Chemical reaction dynamics and kinetics

Stickstoff- und Kohlenstoffverbindungen im interstellaren Staub verraten, wie Sterne entstehen. Diese Moleküle haben Weltraumforscher:innen mit hochauflösender Rotationsspektroskopie detektiert und dazu die Verhältnisse im All im Labor nachgestellt. Wie organische Reaktionen wie nukleophile Substitution auf Molekülebene ablaufen, lässt sich mit Molekularstrahlmethoden herausfinden. Streumethoden dienen dazu, Reaktionen auf Oberflächen auf atomarer Ebene zu erfassen. Zeitaufgelöste Beugungsmethoden mit ultrakurzen Elektronen oder Röntgenphotonen werden zunehmend auf chemische Fragen angewandt, um Strukturen transienter Zustände zu beobachten.

Chemical reaction dynamics and kinetics

Gas phase: Dynamics and kinetics at the molecular level

Probing a reactive collision allows us to gain insight into how molecules rearrange at the atomic level and how energy is redistributed during the elementary chemical reaction. Reactions can happen upon impact, which generally leads to rapidly formed product ions. Or, the reactants can form an interaction complex, the lifetime of which exceeds several rotational periods, and during that time energy redistribution is feasible leading to slowly formed product ions. We refer to this as indirect dynamics.

The impact parameter – the nearest distance between the two reactant centers upon collision – influences the momentum transfer and thus the scattering angle as the particles move away from each other. Hence, scattering angle and product ion velocity encode information on the molecular level processes happening during the collision, including possible quantum effects. Ion imaging,¹⁾ which lead to velocity map imaging (VMI),²⁾ gives us an experimental tool to measure the product ion velocity distribution, mapping ions with the same velocity onto the same spot on a position sensitive detector. While the investigated systems span a wide range of molecules and collision energies, two major objectives of the field of molecular reaction dynamics have always remained: To achieve full quantum state control of the reaction, and to increase chemical complexity of the reactants. Both objectives push experimental technology and theoretical methodology to its limits and beyond with the aim to merge both goals and reach full quantum state control for larger and larger systems.

For few atom reactions full quantum state control can be achieved; this means that state-to-state differential cross sections can be measured and quantum phenomena identified.^3,4) Here we will focus on the second objective, i.e. increasing chemical complexity, with the aim to study the dynamics of elementary reactions of classic organic reaction mechanisms. By transferring these reactions into the gas phase, we can study a system in which the interactions with the environment can be controlled in the experiment. Probing (differential) cross sections and product energy distributions offer new experimental insights into seemingly well-understood classic mechanisms. Several reviews have been published on the topic in recent years.^5–8) In the present review, we highlight

the synergy of experiment and theory for ion-molecule crossed beam imaging experiments,reactions with conformer selected reactants paving the way towards quantum state control, andopen-shell systems involving multiple spin states along the reaction coordinate.

Nucleophilic substitutions and eliminations

One of most prominent mechanistic competitions in synthetic chemistry is between bimolecular nucleophilic substitution, S_N2, and base induced elimination, E2. Since the same ionic product is formed in both reactions, it is a challenge to disentangle them in an experiment which relies on mass spectrometric detection alone – we require another observable besides counting ions. In a joint effort, experimentalists, led by Roland Wester, and theoreticians, led by Gábor Czakó, investigated the reaction between fluoride anions and chloroethane (F^– + CH₃CH₂Cl) by measuring energy and angle differential cross sections, and combining those with quasi classical trajectory simulations.⁹⁾ Scattering signatures for S_N2 and E2^10–12) are distinct due to the very different nature of the transition state geometry, a fact and property to which the differential cross section is sensitive. The agreement between experiment and theory for the total product ion angular and kinetic energy distributions allowed them to confidently disentangle contributions from all S_N2 and E2 reactions (Figure 1).

Recently, Dong H. Zhang and co-workers pushed the size limit for quasi classical trajectory simulations even further by studying the reaction of F⁻ with tert-butyl iodide.¹³⁾ Using a neural network approach, they constructed a full dimensional potential energy surface, upon which they ran quasi classical trajectories leading to a good agreement with experimental data.¹²⁾

Cyclo-additions

Another prominent reaction is the Diels-Alder cyclo-addition. Its transition state is very restrictive, and it is still up for debate whether the reaction proceeds in either a concerted or step-wise fashion for highly assymetric reactants with only the stereochemistry of the product obtained shedding any light on the problem. Stefan Willitsch and co-workers set out to provide a more conclusive answer by studying the reaction and comparing the reactivity of two conformers of 2,3-dibromo-1,3-dibutadiene, as only the gauche conformer allows for a concerted reaction.¹⁴⁾

