Sampling Real-Time Atomic Dynamics in Metal Nanoparticles by Combining Experiments, Simulations, and Machine Learning.

Even at low temperatures, metal nanoparticles (NPs) possess atomic dynamics that are key for their properties but challenging to elucidate. Recent experimental advances allow obtaining atomic-resolution snapshots of the NPs in realistic regimes, but data acquisition limitations hinder the experimental reconstruction of the atomic dynamics present within them. Molecular simulations have the advantage that these allow directly tracking the motion of atoms over time. However, these typically start from ideal/perfect NP structures and, suffering from sampling limits, provide results that are often dependent on the initial/putative structure and remain purely indicative. Here, by combining state-of-the-art experimental and computational approaches, how it is possible to tackle the limitations of both approaches and resolve the atomistic dynamics present in metal NPs in realistic conditions is demonstrated. Annular dark-field scanning transmission electron microscopy enables the acquisition of ten high-resolution images of an Au NP at intervals of 0.6 s. These are used to reconstruct atomistic 3D models of the real NP used to run ten independent molecular dynamics simulations. Machine learning analyses of the simulation trajectories allow resolving the real-time atomic dynamics present within the NP. This provides a robust combined experimental/computational approach to characterize the structural dynamics of metal NPs in realistic conditions.

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.

Machine learning of atomic dynamics and statistical surface identities in gold nanoparticles.

It is known that metal nanoparticles (NPs) may be dynamic and atoms may move within them even at fairly low temperatures. Characterizing such complex dynamics is key for understanding NPs' properties in realistic regimes, but detailed information on, e.g., the stability, survival, and interconversion rates of the atomic environments (AEs) populating them are non-trivial to attain. In this study, we decode the intricate atomic dynamics of metal NPs by using a machine learning approach analyzing high-dimensional data obtained from molecular dynamics simulations. Using different-shape gold NPs as a representative example, an AEs' dictionary allows us to label step-by-step the individual atoms in the NPs, identifying the native and non-native AEs and populating them along the MD simulations at various temperatures. By tracking the emergence, annihilation, lifetime, and dynamic interconversion of the AEs, our approach permits estimating a "statistical equivalent identity" for metal NPs, providing a comprehensive picture of the intrinsic atomic dynamics that shape their properties.

Innate dynamics and identity crisis of a metal surface unveiled by machine learning of atomic environments.

Metals are traditionally considered hard matter. However, it is well known that their atomic lattices may become dynamic and undergo reconfigurations even well below the melting temperature. The innate atomic dynamics of metals is directly related to their bulk and surface properties. Understanding their complex structural dynamics is, thus, important for many applications but is not easy. Here, we report deep-potential molecular dynamics simulations allowing to resolve at an atomic resolution the complex dynamics of various types of copper (Cu) surfaces, used as an example, near the Hüttig (∼1/3 of melting) temperature. The development of deep neural network potential trained on density functional theory calculations provides a dynamically accurate force field that we use to simulate large atomistic models of different Cu surface types. A combination of high-dimensional structural descriptors and unsupervized machine learning allows identifying and tracking all the atomic environments (AEs) emerging in the surfaces at finite temperatures. We can directly observe how AEs that are non-native in a specific (ideal) surface, but that are, instead, typical of other surface types, continuously emerge/disappear in that surface in relevant regimes in dynamic equilibrium with the native ones. Our analyses allow estimating the lifetime of all the AEs populating these Cu surfaces and to reconstruct their dynamic interconversions networks. This reveals the elusive identity of these metal surfaces, which preserve their identity only in part and in part transform into something else under relevant conditions. This also proposes a concept of "statistical identity" for metal surfaces, which is key to understanding their behaviors and properties.

How Collective Phenomena Impact CO2 Reactivity and Speciation in Different Media.

CO2 has attracted considerable attention in recent years due to its role in the greenhouse effect and environmental management. While its reaction with water has been studied extensively, the same cannot be said for reactivity in the supercritical CO2 phase, where the conjugate acid/base equilibria proceed through different mechanisms and activation barriers. In spite of the apparent simplicity of the CO2 + H2O reaction, the collective effect of different environments has a drastic influence on the free energy profile. Enhanced sampling techniques and well-tailored collective variables provide a detailed picture of the enthalpic and entropic drivers underscoring the differences in the formation mechanism of carbonic acid in the gas, aqueous, and supercritical CO2 phases.

Kinetics of Aqueous Media Reactions via Ab Initio Enhanced Molecular Dynamics: The Case of Urea Decomposition.

