Dynamics of carbene formation in the reaction of methane with the tantalum cation in the gas phase

The controlled activation of methane has drawn significant attention throughout various disciplines over the last few decades. In gas-phase experiments, the use of model systems with reduced complexity compared to condensed-phase catalytic systems allows us to investigate the intrinsic reactivity of elementary reactions down to the atomic level. Methane is rather inert in chemical reactions, as the weakening or cleavage of a C-H bond is required to make use of methane as C1-building block. The simplest model system for transition-metal-based catalysts is a mono-atomic metal ion. Only a few atomic transition-metal cations activate methane at room temperature. One of the most efficient elements is tantalum, which forms a carbene and releases molecular hydrogen in the reaction with methane: Ta+ + CH4 → TaCH2+ + H2. The reaction takes place at room temperature due to efficient intersystem crossing from the quintet to the triplet surface, i.e., from the electronic ground state of the tantalum cation to the triplet ground state of the tantalum carbene. This multi-state reactivity is often seen for reactions involving transition-metal centres, but leads to their theoretical treatment being a challenge even today. Chemical reactions, or to be precise reactive collisions, are dynamic processes making their description even more of a challenge to experiment and theory alike. Experimental energy- and angle-differential cross sections allow us to probe the rearrangement of atoms during a reactive collision. By interpreting the scattering signatures, we gain insight into the atomistic mechanisms and can move beyond stationary descriptions. Here, we present a study combining collision energy dependent experimentally measured differential cross sections with ab initio calculations of the minimum energy pathway. Product ion velocity distributions were recorded using our crossed-beam velocity map imaging experiment dedicated to studying transition-metal ion molecule reactions. TaCH2+ velocity distributions reveal a significant degree of indirect dynamics. However, the scattering distributions also show signatures of rebound dynamics. We compare the present results to the oxygen transfer reaction between Ta+ and carbon dioxide, which we recently studied.

Spiers Memorial Lecture: New directions in molecular scattering

The field of molecular scattering is reviewed as it pertains to gas-gas as well as gas-surface chemical reaction dynamics. We emphasize the importance of collaboration of experiment and theory, from which new directions of research are being pursued on increasingly complex problems. We review both experimental and theoretical advances that provide the modern toolbox available to molecular-scattering studies. We distinguish between two classes of work. The first involves simple systems and uses experiment to validate theory so that from the validated theory, one may learn far more than could ever be measured in the laboratory. The second class involves problems of great complexity that would be difficult or impossible to understand without a partnership of experiment and theory. Key topics covered in this review include crossed-beams reactive scattering and scattering at extremely low energies, where quantum effects dominate. They also include scattering from surfaces, reactive scattering and kinetics at surfaces, and scattering work done at liquid surfaces. The review closes with thoughts on future promising directions of research.

Role of the Vibrational and Translational Energies in the CN(v)+C2H6(ν1, ν2, ν5 and ν9) Reactions. A Theoretical QCT Study

Quasi-classical trajectory (QCT) calculations were conducted on the newly developed full-dimensional potential energy surface, PES-2023, to analyse two critical aspects: the influence of vibrational versus translational energy in promoting reactivity, and the impact of vibrational excitation within similar vibrational modes. The former relates to Polanyi's rules, while the latter concerns mode selectivity. Initially, the investigation revealed that independent vibrational excitation by a single quantum of ethane's symmetric and asymmetric stretching modes (differing by only 15 cm-1) yielded comparable dynamics, reaction cross-sections, HCN(v) vibrational product distributions, and scattering distributions. This observation dismisses any significant mode selectivity. Moreover, an equivalent amount of energy provided as translational energy (at total energies of 9.6 and 20.0 kcal mol-1) gave rise to slightly lower reactivity compared to the same amount of energy provided as vibrational energy. This effect is more evident at low energies, presenting a counterintuitive scenario in an 'early transition state' reaction. These findings challenge the straightforward application of Polanyi's rules in polyatomic systems. Regarding CN(v) vibrational excitation, our calculations reveal that the reaction cross-section remains practically unaffected by this vibrational excitation, suggesting that the CN stretching mode is a spectator mode. The results were rationalized by considering several factors: the strong coupling between different vibrational modes, and between vibrational modes and the reaction coordinate; and a significant vibrational energy redistribution within the ethane reactant before collision. This redistribution creates an unphysical energy flow, resulting in loss of adiabaticity and vibrational memory before the reactants' collision. These theoretical findings require future confirmation through experimental or theoretical quantum mechanical studies, which are currently unavailable.

