Accurate Probabilities for Highly Activated Reaction of Polyatomic Molecules on Surfaces Using a High-Dimensional Neural Network Potential: CHD3 + Cu(111)

How to simulate dissociative chemisorption of methane on metal surfaces

The dissociation of methane is not only an important reaction step in catalytic processes, but also of fundamental interest. Dynamical effects during the dissociative chemisorption of methane on metal surfaces cause significant differences in computed reaction rates, compared to what is predicted by typical transition state theory (TST) models. It is clear that for a good understanding of the catalytic activation of methane dynamical simulations are required. In this paper, a general blueprint is provided for performing dynamical simulations of the dissociative chemisorption of methane on metal surfaces, by employing either the quasi-classical trajectory or ring polymer molecular dynamics approach. If the computational setup is constructed with great care-since results can be affected considerably by the setup - chemically accurate predictions are achievable. Although this paper concerns methane dissociation, the provided blueprint is, so far, applicable to the dissociative chemisorption of most molecules.

Efficient machine learning approach for accurate free-energy profiles and kinetic rates

The computational exploration of reactive processes is challenging due to the requirement of thorough sampling across the free energy landscape using accurate ab initio methods. To address these constraints, machine learning potentials are employed, yet their training for this kind of problem is still a laborious and tedious task. In this study, we present an efficient approach to train these potentials by cleverly using a single batch of unbiased trajectories that avoid the pitfalls of trajectories artificially biased along a suboptimal collective variable. This strategy, when integrated with current enhanced sampling techniques, allows to obtain free energy profiles and kinetic rates of ab initio quality, yet dramatically reducing the computational cost.

Plasma Catalysis Modeling: How Ideal Is Atomic Hydrogen for Eley-Rideal?

Plasma catalysis is an emerging technology, but a lot of questions about the underlying surface mechanisms remain unanswered. One of these questions is how important Eley-Rideal (ER) reactions are, next to Langmuir-Hinshelwood reactions. Most plasma catalysis kinetic models predict ER reactions to be important and sometimes even vital for the surface chemistry. In this work, we take a critical look at how ER reactions involving H radicals are incorporated in kinetic models describing CO2 hydrogenation and NH3 synthesis. To this end, we construct potential energy surface (PES) intersections, similar to elbow plots constructed for dissociative chemisorption. The results of the PES intersections are in agreement with ab initio molecular dynamics (AIMD) findings in literature while being computationally much cheaper. We find that, for the reactions studied here, adsorption is more probable than a reaction via the hot atom (HA) mechanism, which in turn is more probable than a reaction via the ER mechanism. We also conclude that kinetic models of plasma-catalytic systems tend to overestimate the importance of ER reactions. Furthermore, as opposed to what is often assumed in kinetic models, the choice of catalyst will influence the ER reaction probability. Overall, the description of ER reactions is too much "ideal" in models. Based on our findings, we make a number of recommendations on how to incorporate ER reactions in kinetic models to avoid overestimation of their importance.

On the quantum dynamical treatment of surface vibrational modes for reactive scattering of H2 from Cu(111) at 925 K

We construct the effective Hartree potential for H2 on Cu(111) as introduced in our earlier work [Dutta et al., J. Chem. Phys. 154, 104103 (2021), and Dutta et al., J. Chem. Phys. 157, 194112 (2022)] starting from the same gas-metal interaction potential obtained for 0 K. Unlike in that work, we now explicitly account for surface expansion at 925 K and investigate different models to describe the surface vibrational modes: (i) a cluster model yielding harmonic normal modes at 0 K and (ii) slab models resulting in phonons at 0 and 925 K according to the quasi-harmonic approximation-all consistently calculated at the density functional theory level with the same exchange-correlation potential. While performing dynamical calculations for the H2(v = 0, j = 0)-Cu(111) system employing Hartree potential constructed with 925 K phonons and surface temperature, (i) the calculated chemisorption probabilities are the highest compared to the other approaches over the energy domain and (ii) the threshold for the reaction probability is the lowest, in close agreement with the experiment. Although the survival probabilities (v' = 0) depict the expected trend (lower in magnitude), the excitation probabilities (v' = 1) display a higher magnitude since the 925 K phonons and surface temperature are more effective for the excitation process compared to the phonons/normal modes obtained from the other approaches investigated to describe the surface.