Aqueous solutions provide a medium for many important reactions in chemical synthesis, industrial processes, environmental chemistry, and biological functions. It is an accepted fact that aqueous solvents can be direct participants in the reaction process and not act only as simple passive dielectrics. Assisting water molecules and proton wires are thus essential for the efficiency of many reactions. Here, we study the decomposition of urea into ammonia and isocyanic acid by means of enhanced ab initio molecular dynamics simulations. We highlight the role of the solvent molecules and their interactions with the reactants providing a proper description of the reaction mechanism and how the water hydrogen-bond network affects the reaction dynamics. Reaction free energy and rates have been calculated taking into account this important effect.

The Onset of Dehydrogenation in Solid Ammonia Borane: An Ab Initio Metadynamics Study.

The discovery of effective hydrogen storage materials is fundamental for the progress of a clean energy economy. Ammonia borane (H3 BNH3 , AB) has attracted great interest as a promising candidate but the reaction path that leads from its solid phase to hydrogen release is not yet fully understood. To address the need for insights in the atomistic details of such a complex solid state process, in this work we use ab-initio molecular dynamics and metadynamics to study the early stages of AB dehydrogenation. We show that the formation of ammonia diborane (H3 NBH2 (µ-H)BH3 ) leads to the release of NH4 + , which in turn triggers an autocatalytic H2 production cycle. Our calculations provide a model for how complex solid state reactions can be theoretically investigated and rely upon the presence of multiple ammonia borane molecules, as substantiated by standard quantum-mechanical simulations on a cluster.

Revealing the role of phosphoric acid in all-vanadium redox flow batteries with DFT calculations and in situ analysis.

The present work suggests the use of a mixed water-based electrolyte containing sulfuric and phosphoric acid for both negative and positive electrolytes of a vanadium redox flow battery. Computational and experimental investigations reveal insights on the possible interactions between the vanadium ions in all oxidation states and sulphate, bisulphate, dihydrogen phosphate ions and phosphoric acid. In situ cycling experiments and ion-specific electrochemical impedance measurements confirmed a significant lowering of the charge-transfer resistance for the reduction of V(iii) ions and, consequently, an increase of the voltaic efficiency associated with the negative side of the battery. This increase of performance is attributable to the complexation of this oxidation state by phosphoric acid. So far, mixed acids have mainly been discussed with the focus on V(v) solubility. In this work we rationalize the impact of the mixed acids on the electrochemical efficiency opening new strategies on how to improve the cycling performance with ionic additives.

Identifying Slow Molecular Motions in Complex Chemical Reactions.

We have studied the cyclization reaction of deprotonated 4-chloro-1-butanethiol to tetrahydrothiophene by means of well-tempered metadynamics. To properly select the collective variables, we used the recently proposed variational approach to conformational dynamics within the framework of metadyanmics. This allowed us to select the appropriate linear combinations from a set of collective variables representing the slow degrees of freedom that best describe the slow modes of the reaction. We performed our calculations at three different temperatures, namely, 300, 350, and 400 K. We show that the choice of such collective variables allows one to easily interpret the complex free-energy surface of such a reaction by univocal identification of the conformers belonging to reactants and product states playing a fundamental role in the reaction mechanism.

Combustion chemistry via metadynamics: benzyl decomposition revisited.

Large polycyclic aromatic hydrocarbons (PAHs) are thought to be responsible for the formation of soot particles in combustion processes. However, there are still uncertainties on the course that leads small molecules to form PAHs. This is largely due to the high number of reactions and intermediates involved. Metadynamics combined with ab initio molecular dynamics can provide a very precious contribution because offers the possibility to explore new possible pathways and suggest new mechanisms. Here, we adopt this method to investigate the chemical evolution of the benzyl radical, whose role is very important in PAHs growth. This species has been intensely studied, and though most of its chemistry is known, there are still open questions regarding its decomposition. The simulation reproduces the most commonly accepted decomposition pathway and it suggests also a new one which can explain recent experimental data that are in contradiction with the old mechanism. In addition, quantitative free energy evaluation of some key reaction steps sheds light on the role of entropy.

Predictive theory for the addition and insertion kinetics of 1CH2 reacting with unsaturated hydrocarbons.