Probing the activated complex of the F + NH3 reaction via a dipole-bound state

Experimental characterization of the transition state poses a significant challenge due to its fleeting nature. Negative ion photodetachment offers a unique tool for probing transition states and their vicinity. However, this approach is usually limited to Franck-Condon regions. For example, high-lying Feshbach resonances with an excited HF stretching mode (vHF = 2-4) were recently identified in the transition-state region of the F + NH3 → HF + NH2 reaction through photo-detaching FNH3- anions, but the direct photodetachment failed to observe the lower-lying vHF = 0,1 resonances and bound states due apparently to negligible Franck-Condon factors. Indeed, these weak transitions can be resonantly enhanced via a dipole-bound state (DBS) formed between an electron and the polar FNH3 species. In this study, we unveil a series of Feshbach resonances and bound states along the F + NH3 reaction path via a DBS by combining high-resolution photoelectron spectroscopy with high-level quantum dynamical computations. This study presents an approach for probing the activated complex in a reaction by negative ion photodetachment through a DBS.

Generation of High-Lying Vibrational States in Carbon Dioxide through Coherent Ladder Climbing

Mid-infrared laser excitation of molecules into high-lying vibrational states offers a novel route to realize controlled ground-state chemistry. Here we successfully demonstrate vibrational ladder climbing in the antisymmetric stretch of CO2 in the condensed phase by using intense down-chirped mid-infrared pulses. Spectrally resolved pump-probe measurements directly observe excited-state absorptions attributed to vibrational populations up to the v = 9 state, whose corresponding energy of 2.5 eV is 46% of the dissociation energy. By the use of global fitting analysis, important spectroscopic parameters in the high-lying vibrational states, such as transition frequencies and relaxation times, are quantitatively characterized. Remarkably, our analysis shows that 40% of the molecules are excited above the typical activation barriers in the metal-catalyzed CO2 conversions. These results not only demonstrate the promising ability of infrared excitation to produce elevated vibrational states but also represent a significant step toward accelerating CO2 conversions and other chemical processes via mode-specific vibrational excitation.

Vibration to Vibration: Product Energy Distribution of F + HD Crossed Molecular Beam Experiments

We investigated the F + HD(v = 1, j = 0) → HF + D reaction using the crossed molecular beam technique combined with the D atom Rydberg tagging time-of-flight spectroscopy. By detecting the products at various scattering angles for different collision energies in the range of 0.8-1.2 kcal/mol, we observed the forward-scattering products of HF(v' = 4) and determined the threshold energy for the opening of this reaction channel. Similar experiments were conducted for the F + HD(v = 0, j = 0) → HF + D reaction within the range of 1.1-1.6 kcal/mol, where forward-scattering products of HF(v' = 3) were observed, and the threshold energy for this reaction channel was determined as well. Furthermore, we measured the differential cross-sections for the F + HD → HF + D reaction in both the vibrational ground state and the excited state of HD and analyzed the vibrational quantum-state distribution of the HF products. It was found that the population of vibrational quantum states of the HF products increases synchronously with the excitation of the reactant HD vibrationally.

Spin-Dependent Stereochemistry: A Nonadiabatic Quantum Dynamics Case Study of S + H2 → SH + H Reaction

We study the spin-dependent stereodynamics of the S + H2 → SH + H reaction by using full-dimensional quantum dynamics calculations with zero total nuclear angular momentum along the triplet 3A″ states and singlet 1A' states. We find that the interplay between the electronic spin direction and the molecular geometry has a measurable influence on the singlet-triplet intersystem crossing reaction probabilities. Our results show that for some incident scattering angles in the body-fixed frame, the relative difference in intersystem crossing reaction probabilities (as determined between spin up and spin down initial states) can be as large as 15%. Our findings are an ab initio demonstration of spin-dependent nonadiabatic dynamics, which we hope will shine light as far as understanding the chiral-induced spin selectivity effect.