Construction of High Accuracy Machine Learning Interatomic Potential for Surface/Interface of Nanomaterials-A Review

The inherent discontinuity and unique dimensional attributes of nanomaterial surfaces and interfaces bestow them with various exceptional properties. These properties, however, also introduce difficulties for both experimental and computational studies. The advent of machine learning interatomic potential (MLIP) addresses some of the limitations associated with empirical force fields, presenting a valuable avenue for accurate simulations of these surfaces/interfaces of nanomaterials. Central to this approach is the idea of capturing the relationship between system configuration and potential energy, leveraging the proficiency of machine learning (ML) to precisely approximate high-dimensional functions. This review offers an in-depth examination of MLIP principles and their execution and elaborates on their applications in the realm of nanomaterial surface and interface systems. The prevailing challenges faced by this potent methodology are also discussed.

Accurate Reaction Probabilities for Translational Energies on Both Sides of the Barrier of Dissociative Chemisorption on Metal Surfaces

Molecular dynamics simulations are essential for a better understanding of dissociative chemisorption on metal surfaces, which is often the rate-controlling step in heterogeneous and plasma catalysis. The workhorse quasi-classical trajectory approach ubiquitous in molecular dynamics is able to accurately predict reactivity only for high translational and low vibrational energies. In contrast, catalytically relevant conditions generally involve low translational and elevated vibrational energies. Existing quantum dynamics approaches are intractable or approximate as a result of the large number of degrees of freedom present in molecule-metal surface reactions. Here, we extend a ring polymer molecular dynamics approach to fully include, for the first time, the degrees of freedom of a moving metal surface. With this approach, experimental sticking probabilities for the dissociative chemisorption of methane on Pt(111) are reproduced for a large range of translational and vibrational energies by including nuclear quantum effects and employing full-dimensional simulations.

Hydrogen atom scattering at the Al2O3(0001) surface: a combined experimental and theoretical study

Investigating atom-surface interactions is the key to an in-depth understanding of chemical processes at interfaces, which are of central importance in many fields - from heterogeneous catalysis to corrosion. In this work, we present a joint experimental and theoretical effort to gain insights into the atomistic details of hydrogen atom scattering at the α-Al2O3(0001) surface. Surprisingly, this system has been hardly studied to date, although hydrogen atoms as well as α-Al2O3 are omnipresent in catalysis as reactive species and support oxide, respectively. We address this system by performing hydrogen atom beam scattering experiments and molecular dynamics (MD) simulations based on a high-dimensional machine learning potential trained to density functional theory data. Using this combination of methods we are able to probe the properties of the multidimensional potential energy surface governing the scattering process. Specifically, we compare the angular distribution and the kinetic energy loss of the scattered atoms obtained in experiment with a large number of MD trajectories, which, moreover, allow to identify the underlying impact sites at the surface.

The role of dynamics in heterogeneous catalysis: Surface diffusivity and N2 decomposition on Fe(111)

Dynamics has long been recognized to play an important role in heterogeneous catalytic processes. However, until recently, it has been impossible to study their dynamical behavior at industry-relevant temperatures. Using a combination of machine learning potentials and advanced simulation techniques, we investigate the cleavage of the N[Formula: see text] triple bond on the Fe(111) surface. We find that at low temperatures our results agree with the well-established picture. However, if we increase the temperature to reach operando conditions, the surface undergoes a global dynamical change and the step structure of the Fe(111) surface is destabilized. The catalytic sites, traditionally associated with this surface, appear and disappear continuously. Our simulations illuminate the danger of extrapolating low-temperature results to operando conditions and indicate that the catalytic activity can only be inferred from calculations that take dynamics fully into account. More than that, they show that it is the transition to this highly fluctuating interfacial environment that drives the catalytic process.

