential energy surface (2.56 kJ mol$^{-1}$) differ strongly from the effective diffusion barrier obtained from the diffusion coefficient for a bare surface (6.06 kJ mol$^{-1}$) and are, thus, inappropriate for diffusion modeling. Our findings suggest that the thermal diffusion of N on water ice is a process that is highly dependent on the physical conditions of the ice., Comment: Accepted in MNRAS

We report new computational and experimental evidence of an efficient and astrochemically relevant formation route to formaldehyde (H$_2$CO). This simplest carbonylic compound is central to the formation of complex organics in cold interstellar clouds, and is generally regarded to be formed by the hydrogenation of solid-state carbon monoxide. We demonstrate H$_2$CO formation via the reaction of carbon atoms with amorphous solid water. Crucial to our proposed mechanism is a concerted proton transfer catalyzed by the water hydrogen bonding network. Consequently, the reactions $^3$C + H$_2$O -> $^3$HCOH and $^1$HCOH -> $^1$H$_2$CO can take place with low or without barriers, contrary to the high-barrier traditional internal hydrogen migration. These low barriers or absence thereof explain the very small kinetic isotope effect in our experiments when comparing the formation of H$_2$CO to D$_2$CO. Our results reconcile the disagreement found in the literature on the reaction route: C + H$_2$O -> H$_2$CO., Comment: Accepted for publication in JPCL

Artificial neural networks (NNs) are one of the most frequently used machine learning approaches to construct interatomic potentials and enable efficient large-scale atomistic simulations with almost ab initio accuracy. However, the simultaneous training of NNs on energies and forces, which are a prerequisite for, e.g., molecular dynamics simulations, can be demanding. In this work, we present an improved NN architecture based on the previous GM-NN model [V. Zaverkin and J. K\"astner, J. Chem. Theory Comput. 16, 5410-5421 (2020)], which shows an improved prediction accuracy and considerably reduced training times. Moreover, we extend the applicability of Gaussian moment-based interatomic potentials to periodic systems and demonstrate the overall excellent transferability and robustness of the respective models. The fast training by the improved methodology is a pre-requisite for training-heavy workflows such as active learning or learning-on-the-fly., Comment: Manuscript accepted for publication in J. Chem. Theory Comput.; Code published at https://gitlab.com/zaverkin_v/gmnn

Machine learning techniques allow a direct mapping of atomic positions and nuclear charges to the potential energy surface with almost ab-initio accuracy and the computational efficiency of empirical potentials. In this work we propose a machine learning method for constructing high-dimensional potential energy surfaces based on feed-forward neural networks. As input to the neural network we propose an extendable invariant local molecular descriptor constructed from geometric moments. Their formulation via pairwise distance vectors and tensor contractions allows a very efficient implementation on graphical processing units (GPUs). The atomic species is encoded in the molecular descriptor, which allows the restriction to one neural network for the training of all atomic species in the data set. We demonstrate that the accuracy of the developed approach in representing both chemical and configurational spaces is comparable to the one of several established machine learning models. Due to its high accuracy and efficiency, the proposed machine-learned potentials can be used for any further tasks, for example the optimization of molecular geometries, the calculation of rate constants or molecular dynamics.

The recent wave of detections of interstellar aromatic molecules has sparked interest in the chemical behavior of aromatic molecules under astrophysical conditions. In most cases, these detections have been made through chemically related molecules, called proxies, that implicitly indicate the presence of a parent molecule. In this study, we present the results of the theoretical evaluation of the hydrogenation reactions of different aromatic molecules (benzene, pyridine, pyrrole, furan, thiophene, silabenzene, and phosphorine). The viability of these reactions allows us to evaluate the resilience of these molecules to the most important reducing agent in the interstellar medium, the hydrogen atom (H). All significant reactions are exothermic and most of them present activation barriers, which are, in several cases, overcome by quantum tunneling. Instanton reaction rate constants are provided between 50 K and 500 K. For the most efficiently formed radicals, a second hydrogenation step has been studied. We propose that hydrogenated derivatives of furan, pyrrole, and specially 2,3-dihydropyrrole, 2,5-dihydropyrrole, 2,3-dihydrofuran, and 2,5-dihydrofuran are promising candidates for future interstellar detections.