Ta+ and Nb+ + CO2: intersystem crossing in ion-molecule reactions

The reactions of Ta+ and Nb+ with CO2 proceed only by a highly efficient oxygen atom transfer reaction to the respective oxide at room temperature in the gas phase. Although the product spin states are not determined, thermochemistry dictates that they must be different from ground state quintet Ta+ and Nb+, implying that intersystem crossing (ISC) has occurred. Recent reactive scattering experiments found dominant indirect dynamics for the reaction with Ta+ hinting at a bottleneck along the reaction path. The question on the nature of the bottleneck, whether it involves a crossing point or a transition state, could not be finally answered because theory located both close to each other. Here, we aim at shedding further light onto the impact of intersystem crossing on the reaction dynamics and ultimately the reactivity of transition metal ion reactions in the gas phase. We employ a combination of thermal kinetics for Ta+ and Nb+ with CO2 using a selected-ion flow tube (SIFT) apparatus and differential scattering cross sections for Nb+ + CO2 from crossed-beam velocity map imaging. The reaction with niobium again shows dominant indirect dynamics and in general very similar dynamics compared to Ta+ + CO2. At thermal energies, both reactions show sub-collisional rate constants with small negative temperature dependencies. Experiments are complemented by high level quantum chemical calculations of the minimum energy pathway. Statistical modelling well-reproduces the experimental thermal rate constants, and suggests that the Nb+ reaction is rate-limited by the intersystem crossing at thermal energies.

High vibrational excitation of the reagent transforms the late-barrier H + HOD reaction into an early-barrier reaction

Polanyi's rules predict that a late-barrier reaction yields vibrationally cold products; however, experimental studies showed that the H2 product from the late-barrier H + H2O(|04⟩-) and H + HOD(vOH = 4) reactions is vibrationally hot. Here, we report a potential-averaged five-dimensional state-to-state quantum dynamics study for the H + HOD(vOH = 0-4) → H2 + OD reactions on a highly accurate potential energy surface with the total angular momentum J = 0. It is found that with the HOD vibration excitation increasing from vOH = 1 to 4, the product H2 becomes increasingly vibrationally excited and manifests a typical characteristic of an early barrier reaction for vOH = 3 to 4. Analysis of the scattering wave functions revealed that vibrational excitation in the breaking OH bond moves the location of dynamical saddle point from product side to reactant side, transforming the reaction into an early barrier reaction. Interestingly, pronounced oscillatory structures in the total and product vibrational-state-resolved reaction probabilities were observed for the H + HOD(vOH = 3, 4) reactions, in particular at low collision energies, which originate from the Feshbach resonance states trapped in the bending/torsion excited vibrational adiabatic potential wells in the entrance region due to van der Waals interactions.

State-to-State Dynamics in Mode-Selective Polyatomic Reactions

Chemical reactions are intrinsically quantum mechanical transformations of reactants to products. Recent experimental and theoretical advances have enabled the exploration of reaction dynamics with a quantum state resolution for both reactants and products. To this end, reactions involving more than three atoms are of particular interest, because they exhibit rich dynamics concerning the role of different reactant modes in controlling reactivity and product energy disposal. A clear understanding of the state-to-state dynamics requires new paradigms. In this Perspective, we examine some new concepts that have emerged from recent state-to-state studies of polyatomic reactions and illustrate the key role played by the transition state.

Correlation Study of the Spin-Orbit State-Resolved Scattering of Al(2P) in Oxidation Reaction and Nonreactive Collision

Spin-orbit coupling plays an important role in chemical reactivity, especially in reactions that require the change of electron spin states. However, it is difficult to measure and analyze the reaction dynamics between spin-orbit splitting states, particularly for splitting states with a small energy difference. In this study, we find that nonreactive scattering of spin-orbit splitting states can provide complementary information that is overlooked in chemical reaction studies. Here, the oxidation reactivities of spin-orbit Al(2P1/2,3/2) states with small energy difference of 112 cm-1 are clearly distinguished in the high rotational AlO(v = 0 and 1, N) products at low collision energy of 507 cm-1 using a laser ablation crossed-beam and time-sliced ion velocity mapping technique, in conjunction with state-selected nonreactive scattering studies. For both the AlO(v = 0 and 1) channels, the spin-orbit relative reactivity σ3/2/σ1/2 increases with the increase of rotational level N of AlO products. However, for AlO(v = 0), the reactivity of the Al(2P3/2) excited state is consistently lower than that of the Al(2P1/2) ground state, whereas for AlO(v = 1), the reactivity of Al(2P3/2) is higher than that of Al(2P1/2) at a higher rotational state. The relative reactivity of spin-orbit split Al(2P) states at different scattering angles shows a more pronounced enhancement of forward scattering relative to side and backward scattering for Al(2P3/2) when a higher rotationally excited AlO is produced. Nonreactive scattering studies of Al(2P) suggest that the Al(2P3/2) state is deexcited to the ground Al(2P1/2) state at the sideways and backward scattering directions, and the deexcitation is supposed to reduce the reactivity of the excited Al(2P3/2) at the corresponding direction.