Neural Network with Optimal Neuron Activation Functions Based on Additive Gaussian Process Regression

Feed-forward neural networks (NNs) are a staple machine learning method widely used in many areas of science and technology, including physical chemistry, computational chemistry, and materials informatics. While even a single-hidden-layer NN is a universal approximator, its expressive power is limited by the use of simple neuron activation functions (such as sigmoid functions) that are typically the same for all neurons. More flexible neuron activation functions would allow the use of fewer neurons and layers and thereby save computational cost and improve expressive power. We show that additive Gaussian process regression (GPR) can be used to construct optimal neuron activation functions that are individual to each neuron. An approach is also introduced that avoids nonlinear fitting of neural network parameters by defining them with rules. The resulting method combines the advantage of robustness of a linear regression with the higher expressive power of an NN. We demonstrate the approach by fitting the potential energy surfaces of the water molecule and formaldehyde. Without requiring any nonlinear optimization, the additive-GPR-based approach outperforms a conventional NN in the high-accuracy regime, where a conventional NN suffers more from overfitting.

Modeling Equilibration Dynamics of Hyperthermal Products of Surface Reactions Using Scalable Neural Network Potential with First-Principles Accuracy

Equilibration dynamics of hot oxygen atoms following the dissociation of O2 on Pd(100) and Pd(111) surfaces are investigated by molecular dynamics simulations based on a scalable neural network potential enabling first-principles description of the interaction of O2 and O interacting with variable Pd supercells. By analyzing hundreds of trajectories with appropriate initial sampling, the measured distance distribution of equilibrated atom pairs on Pd(111) is well reproduced. However, our results on Pd(100) suggest that the ballistic motion of hot atoms predicted previously is a rare event under ideal conditions, while initial molecular orientation and surface thermal fluctuation could significantly affect the overall postdissociation dynamics. On both surfaces, dissociated hyperthermal oxygen atoms primarily locate their nascent positions and experience a similar random walk motion nearby.

Challenges for Kinetics Predictions via Neural Network Potentials: A Wilkinson's Catalyst Case

Ab initio kinetic studies are important to understand and design novel chemical reactions. While the Artificial Force Induced Reaction (AFIR) method provides a convenient and efficient framework for kinetic studies, accurate explorations of reaction path networks incur high computational costs. In this article, we are investigating the applicability of Neural Network Potentials (NNP) to accelerate such studies. For this purpose, we are reporting a novel theoretical study of ethylene hydrogenation with a transition metal complex inspired by Wilkinson's catalyst, using the AFIR method. The resulting reaction path network was analyzed by the Generative Topographic Mapping method. The network's geometries were then used to train a state-of-the-art NNP model, to replace expensive ab initio calculations with fast NNP predictions during the search. This procedure was applied to run the first NNP-powered reaction path network exploration using the AFIR method. We discovered that such explorations are particularly challenging for general purpose NNP models, and we identified the underlying limitations. In addition, we are proposing to overcome these challenges by complementing NNP models with fast semiempirical predictions. The proposed solution offers a generally applicable framework, laying the foundations to further accelerate ab initio kinetic studies with Machine Learning Force Fields, and ultimately explore larger systems that are currently inaccessible.

Simulating Highly Activated Sticking of H2 on Al(110): Quantum versus Quasi-Classical Dynamics

We evaluate the importance of quantum effects on the sticking of H₂ on Al(110) for conditions that are close to those of molecular beam experiments that have been done on this system. Calculations with the quasi-classical trajectory (QCT) method and with quantum dynamics (QD) are performed using a model in which only motion in the six molecular degrees of freedom is allowed. The potential energy surface used has a minimum barrier height close to the value recently obtained with the quantum Monte Carlo method. Monte Carlo averaging over the initial rovibrational states allowed the QD calculations to be done with an order of magnitude smaller computational expense. The sticking probability curve computed with QD is shifted to lower energies relative to the QCT curve by 0.21 to 0.05 kcal/mol, with the highest shift obtained for the lowest incidence energy. Quantum effects are therefore expected to play a small role in calculations that would evaluate the accuracy of electronic structure methods for determining the minimum barrier height to dissociative chemisorption for H₂ + Al(110) on the basis of the standard procedure for comparing results of theory with molecular beam experiments.