Imaging of liquids and cryogenic biological materials by electron microscopy has been recently enabled by innovative approaches for specimen preparation and the fast development of optimised instruments for cryo-enabled electron microscopy (cryo-EM). Yet, Cryo-EM typically lacks advanced analytical capabilities, in particular for light elements. With the development of protocols for frozen wet specimen preparation, atom probe tomography (APT) could advantageously complement insights gained by cryo-EM. Here, we report on different approaches that have been recently proposed to enable the analysis of relatively large volumes of frozen liquids from either a flat substrate or the fractured surface of a wire. Both allowed for analysing water ice layers which are several microns thick consisting of pure water, pure heavy-water and aqueous solutions. We discuss the merits of both approaches, and prospects for further developments in this area. Preliminary results raise numerous questions, in part concerning the physics underpinning field evaporation. We discuss these aspects and lay out some of the challenges regarding the APT analysis of frozen liquids., Comment: submitted for publication assocaited to the APT&M 2020 conference

Recent advances in machine-learning interatomic potentials have enabled the efficient modeling of complex atomistic systems with an accuracy that is comparable to that of conventional quantum mechanics based methods. At the same time, the construction of new machine-learning potentials can seem a daunting task, as it involves data-science techniques that are not yet common in chemistry and materials science. Here, we provide a tutorial-style overview of strategies and best practices for the construction of artificial neural network (ANN) potentials. We illustrate the most important aspects of (i) data collection, (ii) model selection, (iii) training and validation, and (iv) testing and refinement of ANN potentials on the basis of practical examples. Current research in the areas of active learning and delta learning are also discussed in the context of ANN potentials. This tutorial review aims at equipping computational chemists and materials scientists with the required background knowledge for ANN potential construction and application, with the intention to accelerate the adoption of the method, so that it can facilitate exciting research that would otherwise be challenging with conventional strategies., Comment: 19 pages, 11 figures

Dynamics of adsorption and desorption of (4S)-N on amorphous solid water are analyzed using molecular dynamics simulations. The underlying potential energy surface was provided by machine-learned interatomic potentials. Binding energies confirm the latest available theoretical and experimental results. The nitrogen sticking coefficient is close to unity at dust temperatures of 10 K but decreases at higher temperatures. We estimate a desorption time scale of 1 {\mu}s at 28 K. The estimated time scale allows chemical processes mediated by diffusion to happen before desorption, even at higher temperatures. We found that the energy dissipation process after a sticking event happens on the picosecond timescale at dust temperatures of 10 K, even for high energies of the incoming adsorbate. Our approach allows the simulation of large systems for reasonable time scales at an affordable computational cost and ab-initio accuracy. Moreover, it is generally applicable for the study of adsorption dynamics of interstellar radicals on dust surfaces.

We implemented a geometry optimizer based on Gaussian process regression (GPR) to find minimum structures on potential energy surfaces. We tested both a two times differentiable form of the Mat\'{e}rn kernel and the squared exponential kernel. The Mat\'{e}rn kernel performs much better. We give a detailed description of the optimization procedures. These include overshooting the step resulting from GPR in order to obtain a higher degree of interpolation vs. extrapolation. In a benchmark against the L-BFGS optimizer of the DL-FIND library on 26 test systems, we found the new optimizer to generally reduce the number of required optimization steps.

We implemented a gradient-based algorithm for transition state search which uses Gaussian process regression. Besides a description of the algorithm, we provide a method to find the starting point for the optimization if only the reactant and product minima are known. We perform benchmarks on 27 test systems against the dimer method and partitioned rational function optimization as implemented in the DL-FIND library. We found the new optimizer to significantly decrease the number of required energy and gradient evaluations.

A trivial flaw in the utilization of artificial neural networks in interpolating chemical potential energy surfaces (PES) whose descriptors are Cartesian coordinates is their dependence on simple translations and rotations of the molecule under consideration. A different set of descriptors can be chosen to circumvent this problem, internuclear distances, inverse internuclear distances or z-matrix coordinates are three such descriptors. The objective is to use an interpolated PES in instanton rate constant calculations, hence information on the energy, gradient and Hessian is required at coordinates in the vicinity of the tunneling path. Instanton theory relies on smoothly fitted Hessians, therefore we use energy, gradients and Hessians in the training procedure. A major challenge is presented in the proper back-transformation of the output gradients and Hessians from internal coordinates to Cartesian coordinates. We perform comparisons between our method, a previous approach and on-the-fly rate constant calcuations on the hydrogen abstraction from methanol and on the hydrogen addition to isocyanic acid.