Differential Cross Sections for the H + H2S → H2 + SH Reaction: A Full-Dimensional State-to-State Quantum Dynamics Study

We utilized the time-dependent wave packet approach to compute the first full-dimensional (6D) state-to-state differential cross sections (DCSs) for the title reaction with the initial nonrotating H2S in the ground and the (100) and (001) vibrational excited states. It is found that the fundamental symmetric and asymmetric stretching excitations of H2S exhibit almost the same influence on the DCS, but unlike the H + H2O → H2 + OH reaction, they greatly increase the vibrational excitation of both the H2 and SH products. The hot vibrational state distributions of H2 are consistent with the prediction of product energy disposal by Polanyi's rules for an early barrier reaction. Because the incident H atom reacts strongly with both the ground and excited S-H states, the large populations of product SH(v2 = 1), which are very close to the relative reactivity of the initial S-H(v = 0) state, can still be explained by the local mode picture for H2S and the nonreacting SH bond's spectator nature.

Theoretical Insights into the Dynamics of Gas-Phase Bimolecular Reactions with Submerged Barriers

Much attention has been paid to the dynamics of both activated gas-phase bimolecular reactions, which feature monotonically increasing integral cross sections and Arrhenius kinetics, and their barrierless capture counterparts, which manifest monotonically decreasing integral cross sections and negative temperature dependence of the rate coefficients. In this Perspective, we focus on the dynamics of gas-phase bimolecular reactions with submerged barriers, which often involve radicals or ions and are prevalent in combustion, atmospheric chemistry, astrochemistry, and plasma chemistry. The temperature dependence of the rate coefficients for such reactions is often non-Arrhenius and complex, and the corresponding dynamics may also be quite different from those with significant barriers or those completely dominated by capture. Recent experimental and theoretical studies of such reactions, particularly at relatively low temperatures or collision energies, have revealed interesting dynamical behaviors, which are discussed here. The new knowledge enriches our understanding of the dynamics of these unusual reactions.

Dynamics of the Oxygen Atom Transfer Reaction between Carbon Dioxide and the Tantalum Cation

The understanding of fundamental atomic-level processes often requires well-defined model systems. The oxygen atom transfer from CO₂ to a transition metal cation in the gas phase presents such a model system. We investigate the reaction of Ta⁺ + CO₂ for which the formation of TaO⁺ is highly efficient and attributed to multistate reactivity. Here, we study the atomistic dynamics of the oxygen atom transfer reaction by recording experimental energy and angle differential cross sections by crossed beam velocity map imaging supported by ab initio quantum chemical calculations. Product ion velocity distributions are dominated by signatures for indirect dynamics, despite the reaction being highly exothermic. Product kinetic energy distributions show little dependence on additional collision energy even with only four atoms involved, which hints at dynamical trapping behind a submerged barrier.

State-to-State Dynamics in Mode-Specific Reactions of Cl + CH3D(v1-I, v1-II, and v4 = 1; |10⟩): Loss of Memory or Not

Several decades of the study of reaction dynamics culminate in the concept of mode specificity and bond selectivity in polyatomic systems. Until very recently, the main concern of those studies has been total reactivity and little attention has been paid to the mode-specific effects on the more detailed product-state and angular distributions. Conventional wisdom would anticipate that the fine detail should reveal a more pronounced mode dependency. However, a few recent studies showed that the product distributions could appear to be surprisingly insensitive to the modes of internal excitation of reagents. This counterintuitive finding led to a concept of loss of memory. Here, we present detailed experimental results in the reactions of the Cl atom with three distinct stretching-excited CH₃D(v_CH3 = 1) reagents. In conjunction with the previous reports on various aspects of this reaction, such a comprehensive set of data enables us to perform an in-depth examination of the validity of this new concept.