Investigating the Eley-Rideal recombination of hydrogen atoms on Cu (111) via a high-dimensional neural network potential energy surface

As a prototypical system for studying the Eley-Rideal (ER) mechanism at the gas-surface interface, the reaction between incident H/D atoms and pre-covered D/H atoms on Cu (111) has attracted much experimental and theoretical interest. Detailed final state-resolved experimental data have been available for about thirty-years, leading to the discovery of many interesting dynamical features. However, previous theoretical models have suffered from reduced-dimensional approximations and/or omitting energy transfer to surface phonons and electrons, or the high cost of on-the-fly ab initio molecular dynamics, preventing quantitative comparisons with experimental data. Herein, we report the first high-dimensional neural network potential (NNP) for this ER reaction based on first-principles calculations including all molecular and surface degrees of freedom. Thanks to the high efficiency of this NNP, we are able to perform extensive quasi-classical molecular dynamics simulations with the inclusion of the excitation of low-lying electron-hole pairs (EHPs), which generally yield good agreement with various experimental results. More importantly, the isotopic and/or EHP effects in total reaction cross-sections and distributions of the product energy, scattering angle, and individual ro-vibrational states have been more clearly shown and discussed. This study sheds valuable light on this important ER prototype and opens a new avenue for further investigations of ER reactions using various initial conditions, surface temperatures, and coverages in the future.

Combining Machine Learning Approaches and Accurate Ab Initio Enhanced Sampling Methods for Prebiotic Chemical Reactions in Solution

The study of the thermodynamics, kinetics, and microscopic mechanisms of chemical reactions in solution requires the use of advanced free-energy methods for predictions to be quantitative. This task is however a formidable one for atomistic simulation methods, as the cost of quantum-based ab initio approaches, to obtain statistically meaningful samplings of the relevant chemical spaces and networks, becomes exceedingly heavy. In this work, we critically assess the optimal structure and minimal size of an ab initio training set able to lead to accurate free-energy profiles sampled with neural network potentials. The results allow one to propose an ab initio protocol where the ad hoc inclusion of a machine-learning (ML)-based task can significantly increase the computational efficiency, while keeping the ab initio accuracy and, at the same time, avoiding some of the notorious extrapolation risks in typical atomistic ML approaches. We focus on two representative, and computationally challenging, reaction steps of the classic Strecker-cyanohydrin mechanism for glycine synthesis in water solution, where the main precursors are formaldehyde and hydrogen cyanide. We demonstrate that indistinguishable ab initio quality results are obtained, thanks to the ML subprotocol, at about 1 order of magnitude less of computational load.

Mode Selective Chemistry for the Dissociation of Methane on Efficient Ni/Pt-Bimetallic Alloy Catalysts

The mode selectivity of methane dissociation is studied on three different Ni/Pt-bimetallic alloy surfaces using a fully quantum approach based on reaction path Hamiltonian. Dissociative sticking probability depends on the...

Accurate Simulations of the Reaction of H2 on a Curved Pt Crystal through Machine Learning

Theoretical studies on molecule-metal surface reactions have so far been limited to small surface unit cells due to computational costs. Here, for the first time molecular dynamics simulations on very large surface unit cells at the level of density functional theory are performed, allowing a direct comparison to experiments performed on a curved crystal. Specifically, the reaction of D2 on a curved Pt crystal is investigated with a neural network potential (NNP). The developed NNP is also accurate for surface unit cells considerably larger than those that have been included in the training data, allowing dynamical simulations on very large surface unit cells that otherwise would have been intractable. Important and complex aspects of the reaction mechanism are discovered such as diffusion and a shadow effect of the step. Furthermore, conclusions from simulations on smaller surface unit cells cannot always be transfered to larger surface unit cells, limiting the applicability of theoretical studies of smaller surface unit cells to heterogeneous catalysts with small defect densities.