Propene cations were prepared at ultra-low temperatures by loading them into a Coulomb crystal formed of calcium ions. A beam of conformationally selected 2,3-dibromo-1,3-dibutadiene was focused onto the crystal, and product formation was followed by monitoring the loss of propene ions from the Coulomb crystal. Conformer selection was achieved by the different degrees of deflection of the isomers in an inhomogeneous electric field due to their dipole moment. Aided by quantum chemical calculations, they demonstrated the competition between the step-wise and concerted mechanisms, with both processes being highly efficient at the collision rate limit (Figure 2). The different reactivity observed for both conformers can be explained by their different dipole moments, which influence the attractive long-range interactions.

The next step for understanding the influence of molecular conformations on the reactivity are dynamics experiments seeking to determine differential cross sections of conformationally selected reactants.¹⁵⁾

Open-shell systems

An option to increase the complexity of a reaction is by using open shell reactants. A common quantum effect associated with such systems is the crossing of spin surfaces along the reaction coordinate, known as intersystem crossing or multi-state reactivity. If the reaction in its electronic ground state is associated with a high barrier, crossing over to a second spin surface with a lower barrier, or even no barrier at all, can occur.

In a crossed beam study of O(³P) radicals with pyridine, a team led by Nadia Balucani found a complex ring opening mechanism only occurred if the reaction crossed spin surfaces while moving from the pre-reaction complex to the transition state region and finally crossing over the reaction barrier.¹⁶⁾ This phenomenon of spin crossing is even more prevalent in transition metal chemistry.¹⁷⁾

Our new crossed beam imaging experiment in Kaiserslautern focuses on transition metal ion molecule reactions with the aim to understand the dynamics of these reactions. In a first set of experiments, we studied the activation of carbon dioxide by 5d and 4d transition metal cations. Although these systems are small compared to the ones presented above, only four atoms, the electronic structure of the transition metal ion with its high number of close lying electronic states makes them a challenge for experiment and theory alike.

Elementary processes in heterogeneous catalysis

Most surface reactions, relevant to heterogeneous catalysis, proceed through the Langmuir-Hinshelwood mechanism, where reaction occurs upon adsorption of molecules onto the surface. Adsorption does not guarantee a successful reaction because of the competition between desorption and diffusion processes and the reactive events. Furthermore, reactions can take place at different active sites of a catalytic surface, such as steps and kinks, where transition states for reactions are stabilized. The absence of well-defined reactive encounters, such as collisions in the gas phase, raise additional challenges for studying surface chemistry in atomic detail.

Moreover, only the temperature of a surface can be controlled in the experiment. As a consequence, energy conservation between reactants and products does not hold in surface chemistry, since molecules adsorbed on surfaces exchange energy with a macroscopic object. This requires us to find ways to understand how thermalization of molecules at surfaces takes place, or how to measure thermal reaction rates, and learn to draw conclusions on the underling elementary processes from them.

In order for a reactant to adsorb at the surface, it has to lose translational energy on the first encounter with the catalyst to become trapped. A trapped molecule has not yet thermalized with the catalyst, but remains on the surface long enough in order to do so. A fully thermalized molecule is called an adsorbate.

Scattered atoms and molecules are less important to catalysis, but studying translational energy transferred to the solid or the internal degrees of freedom of the molecule provides us with understanding of the mechanisms to adsorption.

Mechanisms for energy loss of H-atoms at surfaces

H-atom surface scattering has been insightful in recent years. Photolytic dissociation of hydrogen halides provides H-atoms at well-defined translational energies. These beams are scattered from surfaces, and the resulting translational energy distribution is obtained via Rydberg Atom Tagging.¹⁸⁾ The mechanisms for translational energy loss differ substantially between insulator, semiconductor and metal surfaces. Atoms scattered from Xe-ice experience low translational energy loss, which is easily explained by mechanical energy transfer between the H and Xe-atom.¹⁹⁾

High energy loss is observed when H-atoms are scattered from metals. Excitations of electron-hole pairs in the metal are responsible for efficient sticking of H-atoms on metals.^18,20)

When scattering from germanium – a semiconductor – two energy loss channels are found. The first channel is due to energy transfer to phonons, similarly seen in scattering from Xe. The second channel is similar to the energy loss observed in metals, with the exception that it is offset by the semiconductor bandgap of the surface. This finding indicates that the translational energy of the H-atom is able to promote electrons from the valence to the conduction band. Describing this effect is a challenge to theory.²¹⁾