Observation of resonances in the transition state region of the F + NH3 reaction using anion photoelectron spectroscopy

The transition state of a chemical reaction is a dividing surface on the reaction potential energy surface (PES) between reactants and products and is thus of fundamental interest in understanding chemical reactivity. The transient nature of the transition state presents challenges to its experimental characterization. Transition-state spectroscopy experiments based on negative-ion photodetachment can provide a direct probe of this region of the PES, revealing the detailed vibrational structure associated with the transition state. Here we study the F + NH₃ → HF + NH₂ reaction using slow photoelectron velocity-map imaging spectroscopy of cryogenically cooled FNH₃^- anions. Reduced-dimensionality quantum dynamical simulations performed on a global PES show excellent agreement with the experimental results, enabling the assignment of spectral structure. Our combined experimental-theoretical study reveals a manifold of vibrational Feshbach resonances in the product well of the F + NH₃ PES. At higher energies, the spectra identify features attributed to resonances localized across the transition state and into the reactant complex that may impact the bimolecular reaction dynamics.

Stereodynamical control of the H + HD → H2 + D reaction through HD reagent alignment

Prealigning nonpolar reacting molecules leads to large stereodynamical effects because of their weak steering interaction en route to the reaction barrier. However, experimental limitations in preparing aligned molecules efficiently have hindered the investigation of steric effects in bimolecular reactions involving hydrogen. Here, we report a high-resolution crossed-beam study of the reaction H + HD(v = 1, j = 2) → H₂(v', j') + D at collision energies of 0.50, 1.20, and 2.07 electron volts in which the vibrationally excited hydrogen deuteride (HD) molecules were prepared in two collision configurations, with their bond preferentially aligned parallel and perpendicular to the relative velocity of collision partners. Notable stereodynamical effects in differential cross sections were observed. Quantum dynamics calculations revealed that strong constructive interference in the perpendicular configuration plays an important role in the stereodynamical effects observed.

Imaging the Complex-Forming Reaction Dynamics in Al + CO2 → AlO + CO

For indirect reactions involving more than one intermediate complex from reactant valley to product valley, the reaction dynamics becomes very complicated for researchers due to competition between pathways. In order to resolve the large discrepancy between theoretical and experimental studies on the linear or bent structures of complexes involved in the title endothermic reaction, we performed a crossed-beam experiment at a large collision energy (E_c) range with mapping of the velocity distributions of Al reactants and AlO products. We found that the reaction proceeds through different complex-forming mechanisms with the increase of E_c: at low E_c near the reaction threshold, only low impact-parameter collisions contribute through a collinear Al-OCO short-lived complex, and at high E_c, the bent-structure complexes, formed by either isomerization or noncollinear collisions, come into play.

Stretching-mode specificity in the Cl + CH3D(v1-I, v1-II, and v4 = 1; |jK〉) reactions: dependency on the initial |jK〉 selectivity

The title reactions were studied at a collisional energy of 5.4 kcal mol^-1 in a crossed-beam product-imaging experiment. The dynamics attributes of the dominant ground-state CH₂D(0₀) and the accompanied C-D bend-excited CH₂D(6₁) products were imaged in reactions with totally 16 ro-vibrationally selected states of the CH₃D(v_i, |jK〉) reagents. We found that all three vibrational excitations yielded marked |jK〉-dependent rate-enhancements in forming the (0₀, 0/1)_s product pairs. Furthermore, for a given rotational |jK〉-mode, a vibrational-mode propensity of v₄ > v₁-I > v₁-II in rate promotion and a clear manifestation of the Fermi-phase-induced interference effect of the latter two were observed. Compared to the reactivity of the rotationless state |jK〉 = |00〉, a minute rotational-excitation of all three stretch-excited CH₃D(v_i = 1) reagents could yield significantly higher reaction rates for the product pair (0₀, 0)_s, but not so for (0₀, 1)_s. The signals in forming the (6₁, 0)_s pair were clearly notable but smaller than that of the ground-state reaction product pair, (0₀, 0)_g. An opposite propensity of v₁-II ≈ v₁-I > v₄ with a milder dependency on the initial |jK〉-states was observed. The angular distributions of the (0₀, 0)_s pairs were nearly identical for all ro-vibrationally excited reagents, displaying the typical trait for a direct abstraction of the rebound mechanism. Similar distributions were found for the (6₁, 0)_s pairs; yet, both pairs deviated substantially from the peripheral feature of the ground-state reaction pair of (0₀, 0)_g. Those of the (0₀, 1)_s pairs in reactions with v₄-excitation featured a prominent forward-peaking distribution-suggestive of a time-delayed, resonance-mediated pathway, again with little dependency on the initial |jK〉-states. As for the reactions with the two Fermi-dyads, v₁-I and v₁-II, albeit showing globally similar distributions to that for v₄, a substantial variation with the initial rotational-mode excitation could be discerned in the forward-peaking features. To unravel the impact of the Fermi-phase on the |jK〉-dependent attributes, we adopted a comparative approach by contrasting the observations in reactions with the Fermi-dyad reagents (the superposition states) to those with the pure-state reagents. Remarkable distinctions are unveiled and elucidated with the unexplained results explicitly pointed out, which call for future theoretical investigations for deeper understanding.