Canonical instanton theory is a widespread approach to describe the dynamics of chemical reactions in low temperature environments when tunneling effects become dominant. It is a semiclassical theory which requires locating classical periodic orbits on the upside-down potential energy surface, so-called instantons, and the computation of second order quantum corrections. The calculation of these corrections usually involves a matrix diagonalization. In this paper we present an alternative approach, which requires to solve only linear systems of equations involving sparse matrices. Furthermore, the proposed method provides a reliable and numerically stable way to obtain stability parameters in multidimensional systems, which are of particular interest in the context of microcanonical instanton theory.

Canonical instanton theory is known to overestimate the rate constant close to a system-dependent crossover temperature and is inapplicable above that temperature. We compare the accuracy of the reaction rate constants calculated using recent semi-classical rate expressions to those from canonical instanton theory. We show that rate constants calculated purely from solving the stability matrix for the action in degrees of freedom orthogonal to the instanton path is not applicable at arbitrarily low temperatures and employ two methods to overcome this. Furthermore, as a by-product of the developed methods, we derive a simple correction to canonical instanton theory that can alleviate this known overestimation of rate constants close to the crossover temperature. The combined methods accurately reproduce the rate constants of the canonical theory along the whole temperature range without the spurious overestimation near the crossover temperature. We calculate and compare rate constants on three different reactions: H in the M\"uller--Brown potential, methylhydroxycarbene $\to$ acetaldehyde and H$_2$ + OH $\to$ H + H$_2$O.

Formaldehyde (H2CO) is one of the most abundant molecules observed in the icy mantle covering interstellar grains. Studying its evolution can contribute to our understanding of the formation of complex organic molecules in various interstellar environments. In this work, we investigated the hydrogenation reactions of H2CO yielding CH3O, CH2OH, and the hydrogen abstraction resulting in H2+HCO on an amorphous solid water (ASW) surface using a quantum mechanics/molecular mechanics (QM/MM) model. The binding energies of H2CO on the ASW surface vary broadly, from 1000 to 9370 K. No correlation was found between binding energies and activation energies of hydrogenation reactions. Combining instanton theory with QM/MM modeling, we calculated rate constants for the Langmuir Hinshelwood and the Eley Rideal mechanisms for the three product channels of H+H2CO surface reactions down to 59 K. We found that the channel producing CH2OH can be ignored, owing to its high activation barrier leading to significantly lower rates than the other two channels. The ASW surface influences the reactivity in favor of formation of CH3O (branching ratio 80%) and hinders the H2CO dissociation into H2+HCO. In addition, kinetic isotope effects are strong in all reaction channels and vary strongly between the channels. Finally, we provide fits of the rate constants to be used in astrochemical models.

The vibrational spectra of simple CH$_3^+$-Rg (Rg=He, Ne, Ar, Kr) complexes have been studied by vibrational configuration interaction (VCI) theory relying on multidimensional potential energy surfaces (PES) obtained from explicitly correlated coupled cluster calculations, CCSD(T)-F12a. In agreement with experimental results, the series of rare gas atoms leads to rather unsystematic results and indicates huge zero point vibrational energy effects for the helium complex. In order to study these sensitive complexes more consistently, we also introduce configuration averaged vibrational self-consistent field theory (CAVSCF), which is a generalization of standard VSCF theory to several configurations. The vibrational spectra of the complexes are compared to that of the methyl cation, for which corrections due to scalar-relativistic effects, high-level coupled-cluster terms, i.e. CCSDTQ, and core-valence correlation have explicitly been accounted for. The occurrence of tunneling splittings for the vibrational ground-state of CH$_3^+$-He has been investigated on the basis of semiclassical instanton theory. These calculations and a direct comparison of the energy profiles along the intrinsic reaction coordinates (IRC) with that of the hydronium cation, H$_3$O$^+$, suggest that tunneling effects for vibrationally excited states should be very small.