CO organization at ambient pressure on stepped Pt surfaces: first principles modeling accelerated by neural networks

Step and kink sites at Pt surfaces have crucial importance in catalysis. We employ a high dimensional neural network potential (HDNNP) trained using first-principles calculations to determine the adsorption structure of CO under ambient conditions (T = 300 K and P = 1 atm) on these surfaces. To thoroughly explore the potential energy surface (PES), we use a modified basin hopping method. We utilize the explored PES to identify the adsorbate structures and show that under the considered conditions several low free energy structures exist. Under the considered temperature and pressure conditions, the step edge (or kink) is totally occupied by on-top CO molecules. We show that the step structure and the structure of CO molecules on the step dictate the arrangement of CO molecules on the lower terrace. On surfaces with (111) steps, like Pt(553), CO forms quasi-hexagonal structures on the terrace with the top site preferred, with on average two top site CO for one multiply bonded CO, while in contrast surfaces with (100) steps, like Pt(557), present a majority of multiply bonded CO on their terrace. Short terraced surfaces, like Pt(643), with square (100) steps that are broken by kink sites constrain the CO arrangement parallel to the step edge. Overall, this effort provides detailed analysis on the influence of the step edge structure, kink sites, and terrace width on the organization of CO molecules on non-reconstructed stepped surfaces, yielding initial structures for understanding restructuring events driven by CO at high coverages and ambient pressure.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Highly Efficient Activation of HCl Dissociation on Au(111) via Rotational Preexcitation

The probability for dissociation of molecules on metal surfaces, which often controls the rate of industrially important catalytic processes, can depend strongly on how energy is partitioned in the incident molecule. There are many example systems where the addition of vibrational energy promotes reaction more effectively than the addition of translational energy, but for rotational pre-excitation similar examples have not yet been discovered. Here, we make an experimentally testable theoretical prediction that adding energy to the rotation of HCl can promote its dissociation on Au(111) 20 times more effectively than increasing its translational energy. In the underlying mechanism, the molecule's initial rotational motion allows it to pass through a critical region of the reaction path, where this path shows a strong and nonmonotonic dependence on the molecular orientation.

Photoinduced Desorption Dynamics of CO from Pd(111): A Neural Network Approach

Modeling the ultrafast photoinduced dynamics and reactivity of adsorbates on metals requires including the effect of the laser-excited electrons and, in many cases, also the effect of the highly excited surface lattice. Although the recent ab initio molecular dynamics with electronic friction and thermostats, (T_e,T_l)-AIMDEF [AlducinM.;Phys. Rev. Lett.2019, 123, 246802]31922860, enables such complex modeling, its computational cost may limit its applicability. Here, we use the new embedded atom neural network (EANN) method [ZhangY.;J. Phys. Chem. Lett.2019, 10, 496231397157] to develop an accurate and extremely complex potential energy surface (PES) that allows us a detailed and reliable description of the photoinduced desorption of CO from the Pd(111) surface with a coverage of 0.75 monolayer. Molecular dynamics simulations performed on this EANN-PES reproduce the (T_e,T_l)-AIMDEF results with a remarkable level of accuracy. This demonstrates the outstanding performance of the obtained EANN-PES that is able to reproduce available density functional theory (DFT) data for an extensive range of surface temperatures (90–1000 K); a large number of degrees of freedom, those corresponding to six CO adsorbates and 24 moving surface atoms; and the varying CO coverage caused by the abundant desorption events.

Computational approaches to dissociative chemisorption on metals: towards chemical accuracy