Permutation-Invariant-Polynomial Neural-Network-Based Δ-Machine Learning Approach: A Case for the HO2 Self-Reaction and Its Dynamics Study

Δ-machine learning, or the hierarchical construction scheme, is a highly cost-effective method, as only a small number of high-level ab initio energies are required to improve a potential energy surface (PES) fit to a large number of low-level points. However, there is no efficient and systematic way to select as few points as possible from the low-level data set. We here propose a permutation-invariant-polynomial neural-network (PIP-NN)-based Δ-machine learning approach to construct full-dimensional accurate PESs of complicated reactions efficiently. Particularly, the high flexibility of the NN is exploited to efficiently sample points from the low-level data set. This approach is applied to the challenging case of a HO₂ self-reaction with a large configuration space. Only 14% of the DFT data set is used to successfully bring a newly fitted DFT PES to the UCCSD(T)-F12a/AVTZ quality. Then, the quasiclassical trajectory (QCT) calculations are performed to study its dynamics, particularly the mode specificity.

Imaging the Mode-Specificity in Cl + CH3D(v1-I, v1-II, v4 = 1; |jK⟩ = |10⟩) → CH2D(41) + HCl(v)

We report a crossed-beam imaging experiment on the title reactions at two collisional energies (E_c) of 5.3 and 10 kcal mol^-1. Both the integral cross sections relative to the ground-state reactivity and the differential cross sections were measured and compared. We found that one-quantum excitations of the CH₃-stretching vibrations of the CH₃D reagent exerted profound mode-specificity in forming the umbrella-mode-excited CH₂D(4₁) products with the vibrational efficacy of v₄ > v₁-I > v₁-II at both E_c values. The concomitantly formed HCl(v) coproducts were vibrationally cold. Interestingly, the branching ratios of (v = 1)/(v = 0) appeared invariant to the initial stretch-modes of excitation at E_c = 5.3 kcal mol^-1, yet exhibited a pronounced mode-specific dependency in the order of v₁-II > v₁-I > v₄ at E_c = 10.3 kcal mol^-1. This large and E_c-dependent disparity between the two Fermi-coupled reagents, v₁-I and v₁-II, is particularly significant and could be another facet─in addition to that in the recently reported vibrational enhancement factors─of the Fermi-phase-induced interference effect manifested in the product vibrational branching ratio. The pair-correlated angular distributions (v_CH2D, v_HCl)_s = (4₁, 0)_s in the three stretch-excited reactions were globally alike and resembled that of the ground-state reaction pair (0₀, 0)_g, suggestive of a direct abstraction mechanism of the peripheral type. This is in sharp contrast to all other vibrationally excited pairs of (1₁, 0)_s, (3₁, 0)_s, and (6₁, 0)_s previously reported in the CH₂D + HCl isotopic channel, for which both the direct abstraction and a time-delayed resonance pathway partake.

Fermi-phase-induced interference in the reaction between Cl and vibrationally excited CH3D

Mode selectivity is a well-established concept in chemical dynamics. A polyatomic molecule possesses multiple vibrational modes and the mechanical couplings between them can result in complicated anharmonic motions that defy a simple oscillatory description. A prototypical example of this is Fermi-coupled vibration, in which an energy-split eigenstate executes coherent nuclear motion that is comprised of the constituent normal modes with distinctive phases. Will this vibrational phase affect chemical reactivity? How can this phase effect be disentangled from more classical amplitude effects? Here, to address these questions, we study the reaction of Cl with a pair of Fermi states of CH₃D(v₁-I and v₁-II). We find that the reactivity ratio of (v₁-I)/(v₁-II) in forming the CH₂D(v = 0) + HCl(v) products deviates significantly from that permitted by the conventional reactivity-borrowing framework. Based on a proposed metric, this discrepancy can only be explained when the scattering interferences mediated by the CH₃D vibrational phases are explicitly considered, which expands the concept of vibrational control of chemical reactivity into the quantum regime.