TauD dioxygenase is one of the most studied $\alpha$-ketoglutarate dependent dioxygenases ($\alpha$KGDs), involved in several biotechnological applications. We investigated the key step in the catalytic cycle of the $\alpha$KGDs, the hydrogen transfer process, by a QM/MM approach (B3LYP/CHARMM22). Analysis of the charge and spin densities during the reaction demonstrates that a concerted mechanism takes place, where the H atom transfer happens simultaneously with the electron transfer from taurine to the Fe=O cofactor. We found quantum tunneling of the hydrogen atom to increase the rate constant by a factor of 40 at 5\textcelsius{}. As a consequence a quite high KIE value of close to 60 is obtained, which is consistent with the experimental value.

Atom tunneling in the hydrogen atom transfer reaction of the 2,4,6-tri-tert-butylphenyl radical to 3,5-di-tert-butylneophyl, which has a short but strongly curved reaction path, was investigated using instanton theory. We found the tunneling path to deviate qualitatively from the classical intrinsic reaction coordinate, the steepest-descent path in mass-weighted Cartesian coordinates. To perform that comparison, we implemented a new variant of the predictor-corrector algorithm for the calculation of the intrinsic reaction coordinate. We used the reaction force analysis method as a means to decompose the reaction barrier into structural and electronic components. Due to the narrow energy barrier, atom tunneling is important in the abovementioned reaction, even above room temperature. Our calculated rate constants between 350 K and 100 K agree well with experimental values. We found a H/D kinetic isotope effect of almost 106 at 100 K. Tunneling dominates the protium transfer below 400 K and the deuterium transfer below 300 K. We compared the lengths of the tunneling path and the classical path for the hydrogen atom transfer in the reaction HCl + Cl and quantified the corner cutting in this reaction. At low temperature, the tunneling path is about 40% shorter than the classical path.

Quantum mechanical tunneling of atoms is increasingly found to play an important role in many chemical transformations. Experimentally, atom-tunneling can be indirectly detected by temperature-independent rate constants at low temperature or by enhanced kinetic isotope effects. On the contrary, using computational investigations the influence of tunneling on the reaction rates can directly be monitored. The tunnel effect, for example, changes reaction paths and branching ratios, enables chemical reactions in an astrochemical environment that would be impossible by thermal transition, and influences biochemical processes.

Instanton theory is an established method to calculate rate constants of chemical reactions including atom tunneling. Technical and methodological improvements increased its applicability. Still, a large number of energy and gradient calculations is necessary to optimize the instanton tunneling path and 2$^{\text{nd}}$ derivatives of the potential energy along the tunneling path have to be evaluated, restricting the range of suitable electronic structure methods. To enhance the applicability of instanton theory, we present a dual-level approach in which instanton optimizations and Hessian calculations are performed using an efficient but approximate electronic structure method and the potential energy along the tunneling path is recalculated using a more accurate method. This procedure extends the applicability of instanton theory to high-level electronic structure methods for which analytic gradients may not be available, like local linear-scaling approaches. We demonstrate for the analytical Eckart barrier and three molecular systems how the dual-level instanton approach corrects for the largest part of the error caused by the inaccuracy of the efficient electronic structure method. This reduces the error of the calculated rate constants significantly.

We calculated reaction rate constants including atom tunneling for the hydrogen abstraction reaction CH3OH+H -> CH2OH+H2 with the instanton method. The potential energy was fitted by a neural network, that was trained to UCCSD(T)-F12/VTZ-F12 data. Bimolecular gas-phase rate constants were calculated using microcanonic instanton theory. All H/D isotope patterns on the CH3 group and the incoming H atom are studied. Unimolecular reaction rate constants, representing the reaction on a surface, down to 30 K, are presented for all isotope patterns. At 30 K they range from 4100 for the replacement of the abstracted H by D to ~ 8 for the replacement of the abstracting H to about 2--6 for secondary KIEs. The $^\text{12}$C/$^\text{13}$C kinetic isotope effect is 1.08 at 30 K, while the $^\text{16}$O/$^\text{18}$O kinetic isotope effect is vanishingly small. A simple kinetic surface model using these data predicts high abundances of the deuterated forms of methanol.