The reactions of singlet methylene, (1)CH2, with unsaturated hydrocarbons are of considerable significance to the formation and growth of polycyclic aromatic hydrocarbons (PAHs). In this work, we employ high level ab initio transition state theory to predict the high pressure rate coefficient for singlet methylene reacting with acetylene (C2H2), ethylene (C2H4), propyne (CH3CCH), propene (CH3CHCH2), allene (CH2CCH2), 1,3-butadiene (CH2CHCHCH2), 2-butyne (CH3CCCH3), and benzene (C6H6). Both addition and insertion channels are found to contribute significantly to the kinetics, with the insertion kinetics of increasing importance for larger hydrocarbons due to the increasing number of CH bonds and increasingly attractive interactions. We treat the addition kinetics with direct CASPT2 based variable-reaction-coordinate transition state theory. One-dimensional corrections to the CASPT2 interaction energies are obtained from geometry relaxation calculations and CCSD(T)/CBS evaluations. The insertion kinetics is treated with traditional variational TST methods employing CCSD(T)/CBS energies obtained along the CASPT2/cc-pVTZ distinguished coordinate reaction paths. The overall rate constant and branching fractions are obtained from a multiple transition state model that accounts for the physical distinction between tight inner and loose outer transition states. The predicted rate constants, which cover the range from 200 to 2000 K, are found to be in excellent agreement with the available experimental data, with a maximum observed discrepancy of about 40%.

Analysis of some reaction pathways active during cyclopentadiene pyrolysis.

The cyclopentadienyl radical (cC(5)H(5)) is among the most stable radical species that can be generated during the combustion and pyrolysis of hydrocarbons and it is generally agreed that its contribution to the gas phase reactivity is significant. In this study the kinetics of one key cC(5)H(5) reaction channel, namely the reaction between cC(5)H(5) and cyclopentadiene (cC(5)H(6)), was investigated using ab initio calculations and RRKM/Master Equation theory. It was found that most of the excited C(5)H(5)_C(5)H(6) adducts formed by the addition of cC(5)H(5) to cC(5)H(6) decompose back to reactants and that the major reaction products are, in order of importance, indene, vinylfulvene (a most probable styrene precursor), phenylbutadiene, and benzene. The preferred reaction pathway of the C(5)H(5)_C(5)H(6) adduct is started by the migration of the tertiary hydrogen of the C(5)H(5) ring to a vicinal carbon and followed by the ß-opening of the C(5)H(6) ring, which is the rate determining step. Successive molecular rearrangements lead to decomposition to the four possible products. The kinetic constants for the four reaction channels, calculated at atmospheric pressure and interpolated in cm(3) mol(-1) s(-1) between 900 and 2000 K, are k(indene) = 10(25.197)T(-3.935) exp(-11630/T(K)), k(vinylfulvene) = 10(65.077)T(-14.20) exp(-37567/T(K)), k(benzene) = 10(29.172)T(-4.515) exp(-20570/T(K)), and k(phenylbutadiene) = 10(16.743)T(-1.407) exp(-11804/T(K)). The predictive capability of the reaction set so determined was tested through the simulations of recent cC(5)H(6) pyrolysis and combustion experiments using a detailed kinetic mechanism. A quantitative agreement with experimental data was obtained by assuming that vinylfulvene converts rapidly to stryrene, increasing its reaction channel by a factor of 2, and assuming that phenylbutadiene rapidly decomposes with equal probability to styrene and benzene.

Toluene and benzyl decomposition mechanisms: elementary reactions and kinetic simulations.

The high temperature decomposition kinetics of toluene and benzyl were investigated by combining a kinetic analysis with the ab initio/master equation study of new reaction channels. It was found that similarly to toluene, which decomposes to benzyl and phenyl losing atomic hydrogen and methyl, also benzyl decomposition proceeds through two channels with similar products. The first leads to the formation of fulvenallene and hydrogen and has already been investigated in detail in recent publications. In this work it is proposed that benzyl can decompose also through a second decomposition channel to form benzyne and methyl. The channel specific kinetic constants of benzyl decomposition were determined by integrating the RRKM/master equation over the C(7)H(7) potential energy surface. The energies of wells and saddle points were determined at the CCSD(T) level on B3LYP/6-31+G(d,p) structures. A kinetic mechanism was then formulated, which comprises the benzyl and toluene decomposition reactions together with a recently proposed fulvenallene decomposition mechanism, the decomposition kinetics of the fulvenallenyl radical, and some reactions describing the secondary chemistry originated by the decomposition products. The kinetic mechanism so obtained was used to simulate the production of H atoms measured in a wide pressure and temperature range using different experimental setups. The calculated and experimental data are in good agreement. Kinetic constants of the new reaction channels here examined are reported as a function of temperature at different pressures. The mechanism here proposed is not compatible with the assumption often used in literature kinetic mechanisms that benzyl decomposition can be effectively described through a lumped reaction whose products are the cyclopentadienyl radical and acetylene.

Fulvenallene decomposition kinetics.