Toward a Comprehensive Understanding of Mode-Specific Dynamics of Polyatomic Reactions: A Full-Dimensional Quantum Dynamics Study of the H + NH3 Reaction

Mode specificity not only sheds light on reaction dynamics but also opens the door for chemical reaction control. This work reports a state-of-the-art full-dimensional quantum dynamics study on the prototypical hydrogen abstraction reaction of hydrogen with ammonia, which serves as a benchmark for advancing our fundamental understanding of polyatomic reaction dynamics. By taking advantage of the (3 + 1) Radau-Jacobi coordinates, the bond-specific probabilities are resolved with the reactant NH₃ initiated from either a non-degenerate or degenerate stretching vibrational state. The observed different atom-specific abstraction probabilities from individual states of the degenerate pair are rationalized in the local mode representation according to the different vibrational energy deposited in each N-H bond. It is verified that the three H atoms in NH₃ have the same abstraction probability as that from the degenerate pair and the linear combination of the degenerate pair gives the same reaction probability. In addition, the symmetric and asymmetric stretching modes of the reactant NH₃ have comparable efficacies on driving the reaction.

Atomistic dynamics of elimination and nucleophilic substitution disentangled for the F- + CH3CH2Cl reaction

Chemical reaction dynamics are studied to monitor and understand the concerted motion of several atoms while they rearrange from reactants to products. When the number of atoms involved increases, the number of pathways, transition states and product channels also increases and rapidly presents a challenge to experiment and theory. Here we disentangle the dynamics of the competition between bimolecular nucleophilic substitution (S_N2) and base-induced elimination (E2) in the polyatomic reaction F^- + CH₃CH₂Cl. We find quantitative agreement for the energy- and angle-differential reactive scattering cross-sections between ion-imaging experiments and quasi-classical trajectory simulations on a 21-dimensional potential energy hypersurface. The anti-E2 pathway is most important, but the S_N2 pathway becomes more relevant as the collision energy is increased. In both cases the reaction is dominated by direct dynamics. Our study presents atomic-level dynamics of a major benchmark reaction in physical organic chemistry, thereby pushing the number of atoms for detailed reaction dynamics studies to a size that allows applications in many areas of complex chemical networks and environments.

Mode-specific dynamics in multichannel reaction NH+ + H2

The vibrational- and rotational-mode specificity of the multichannel NH⁺ + H₂ reaction is studied on a recently constructed ab initio-based global potential energy surface using an initial state selected quasi-classical trajectory method, and the trajectories are analyzed using an isometric feature mapping and k-means approach. All excitation modes promote two reactions (R1: NH'⁺ + H₂ → NH⁺ + HH' and R4: NH'⁺ + H₂ → NH₂⁺ + H') where both NH and HH bonds are broken, but reduce the reactivity of the proton-transfer reaction R2 (NH'⁺ + H₂ → N + H'H₂⁺) at low collision energies. For the hydrogen-transfer reaction R3 (NH'⁺ + H₂ → HNH'⁺ + H), the rotational excitation of NH⁺ enhances the reactivity remarkably, while its vibrational excitation has an inhibiting effect on the reaction. The trajectory analyses show that the vibrational and rotational excitations of NH⁺ make R3 tend to go over a submerged saddle point instead of extracting hydrogen atoms directly. On the other hand, the motions of the H₂ reactant facilitate the enhancement of the reactivity but they do not affect the mechanism of R3. In addition, the results suggest that the coupling of the isometric feature mapping and the k-means approach in the trajectory analysis is an appropriate tool for reaction-dynamics studies.

Inducing molecular reactions by selective vibrational excitation of a remote antenna with near-infrared light

We demonstrate here that selective vibrational excitation of a moiety, remotely attached in relation to the molecular reaction site, might offer a generalized strategy for inducing bond-breaking/bond-forming reactions with exquisite precision. As a proof-of-principle, the electrocyclic ring-expansion of a benzazirine to a ketenimine was induced, in a cryogenic matrix, by near-IR light tuned at the overtone stretching frequency of its OH remote antenna. This accomplishment paves the way for harnessing IR vibrational excitation as a tool to guide a variety of molecular structure manipulations in an exceptional highly-selective manner.