Artificial neural networks are used to fit a potential energy surface. We demonstrate the benefits of using not only energies, but also their first and second derivatives as training data for the neural network. This ensures smooth and accurate Hessian surfaces, which are required for rate constant calculations using instanton theory. Our aim was a local, accurate fit rather than a global PES, because instanton theory requires information on the potential only in the close vicinity of the main tunneling path. Elongations along vibrational normal modes at the transition state are used as coordinates for the neural network. The method is applied to the hydrogen abstraction reaction from methanol, calculated on a coupled-cluster level of theory. The reaction is essential in astrochemistry to explain the deuteration of methanol in the interstellar medium.

Microcanonical instanton theory offers the promise of providing rate constants for chemical reactions including quantum tunneling of atoms over the whole temperature range. We discuss different rate expressions, which require the calculation of stability parameters of the instantons. The traditional way of obtaining these stability parameters is shown to be numerically unstable in practical applications. We provide three alternative algorithms to obtain such stability parameters for non-separable systems, i.e., systems in which the vibrational modes perpendicular to the instanton path couple to movement along the path. We show the applicability of our algorithms on two molecular systems: H$_2$ + OH $\rightarrow$ H$_2$O + H using a fitted potential energy surface and HNCO + H $\rightarrow$ NH$_2$CO using a potential obtained on-the-fly from density functional calculations.

In this work, we present the results of our investigation into the chemistry of Z- and E-cyanomethanimine (HNCHCN), both of which are possible precursors to the nucleobase adenine. Ab initio quantum chemical calculations for a number of reactions with atomic hydrogen were carried out. We find that the reaction H + Z/E-HNCHCN leading both to H-addition as well as H$_2$-abstraction proceed via similar short-range barriers with bimolecular rate coefficients on the order of $\sim10^{-17}$ cm$^{3}$ s$^{-1}$. These results were then incorporated into astrochemical models and used in simulations of the giant molecular cloud G+0.693. The calculated abundances obtained from these models were compared with previous observational data and found to be in good agreement, with a predicted [Z/E] ratio of $\sim3$ - somewhat smaller than the previously derived value of $6.1\pm2.4$. We find that the [Z/E] ratio in our simulations is due mostly to ion-molecule destruction rates driven by the different permanent dipoles of the two conformers. Based on these results, we propose a general rule-of-thumb for estimating the abundances of isomers in interstellar environments., Comment: The Astrophysical Journal, accepted: 17 pages, 9 figures, 7 tables

Artificial neural network (ANN) potentials enable the efficient large-scale atomistic modeling of complex materials with near first-principles accuracy. For molecular dynamics simulations, accurate energies and interatomic forces are a prerequisite, but training ANN potentials simultaneously on energies and forces from electronic structure calculations is computationally demanding. Here, we introduce an efficient alternative method for the training of ANN potentials on energy and force information based on an extrapolation of the total energy via a Taylor expansion. By translating the force information to approximate energies, the quadratic scaling with the number of atoms exhibited by conventional force-training methods can be avoided, which enables the training on reference data sets containing complex atomic structures. We demonstrate for different materials systems, clusters of water molecules, bulk liquid water, and a lithium transition-metal oxide, that the proposed force-training approach provides substantial improvements over schemes that train on energies only. Including force information for training reduces the size of the reference data sets required for ANN potential construction, increases the transferability of the potential, and generally improves the force prediction accuracy. For a set of water clusters, the Taylor-expansion approach achieves around 50% of the force error improvement compared to the explicit training on all force components, at a much smaller computational cost. The alternative force training approach thus simplifies the construction of general ANN potentials for the prediction of accurate energies and interatomic forces for diverse types of materials, as demonstrated here for water and a transition-metal oxide., Comment: 19 pages, 13 figures