While the decomposition kinetics of the benzyl radical has been studied in depth both from the experimental and the theoretical standpoint, much less is known about the reactivity of what is likely to be its main decomposition product, fulvenallene. In this work the high temperature reactivity of fulvenallene was investigated on a Potential Energy Surface (PES) consisting of 10 wells interconnected through 11 transition states using a 1 D Master Equation (ME). Rate constants were calculated using RRKM theory and the ME was integrated using a stochastic kinetic Monte Carlo code. It was found that two main decomposition channels are possible, the first is active on the singlet PES and leads to the formation of the fulvenallenyl radical and atomic hydrogen. The second requires intersystem crossing to the triplet PES and leads to acetylene and cyclopentadienylidene. ME simulations were performed calculating the microcanonical intersystem crossing frequency using Landau-Zener theory convoluting the crossing probability with RRKM rates evaluated at the conical intersection. It was found that the reaction channel leading to the cyclopentadienylidene diradical is only slightly faster than that leading to the fulvenallenyl radical, so that it can be concluded that both reactions are likely to be active in the investigated temperature (1500-2000 K) and pressure (0.05-50 bar) ranges. However, the simulations show that intersystem crossing is rate limiting for the first reaction channel, as the removal of this barrier leads to an increase of the rate constant by a factor of 2-3. Channel specific rate constants are reported as a function of temperature and pressure.

Analysis of the reactivity on the c7h6 potential energy surface.

The reactivity and decomposition kinetics on the C(7)H(6) potential energy surface (PES) were investigated, determining structures of stationary points at the B3LYP/6-31+G(d,p) level and energies at the CCSD(T)/cc-pVTZ level with extension to the complete basis set limit. For the reactions characterized by a significant multireference character, the energies were calculated at the CASPT2/cc-pVTZ level. The portion of the PES investigated consisted of 27 wells connected by 39 saddle points. Of the 27 wells, 16 can be accessed through transition states having activation energies smaller than the dissociation threshold. In agreement with previous theoretical studies, it was found that the main interconversion channel takes place on the singlet PES and connects phenylcarbene, cycloheptatetrane, spiroheptatriene, fulvenallene, and three ethynylcyclopentadiene isomers. Two new mechanisms are proposed for the formation of 5-ethynylcyclopentadiene and for the conversion of spiroheptatriene to fulvenallene. The unimolecular decomposition kinetics was thoroughly investigated. It was found that the fastest high pressure decomposition channel, at the temperatures at which C(7)H(6) undergoes unimolecular decomposition (1500--2000 K), leads to the formation of cyclopentadienylidene and acetylene. The rate of crossing from the singlet to the triplet PES may affect considerably this reaction channel, as it is formally spin forbidden. The alternative pathway, which is the decomposition to fulvenallenyl, is however only a factor of 2--3 slower and significantly less activated (82 vs 96 kcal/mol).

Theoretical investigation of germane and germylene decomposition kinetics.

The dissociation kinetics of germane and its decomposition products were studied determining microcanonical kinetic constants with RRKM theory and integrating the master equation using a stochastic approach. Relevant reaction parameters were calculated through first principles calculations. Structures of reactants and transition states were determined at the B3LYP/aug-cc-pvtz level while energies were computed at the CCSD(T) level and extended to the complete basis set limit. Though similar for many aspects to the kinetics of decomposition of SiH(4), GeH(4) has some peculiar features that indicate a different chemical reactivity. It was found that the main decomposition channel leads to the formation of germylene, GeH(2), which rapidly decomposes to atomic Ge and H(2). The dissociation of GeH(2) to Ge and H(2) is a formally spin forbidden reaction characterized by an activation energy of 160.3 kJ mol(-1) calculated at the minimum energy crossing point between the singlet and triplet states. The intersystem crossing probability was explicitly included in the microcanonical simulations through Landau-Zener theory. It was found that its effect on the reaction rate is almost negligible, both because of the large spin-orbit coupling between the singlet and triplet states and for the fall off conditions prevailing in the examined pressure and temperature ranges. Kinetic constants of the main decomposition channels were determined as a function of pressure and temperature between 0.0013 and 10 bar and 1100 and 1700 K. The high and low pressure kinetic constants for GeH(4) decomposition are 6.4 x 10(13) (T/K)(0.272) exp(-26 700 K/T) and 2.7 x 10(48) (T/K)(-9.05) exp(-31 600 K/T), while those for GeH(2) are 6.02 x 10(12) (T/K)(0.203) exp(-19 660 K/T) and 1.6 x 10(26) (T/K)(-3.06) exp(-21 121 K/T), respectively. A quantitative agreement with experimental data for GeH(4) decomposition could be obtained adopting a downward energy transfer parameter of 340 x (T/298 K)(0.85) cm(-1) in the collisional model, and assuming that atomic Ge can react fast with GeH(4) to form Ge(2)H(2) and H(2), thus enhancing the germane decomposition rate and suggesting that a fast kinetic route leading to the Ge(2)H(2) production can be active in the gas phase.