We review the state-of-the-art in the theory of dissociative chemisorption (DC) of small gas phase molecules on metal surfaces, which is important to modeling heterogeneous catalysis for practical reasons, and for achieving an understanding of the wealth of experimental information that exists for this topic, for fundamental reasons. We first give a quick overview of the experimental state of the field. Turning to the theory, we address the challenge that barrier heights (E_b, which are not observables) for DC on metals cannot yet be calculated with chemical accuracy, although embedded correlated wave function theory and diffusion Monte-Carlo are moving in this direction. For benchmarking, at present chemically accurate E_b can only be derived from dynamics calculations based on a semi-empirically derived density functional (DF), by computing a sticking curve and demonstrating that it is shifted from the curve measured in a supersonic beam experiment by no more than 1 kcal mol^-1. The approach capable of delivering this accuracy is called the specific reaction parameter (SRP) approach to density functional theory (DFT). SRP-DFT relies on DFT and on dynamics calculations, which are most efficiently performed if a potential energy surface (PES) is available. We therefore present a brief review of the DFs that now exist, also considering their performance on databases for E_b for gas phase reactions and DC on metals, and for adsorption to metals. We also consider expressions for SRP-DFs and briefly discuss other electronic structure methods that have addressed the interaction of molecules with metal surfaces. An overview is presented of dynamical models, which make a distinction as to whether or not, and which dissipative channels are modeled, the dissipative channels being surface phonons and electronically non-adiabatic channels such as electron-hole pair excitation. We also discuss the dynamical methods that have been used, such as the quasi-classical trajectory method and quantum dynamical methods like the time-dependent wave packet method and the reaction path Hamiltonian method. Limits on the accuracy of these methods are discussed for DC of diatomic and polyatomic molecules on metal surfaces, paying particular attention to reduced dimensionality approximations that still have to be invoked in wave packet calculations on polyatomic molecules like CH₄. We also address the accuracy of fitting methods, such as recent machine learning methods (like neural network methods) and the corrugation reducing procedure. In discussing the calculation of observables we emphasize the importance of modeling the properties of the supersonic beams in simulating the sticking probability curves measured in the associated experiments. We show that chemically accurate barrier heights have now been extracted for DC in 11 molecule-metal surface systems, some of which form the most accurate core of the only existing database of E_b for DC reactions on metal surfaces (SBH10). The SRP-DFs (or candidate SRP-DFs) that have been derived show transferability in many cases, i.e., they have been shown also to yield chemically accurate E_b for chemically related systems. This can in principle be exploited in simulating rates of catalyzed reactions on nano-particles containing facets and edges, as SRP-DFs may be transferable among systems in which a molecule dissociates on low index and stepped surfaces of the same metal. In many instances SRP-DFs have allowed important conclusions regarding the mechanisms underlying observed experimental trends. An important recent observation is that SRP-DFT based on semi-local exchange DFs has so far only been successful for systems for which the difference of the metal work function and the molecule's electron affinity exceeds 7 eV. A main challenge to SRP-DFT is to extend its applicability to the other systems, which involve a range of important DC reactions of e.g. O₂, H₂O, NH₃, CO₂, and CH₃OH. Recent calculations employing a PES based on a screened hybrid exchange functional suggest that the road to success may be based on using exchange functionals of this category.

Effect of surface temperature on quantum dynamics of H2 on Cu(111) using a chemically accurate potential energy surface

The effect of surface atom vibrations on H₂ scattering from a Cu(111) surface at different temperatures is being investigated for hydrogen molecules in their rovibrational ground state (v = 0, j = 0). We assume weakly correlated interactions between molecular degrees of freedom and surface modes through a Hartree product type wavefunction. While constructing the six-dimensional effective Hamiltonian, we employ (a) a chemically accurate potential energy surface according to the static corrugation model [M. Wijzenbroek and M. F. Somers, J. Chem. Phys. 137, 054703 (2012)]; (b) normal mode frequencies and displacement vectors calculated with different surface atom interaction potentials within a cluster approximation; and (c) initial state distributions for the vibrational modes according to Bose-Einstein probability factors. We carry out 6D quantum dynamics with the so-constructed effective Hamiltonian and analyze sticking and state-to-state scattering probabilities. The surface atom vibrations affect the chemisorption dynamics. The results show physically meaningful trends for both reaction and scattering probabilities compared to experimental and other theoretical results.

Deep Eutectic Solvents: A Review of Fundamentals and Applications

Deep eutectic solvents (DESs) are an emerging class of mixtures characterized by significant depressions in melting points compared to those of the neat constituent components. These materials are promising for applications as inexpensive "designer" solvents exhibiting a host of tunable physicochemical properties. A detailed review of the current literature reveals the lack of predictive understanding of the microscopic mechanisms that govern the structure-property relationships in this class of solvents. Complex hydrogen bonding is postulated as the root cause of their melting point depressions and physicochemical properties; to understand these hydrogen bonded networks, it is imperative to study these systems as dynamic entities using both simulations and experiments. This review emphasizes recent research efforts in order to elucidate the next steps needed to develop a fundamental framework needed for a deeper understanding of DESs. It covers recent developments in DES research, frames outstanding scientific questions, and identifies promising research thrusts aligned with the advancement of the field toward predictive models and fundamental understanding of these solvents.