In this work, we reexamine sulfur chemistry occurring on and in the ice mantles of interstellar dust grains, and report the effects of two new modifications to standard astrochemical models; namely, (a) the incorporation of cosmic ray-driven radiation chemistry and (b) the assumption of fast, non-diffusive reactions for key radicals in the bulk. Results from our models of dense molecular clouds show that these changes can have a profound influence on the abundances of sulfur-bearing species in ice mantles, including a reduction in the abundance of solid-phase H$_2$S and HS, and a significant increase in the abundances of OCS, SO$_2$, as well as pure allotropes of sulfur, especially S$_8$. These pure-sulfur species - though nearly impossible to observe directly - have long been speculated to be potential sulfur reservoirs and our results represent possibly the most accurate estimates yet of their abundances in the dense ISM. Moreover, the results of these updated models are found to be in good agreement with available observational data. Finally, we examine the implications of our findings with regard to the as-yet-unknown sulfur reservoir thought to exist in dense interstellar environments., Comment: ApJ, accepted: 37 pages, 8 figures

This paper investigates the impact of the increased reaction rate constant due to tunneling effects on planet-forming disks. Our aim is to quantify the astrophysical implications of atom tunneling for simple molecules that are frequently used to infer disk structure information or to define the initial conditions for planet (atmosphere) formation. We explain the tunneling effect on reaction rates by using a scholarly example in comparison to previous UMIST2012 rate constants. In a chemical network with 1299 reactions, we identify all reactions that could show atom tunneling. We devise a simple formulation of reaction rate constants that overestimates tunneling and screen a standard T Tauri disk model for changes in species abundances. For those reactions found to be relevant, we find values of the most recent literature for the rate constants including tunneling and compare the resulting disk chemistry to the standard disk models. The rate constants in the UMIST2012 database in many cases already capture tunneling effects implicitly. A rigorous screening procedure identified three neutral-neutral reactions where atom tunneling could change simple molecule abundances. However, by adopting recent values of the rate constants of these reactions and due to the layered structure of planet-forming disks, the effects are limited to a small region where cold neutral-neutral chemistry dominates. Abundances of water close to the midplane snowline can increase by a factor of two at most compared to previous results with UMIST2012 rates. Observables from the disk surface, such as high excitation (> 500 K) water line fluxes, decrease by 60% at most when tunneling effects are explicitly excluded. On the other hand, disk midplane quantities relevant for planet formation such as the C-to-O ratio and also the ice-to-rock ratio are clearly affected by these gas-phase tunneling effects., Comment: 17 pages, 12 Figures in main Text. Accepted at A&A

To date, two isomers of H$_2$C$_3$O have been detected, namely, propynal (HCCCHO) and cylclopropenone (c-H$_2$C$_3$O). A third, propadienone (CH$_2$CCO), has thus far eluded observers despite the fact that it is the lowest in energy of the three. This previously noted result is in contradiction of the minimum energy principle, which posits that the abundances of isomers in interstellar environments can be predicted based on their relative stabilities - and suggests, rather, the importance of kinetic over thermodynamic effects in explaining the role of such species. Here, we report results of \textit{ab initio} quantum chemical calculations of the reaction between H and (a) HC$_3$O, (b) H$_2$C$_3$O (both propynal and propadienone), and (c) CH$_2$CHCO. We have found that, among all possible reactions between atomic hydrogen and either propadienone or propynal, only the destruction of propadienone is barrierless and exothermic. That this destruction pathway is indeed behind the non-detection of CH$_2$CCO is further suggested by our finding that the product of this process, the radical CH$_2$CHCO, can subsequently react barrierlessly with H to form propenal (CH$_2$CHCHO) which has, in fact, been detected in regions where the other two H$_2$C$_3$O isomers are observed. Thus, these results not only shed light on a previously unresolved astrochemical mystery, but also further highlight the importance of kinetics in understanding the abundances of interstellar molecules., Comment: ApJ, accepted: 14 pages, 2 figures

The radicals HCO and CH$_3$ on carbon monoxide ice surfaces were simulated using density functional theory. Their binding energy on amorphous CO ice shows broad distributions, with approximative average values of 500 K for HCO and 200 K for CH$_3$. If they are located on the surface close to each other (3 to 4 \AA), molecular dynamics calculations based on density functional theory show that they can form acetaldehyde (CH$_3$CHO) or CH$_4$ + CO in barrier-less reactions, depending on the initial orientation of the molecules with respect to each other. In some orientations, no spontaneous reactions were found, the products remained bound to the surface. Sufficient configurational sampling, inclusion of the vibrational zero point energy, and a thorough benchmark of the applied electronic structure method are important to predict reliable binding energies for such weakly interacting systems. From these results it is clear that complex organic molecules, like acetaldehyde, can be formed by recombination reactions of radicals on CO surfaces., Comment: Accepted in ACS Earth and Space Chemistry