A different mechanism is found in H-atom scattering from graphene/Pt(111). The energy loss and angular distribution of some scattered atoms could be explained by transient bond formation with a C-atom, which was forced from a sp² to sp³ hybridization. As a result of the transient bond formation, vibrational energy from the C-H bond was channeled into vibrations of graphene via internal vibrational redistribution. This energy dissipation is likely responsible for hydrogenation of graphene surfaces.²²⁾

Following the microscopic pathways to adsorption

Exciting experiments have been performed on state-to-state surface scattering of molecules. Insights drawn from these experiments have revealed the pathways of energy flow for molecules and coupling to electrons in metals.²³⁾

cattering of vibrationally excited CO from Au(111) deserves special attention due to the insights into the mechanism of adsorption at surfaces. When CO(v=2) is scattered from Au(111), a trapping-desorption channel of CO(v=1) is observed. Trapping-desorption is when molecules are trapped on the surface and experience a finite residence time before desorption. While it is common that trapping-desorption channels reach full equilibration with the surface, CO(v=1) reaches translational and rotational thermalization, only. Survival of CO(v=1) has been explained through an unexpected high vibrational lifetime of ~50 ps which competes with the thermal desorption rate.^24,25) Since CO on Au(111) is physisorbed in its most stable configuration, it has low orbital overlap with surface electrons. As a consequence, the vibrational lifetime is higher compared to those where CO is chemisorbed, e.g. CO on Cu(111), and couples efficiently to electron-hole pairs.

The temperature dependence of CO(v=1) yields could not be explained with only the physisorbed state until a theoretical study suggested the existence of a metastable chemisorption state for CO on Au(111).²⁶⁾ Modelling of elementary rate constants for desorption and vibrational relaxation from physiosorbed and chemisorbed states of CO on Au(111) has been able to explain the observations from scattering experiments. It was then possible to understand how CO(v=2) is trapped in a chemisorption state and follows different microscopic pathways involving chemisorption and physisorption states until it fully thermalizes with the solid.²⁷⁾ This system is an important example for precursor mediated adsorption. It reflects that the process from molecule-surface collision to adsorption may involve different metastable binding configurations which couple differently to the solid, and transfer energy on different timescales.

Diffusion and active-site exchange

After adsorption, molecules diffuse to the active site of the catalyst where they may react. Although it is believed that diffusion cannot be a rate determining process for catalytic reactions, at high surface coverages the situation is not well understood.

A recent scanning tunneling microscopy study provided atomic scale insights into diffusion at high coverages. The finding was that O-atom diffusion on an otherwise CO saturated surface of Ru(0001) remained as fast as it would be on a clean sample. O-atom diffusion was enabled by the hopping of CO molecules over the surface as CO binds at different binding sites of Ru(0001). This situation allows CO to hop away from its most stable binding site, opening a vacancy for O-atoms to hop. The resulting empty spot can be filled by a CO.. This door-opening mechanism indicates that high diffusion rates may be expected even when sites for hopping are apparently absent (Figure 3).^28.)

A different story emerges from a study on NH₃ diffusion on clean and O-atom covered Pt(111). The ratio between the diffusion barrier and binding energy for NH₃ at Pt(111) is about 65 percent, while most other systems have a ratio of 20 percent. The ratio between diffusion barrier and adsorption energy increases to 85 percent when O-atoms block preferred hopping pathways of NH₃ on Pt(111).²⁹⁾ However, NH₃ oxidation of Pt takes place at steps at the surface. At high temperatures of industrial NH₃ oxidation in the Ostwald process, molecules adsorbing at terraces are unable to reach the steps prior to their desorption. As a result, it is likely that Ostwald chemistry is dominated by NH₃ initially adsorbed in close proximity to a step site.³⁰⁾ This industrially important system contradicts the established belief that surface diffusion is generally fast and cannot be rate limiting in heterogeneous catalysis.

Scaling active sites

Understanding the contribution of active sites of a catalyst is central to obtain an atomic scale picture of surface chemistry. One possibility is to study reaction rates as a function of the density of active sites on the catalyst. A popular strategy is the use of curved single crystal surfaces, where a catalytic metal is cut such that different regions of the crystal contain a different density of mono-atomic steps.³¹⁾ The combination of curved crystals with molecular beams, exposing a small but defined region of the sample, showed how active sites influence the sticking probability of H₂ on Pt, and clarified the active-site specific mechanism of adsorption.³²⁾

Identification of elementary processes at surfaces can also be made by following the desorption dynamics of reaction products. Products may have internal and translational energy release, which is specific to the geometry of the transition state.³³⁾ Catalytic active sites can stabilize transition states for the same chemical reaction differently.