Time-dependent quantum mechanical wave packet dynamics

Starting from a model study of the collinear (H, H₂) exchange reaction in 1959, the time-dependent quantum mechanical wave packet (TDQMWP) method has come a long way in dealing with systems as large as Cl + CH₄. The fast Fourier transform method for evaluating the second order spatial derivative of the wave function and split-operator method or Chebyshev polynomial expansion for determining the time evolution of the wave function for the system have made the approach highly accurate from a practical point of view. The TDQMWP methodology has been able to predict state-to-state differential and integral reaction cross sections accurately, in agreement with available experimental results for three dimensional (H, H₂) collisions, and identify reactive scattering resonances too. It has become a practical computational tool in predicting the observables for many A + BC exchange reactions in three dimensions and a number of larger systems. It is equally amenable to determining the bound and quasi-bound states for a variety of molecular systems. Just as it is able to deal with dissociative processes (without involving basis set expansion), it is able to deal with multi-mode nonadiabatic dynamics in multiple electronic states with equal ease. We present an overview of the method and its strength and limitations, citing examples largely from our own research groups.

Designing new SRP density functionals including non-local vdW-DF2 correlation for H2 + Cu(111) and their transferability to H2 + Ag(111), Au(111) and Pt(111)

Specific reaction parameter density functionals (SRP-DFs) that can describe dissociative chemisorption molecular beam experiments of hydrogen (H₂) on cold transition metal surfaces with chemical accuracy have so far been shown to be only transferable among different facets of the same metal, but not among different metals. We design new SRP-DFs that include non-local vdW-DF2 correlation for the H₂ + Cu(111) system, and evaluate their transferability to the highly activated H₂ + Ag(111) and H₂ + Au(111) systems and the non-activated H₂ + Pt(111) system. We design our functionals for the H₂ + Cu(111) system since it is the best studied system both theoretically and experimentally. Here we demonstrate that a SRP-DF fitted to reproduce molecular beam sticking experiments for H₂ + Cu(111) with chemical accuracy can also describe such experiments for H₂ + Pt(111) with chemical accuracy, and vice versa. Chemically accurate functionals have been obtained that perform very well with respect to reported van der Waals well geometries, and which improve the description of the metal over current generalized gradient approximation (GGA) based SRP-DFs. From a systematic comparison of our new SRP-DFs that include non-local correlation to previously developed SRP-DFs, for both activated and non-activated systems, we identify non-local correlation as a key ingredient in the construction of transferable SRP-DFs for H₂ interacting with transition metals. Our results are in excellent agreement with experiment when accurately measured observables are available. It is however clear from our analysis that, except for the H₂ + Cu(111) system, there is a need for more, more varied, and more accurately described experiments in order to further improve the design of SRP-DFs. Additionally, we confirm that, when including non-local correlation, the sticking of H₂ on Cu(111) is still well described quasi-classically.

Generating transition states of isomerization reactions with deep learning

Lack of quality data and difficulty generating these data hinder quantitative understanding of reaction kinetics. Specifically, conventional methods to generate transition state structures are deficient in speed, accuracy, or scope. We describe a novel method to generate three-dimensional transition state structures for isomerization reactions using reactant and product geometries. Our approach relies on a graph neural network to predict the transition state distance matrix and a least squares optimization to reconstruct the coordinates based on which entries of the distance matrix the model perceives to be important. We feed the structures generated by our algorithm through a rigorous quantum mechanics workflow to ensure the predicted transition state corresponds to the ground truth reactant and product. In both generating viable geometries and predicting accurate transition states, our method achieves excellent results. We envision workflows like this, which combine neural networks and quantum chemistry calculations, will become the preferred methods for computing chemical reactions.