The hydrogen abstraction reaction between H and H$_2$S, yielding HS and H$_2$ as products, has been studied within the framework of interstellar surface chemistry. High-temperature rate constants up to 2000 K are calculated in the gas phase and are in agreement with previously reported values. Subsequently low-temperature rate constants down to 55 K are presented for the first time that are of interest to astrochemistry, i.e., covering both bimolecular and unimolecular reaction mechanisms. For this, a so-called implicit surface model is used. Strictly speaking, this is a structural gas-phase model in which the restriction of the rotation in the solid state is taken into account. The calculated kinetic isotope effects are explained in terms of difference in activation and delocalization. All rate constants are calculated at the UCCSD(T)-F12/cc-VTZ-F12 level of theory. Finally, we show that the energetics of the reaction is only affected to a small extent by the presence of H$_2$O or H$_2$S molecular clusters that simulate an ice surface, calculated at the MPWB1K/def2-TZVP level of theory., Comment: Accepted for publication in Journal of Physical Chemistry A http://pubs.acs.org/doi/pdfplus/10.1021/acs.jpca.7b10296

OH radicals play a key role as an intermediate in the water formation chemistry of the interstellar medium. For example the reaction of OH radicals with H$_2$ molecules is among the final steps in the astrochemical reaction network starting from O, O$_2$, and O$_3$. Experimentally it was shown that even at 10 K this reaction occurs on ice surfaces. As the reaction has a high activation energy only atom tunneling can explain such experimental findings. In this study we calculated reaction rate constants for the title reaction on a water-ice I$_h$ surface. To our knowledge, low-temperature rate constants on a surface are not available in the literature. All surface calculations were done using a QM/MM framework (BHLYP/TIP3P) after a thorough benchmark of different density functionals and basis sets to highly accurate correlation methods. Reaction rate constants are obtained using instanton theory which takes atom tunneling into account inherently, with constants down to 110 K for the Eley-Rideal mechanism and down to 60 K for the Langmuir-Hinshelwood mechanism. We found that the reaction is nearly temperature independent below 80 K. We give kinetic isotope effects for all possible deuteration patterns for both reaction mechanisms. For the implementation in astrochemical networks, we also give fit parameters to a modified Arrhenius equation. Finally, several different binding sites and binding energies of OH radicals on the I$_h$ surface are discussed and the corresponding rate constants are compared to the gas-phase case., Comment: Published online. Supporting information on http://pubs.acs.org/doi/suppl/10.1021/acsearthspacechem.7b00052

On the surface of icy dust grains in the dense regions of the interstellar medium a rich chemistry can take place. Due to the low temperature, reactions that proceed via a barrier can only take place through tunneling. The reaction H + H$_2$O$_2$ $\rightarrow$ H$_2$O + OH is such a case with a gas-phase barrier of $\sim$26.5 kJ/mol. Still the reaction is known to be involved in water formation on interstellar grains. Here, we investigate the influence of a water ice surface and of bulk ice on the reaction rate constant. Rate constants are calculated using instanton theory down to 74 K. The ice is taken into account via multiscale modeling, describing the reactants and the direct surrounding at the quantum mechanical level with density functional theory (DFT), while the rest of the ice is modeled on the molecular mechanical level with a force field. We find that H$_2$O$_2$ binding energies cannot be captured by a single value, but rather depend on the number of hydrogen bonds with surface molecules. In highly amorphous surroundings the binding site can block the routes of attack and impede the reaction. Furthermore, the activation energies do not correlate with the binding energies of the same sites. The unimolecular rate constants related to the Langmuir-Hinshelwood mechanism increase as the activation energy decreases. Thus, we provide a lower limit for the rate constant and argue that rate constants can have values up to two order of magnitude larger than this limit., Comment: Accepted for publication in ApJ