Velocity resolved kinetics

The velocity resolved kinetics (VRK) method^33,35) allows to study surface reaction dynamics and surface reaction kinetics simultaneously and independently. The key to success is an ion imaging detector, which maps the velocity vectors of products formed at the surface upon reactant dosing with molecular beams. The reaction time is scanned by delaying an ionization laser with respect to reactant deposition, allowing to monitor the product formation rate as a function of the reaction time.

VRK was essential in the understanding of the active site-specific mechanism for CO oxidation on Pt. CO₂ formed at steps and terraces of Pt experienced different reaction dynamics and different rates of formation. This observation disproved the belief that different dynamic channels emerged as a consequence of post transition state dynamics, and shows that different elementary reactions are taking place.³⁴⁾

Quantum effects in thermal reaction rates

Dynamical features related to product formation are rare, and it is more likely that products thermalize with the surface prior to desorption. This is a drawback in the exploration of surface reaction dynamics. However, even in the absence of desorption dynamics, ion imaging can be used to calibrate the absolute flux of the molecular beam, helping to determine the reaction rate constants. This is important when second order processes like atom recombination are studied.

Recently, VRK provided thermal elementary rate constants for H-atom recombination on Pt(111), precise enough that comparison to theoretical models became useful. The best theories for surface reaction rates ignored electron spin and have not been able to treat nuclear quantum effects properly, which are crucial even at temperatures as high as 1000 K.³⁶⁾ These findings pave the way to making surface chemistry a more exact science.

Three Questions to: Jennifer Meyer

Which events in the past years surprised you the most?

The corona virus pandemic turned our routines completely upside down. I am amazed what is possible by digital communication in research and teaching, but I am really happy that we are back to in person teaching and scientific exchange. For me personally, the move back to my old university as a member of faculty has been somewhat unexpected.

Which development of the last years impacted your own research?

Reaction dynamics is always a synergy between experiment and theory. The speed with which potential energy surfaces for polyatomic reactions can be calculated today is amazing. The resulting trajectories are important for the interpretation of our experimental results.

Which research topic do you think will make the most progress?

Full state-to-state quantum resolution for crossed beam experiments is the aim for many scientists in reaction dynamics. The recent progress towards realising (British or American?) this goal has been amazing, and I expect there to be huge progress in the years to come, including advances in the study of ion-molecule reactions.

Jennifer Meyer joined the department of chemistry at TU Kaiserslautern (now RPTU Kaiserslautern-Landau) as a Junior Professor in physical chemistry in Fall 2020. After finishing her Ph.D. in the group of Gereon Niedner-Schatteburg (TU Kaiserslautern) in 2014, she joined the group of Roland Wester at the University of Innsbruck. In her research, she combines her interest on transition metal chemistry with reaction dynamics.

Three Questions To: Dmitriy Borodin

Which trend over the past years surprised you?

When I was an undergrad, I received the impression that kinetics can never compete with the degree of detail provided from dynamics experiments to understand basic interactions in chemistry. This established idea has never fully convinced me and was an important leitmotif for my PhD research. During the last few years, our team in Göttingen has continuously shown that kinetics at surfaces is capable of providing unprecedented details for basic molecule-surface interactions determining reactivity at catalytic surfaces. The achievements from surface kinetics have, indeed, positively surprised me.

Which development of the last several years has impacted your own research?

The implementation of Velocity Resolved Kinetics (VRK) is a breakpoint in surface chemistry. The visualization of reaction products makes molecular-beam surface scattering experiments conceptually easier, and allows the focus to be on the complicated nature of surface chemistry. VRK is now the starting point for many experimental techniques for fundamental studies in heterogeneous catalysts research.

Which research topic do you think will make the most progress?

Big progress in science comes with the development of new experimental methods. The implementation of single molecule Electron Spin Resonance in Scanning Tunneling Microscopy (ESR-STM) is truly exciting and has stimulated fantastic work in quantum nanoscience. Although this technique has not yet found its way to surface chemistry, I believe that this can be the next revolution for this field.

Dmitriy Borodin

, the author of the surface science part, is currently a Postdoc at the Center for Quantum Nanoscience in Seoul, South Korea, where he works with Andreas Heinrich on single molecule electron spin resonance on surfaces. Until recently, he studied kinetics and dynamics of surface reactions with Theofanis Kitsopoulos and Alec Wodtke at the Max Planck Institute for Multidisciplinary Sciences in Göttingen. He is a recipient of the Otto-Hahn Medal 2023 for his PhD research.

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