Neural Network Potential Energy Surfaces for Small Molecules and Reactions

We review progress in neural network (NN)-based methods for the construction of interatomic potentials from discrete samples (such as ab initio energies) for applications in classical and quantum dynamics including reaction dynamics and computational spectroscopy. The main focus is on methods for building molecular potential energy surfaces (PES) in internal coordinates that explicitly include all many-body contributions, even though some of the methods we review limit the degree of coupling, due either to a desire to limit computational cost or to limited data. Explicit and direct treatment of all many-body contributions is only practical for sufficiently small molecules, which are therefore our primary focus. This includes small molecules on surfaces. We consider direct, single NN PES fitting as well as more complex methods that impose structure (such as a multibody representation) on the PES function, either through the architecture of one NN or by using multiple NNs. We show how NNs are effective in building representations with low-dimensional functions including dimensionality reduction. We consider NN-based approaches to build PESs in the sums-of-product form important for quantum dynamics, ways to treat symmetry, and issues related to sampling data distributions and the relation between PES errors and errors in observables. We highlight combinations of NNs with other ideas such as permutationally invariant polynomials or sums of environment-dependent atomic contributions, which have recently emerged as powerful tools for building highly accurate PESs for relatively large molecular and reactive systems.

High-Fidelity Potential Energy Surfaces for Gas-Phase and Gas-Surface Scattering Processes from Machine Learning

In this Perspective, we review recent advances in constructing high-fidelity potential energy surfaces (PESs) from discrete ab initio points, using machine learning tools. Such PESs, albeit with substantial initial investments, provide significantly higher efficiency than direct dynamics methods and/or high accuracy at a level that is not affordable by on-the-fly approaches. These PESs not only are a necessity for quantum dynamical studies because of delocalization of wave packets but also enable the study of low-probability and long-time events in (quasi-)classical treatments. Our focus here is on inelastic and reactive scattering processes, which are more challenging than bound systems because of the involvement of continua. Relevant applications and developments for dynamical processes in both the gas phase and at gas-surface interfaces are discussed.

Ensemble-Based Molecular Simulation of Chemical Reactions under Vibrational Nonequilibrium

We present an approach to incorporate the effect of vibrational nonequilibrium in molecular dynamics (MD) simulations. A perturbed canonical ensemble, in which selected modes are excited to higher temperature while all others remain equilibrated at low temperature, is simulated by applying a specifically tailored bias potential. Our method can be readily applied to any (classical or quantum mechanical) MD setup at virtually no additional computational cost and allows the study of reactions of vibrationally excited molecules in nonequilibrium environments such as plasmas. In combination with enhanced sampling methods, the vibrational efficacy and mode selectivity of vibrationally stimulated reactions can then be quantified in terms of chemically relevant observables, such as reaction rates and apparent free energy barriers. We first validate our method for the prototypical hydrogen exchange reaction and then show how it can capture the effect of vibrational excitation on a symmetric S_N2 reaction and radical addition on CO₂.

Unified and transferable description of dynamics of H2 dissociative adsorption on multiple copper surfaces via machine learning

Schematic of the developed neural network potential energy surface enabling a unified and transferable description of dynamics of H₂ dissociative adsorption on multiple copper surfaces.

Dynamical Study of the Dissociative Chemisorption of CHD3 on Pd(111)

The specific reaction parameter (SRP) approach to density functional theory has been shown to model reactions of polyatomic molecules with metal surfaces important for heterogeneous catalysis in the industry with chemical accuracy. However, transferability of the SRP functional among systems in which methane interacts with group 10 metals remains unclear for methane + Pd(111). Therefore, in this work, predictions have been made for the reaction of CHD₃ on Pd(111) using Born-Oppenheimer molecular dynamics while also performing a rough comparison with experimental data for CH₄ + Pd(111) obtained for lower incidence energies. Hopefully, future experiments can test the transferability of the SRP functional among group 10 metals also for Pd(111). We found that the reactivity of CHD₃ on Pd(111) is intermediate between and similar to either Pt(111) or Ni(111), depending on the incidence energy and the initial vibrational state distribution. This is surprising because the barrier height and experiments performed at lower incidence energies than investigated here suggest that the reactivity of Pd(111) should be similar to that of Pt(111) only. The relative decrease in the reactivity of Pd(111) at high incidence energies is attributed to site specificity of the reaction and to dynamical effects such as the bobsled effect and energy transfer from methane to the surface.