We present a combined experimental and theoretical study focussing on the quantum tunneling of atoms in the reaction between CH4 and OH. The importance of this reaction pathway is derived by investigating isotope substituted analogs. Quantitative reaction rates needed for astrochemical models at low temperature are currently unavailable both in the solid state and in the gas phase. Here, we study tunneling effects upon hydrogen abstraction in CH4 + OH by focusing on two reactions: CH4 + OD -> CH3 + HDO and CD4 + OH -> CD3 + HDO. The experimental study shows that the solid-state reaction rate R(CH4 + OD) is higher than R(CD4 + OH) at 15 K. Experimental results are accompanied by calculations of the corresponding unimolecular and bimolecular reaction rate constants using instanton theory taking into account surface effects. From the work presented here, the unimolecular reactions are particularly interesting as these provide insight into reactions following a Langmuir-Hinshelwood process. The resulting ratio of the rate constants shows that the H abstraction (k(CH4 + OD)) is approximately ten times faster than D-abstraction (k(CD4 + OH)) at 65 K. We conclude that tunneling is involved at low temperatures in the abstraction reactions studied here. The unimolecular rate constants can be used by the modeling community as a first approach to describe OH-mediated abstraction reactions in the solid phase. For this reason we provide fits of our calculated rate constants that allow the inclusion of these reactions in models in a straightforward fashion., Comment: Accepted by A&A

The final step of the water formation network on interstellar grain surfaces starting from the H + O$_2$ route is the reaction between H and H$_2$O$_2$. This reaction is known to have a high activation energy and therefore at low temperatures it can only proceed via tunneling. To date, however, no rate constants are available at temperatures below 200 K. In this work, we use instanton theory to compute rate constants for the title reaction with and without isotopic substitutions down to temperatures of 50 K. The calculations are based on density functional theory, with additional benchmarks for the activation energy using unrestricted single-reference and multireference coupled-cluster single-point energies. Gas-phase bimolecular rate constants are calculated and compared with available experimental data not only for H + H$_2$O$_2$ $\rightarrow$ H$_2$O + OH, but also for H + H$_2$O$_2$ $\rightarrow$ H$_2$ + HO$_2$. We find a branching ratio where the title reaction is favored by at least two orders of magnitude at 114 K. In the interstellar medium this reaction predominantly occurs on water surfaces, which increases the probability that the two reactants meet. To mimic this one, two, or three spectator H2O molecules are added to the system. Eley-Rideal bimolecular and Langmuir-Hinshelwood unimolecular rate constants are presented here. The kinetic isotope effects for the various cases are compared to experimental data as well as to expressions commonly used in astrochemical models. Both the rectangular barrier and the Eckart approximations lead to errors of about an order of magnitude. Finally, fits of the rate constants are provided as input for astrochemical models., Comment: Accepted for publication by Phys. Chem. Chem. Phys. 2016. Supplementary information available: http://www.rsc.org/suppdata/c6/cp/c6cp06457d/c6cp06457d1.pdf

Investigating how formamide forms in the interstellar medium is a hot topic in astrochemistry, which can contribute to our understanding of the origin of life on Earth. We have constructed a QM/MM model to simulate the hydrogenation of isocyanic acid on amorphous solid water surfaces to form formamide. The binding energy of HNCO on the ASW surface varies significantly between different binding sites, we found values between $\sim$0 and 100 kJ mol$^{-1}$. The barrier for the hydrogenation reaction is almost independent of the binding energy, though. We calculated tunneling rate constants of H + HNCO $\rightarrow$ NH$_2$CO at temperatures down to 103 K combining QM/MM with instanton theory. Tunneling dominates the reaction at such low temperatures. The tunneling reaction is hardly accelerated by the amorphous solid water surface compared to the gas phase for this system, even though the activation energy of the surface reaction is lower than the one of the gas-phase reaction. Both the height and width of the barrier affect the tunneling rate in practice. Strong kinetic isotope effects were observed by comparing to rate constants of D + HNCO $\rightarrow$ NHDCO. At 103 K we found a KIE of 231 on the surface and 146 in the gas phase. Furthermore, we investigated the gas-phase reaction NH$_2$ + H$_2$CO $\rightarrow$ NH$_2$CHO + H and found it unlikely to occur at cryogenic temperatures. The data of our tunneling rate constants are expected to significantly influence astrochemical models., Comment: Phys. Chem. Chem. Phys. (2016)