Pair-Correlated Imaging of Cl + CH3D(v4, v1-I, v1-II = 1, |jK⟩) → CH2D(vi) + HCl(v)

The title reactions were studied at a collisional energy of 10.0 kcal mol^-1 in a crossed-beam, product-imaging experiment. In terms of integral cross sections, all three CH₃-stretching excited CH₃D(v_CH3 = 1) reagents promote the reactivity in forming the predominant product pair of (v_CH2D, v_HCl)_s = (0₀, 0/1)_s with a prominent mode-propensity of v₄ > v₁-I > v₁-II, where v₄ denotes the degenerate mode of CH₃ asymmetric stretch and v₁-I and v₁-II are a pair of Fermi-coupled, symmetric-stretch states. The vibrationally excited CH₂D product pairs of (6₁, 0)_s, (1₁, 0)_s, and (3₁, 0)_s appear to be minor channels and display a reverse propensity of v₄ < v₁-I ≈ v₁-II for (6₁, 0)_s, while v₄ > v₁-I for (1₁, 0)_s. Based on the observed angular distributions, we conjecture that, irrespective of the initial mode of excitation, the (0₀, 0)_s product pair proceeds by a direct abstraction of the peripheral type, whereas the (0₀,1)_s pair is mediated via a resonance pathway. Intriguingly, the angular distributions of the excited product pairs-(6₁, 0)_s, (1₁, 0)_s, and (3₁, 0)_s-are remarkably similar and comprise the traits of both the peripheral mechanism and resonance pathway. Possible interpretation and implication are suggested. In addition, due to the spectral overlap of the REMPI bands and heavily congested image features, a robust data analysis method is developed, which enables us to extract the dynamics attributes of a weak feature buried in the proximate, more intense ones with high fidelity.

Evidence of IR-Induced Chemistry in a Neat Solid: Tautomerization of Thiotropolone by Thermal, Electronic, and Vibrational Excitations

Thiotropolone isolated in argon and xenon matrices (as monomers) or in a neat solid (as the crystalline or amorphous state) at low temperature was found to exist only in the thione-enol form. Visible light irradiation (λ ≥ 400 nm) leads to thione-enol → thiol-keto tautomerization in matrices and under neat solid conditions at 15 K. The assignment of the IR spectra of the two thiotropolone tautomers (thione-enol and thiol-keto) was carried out with the support of B3LYP/6-311+G(2d,p) computations. The thiol-keto form generated in situ in a neat solid was found to tautomerize back to the thione-enol upon annealing up to 100 K. Gaussian-4 (G4) computations estimate that such a tautomerization process has an energy barrier of ∼25 kJ mol^-1, which is consistent with the observations. Moreover, it was found that narrowband IR irradiation of the thiol-keto form in a neat solid, at the frequency of its CH stretching overtones/combination modes, also induces tautomerization to the thione-enol form. Such a result constitutes an important demonstration of vibrationally induced chemistry under neat solid conditions.

Effects of bending excitation on the reaction dynamics of fluorine atoms with ammonia

Vibrational excitation has been established as an efficient way to control the chemical reaction outcome. Stretching vibration of polyatomic molecules is believed to be efficient to promote abstraction reactions since energy is placed directly into the breaking bond. In this work, we report on a counterexample showing that exciting the low-frequency umbrella bending mode of ammonia enhances its reaction with fluorine atoms much more than exciting the high-frequency symmetric or asymmetric stretching mode over a wide range of collision energy, validated using both quasiclassical trajectory simulations and full-dimensional quantum dynamics calculations under the centrifugal-sudden approximation. This interesting mode-specific reaction dynamic originates from the increased chance of capturing the fluorine atom by ammonia due to the enlarged attractive interaction between them and the enhancement of the direct stripping reaction mediated by two submerged barriers.

Mode- and Bond-Selected Reaction of H with Local Mode Molecule HDS

Understanding mode- and bond-selected dynamics of elementary chemical reactions is of central importance in molecular reaction dynamics. The initial state-selected time-dependent wave packet method is employed to study the mode and bond selectivity, isotopic branching ratio, and temperature dependence of rate constants of the two-channel reaction of H with local mode molecule HDS. For the abstraction channel, fundamental excitation of the HS (DS) bond of the reactant HDS significantly enhances the H-abstraction (D-abstraction) reaction, whose efficacy is higher than the same amount of translational energy except at low energies just above the energy threshold. This is in sharp contrast to the prediction of Polanyi rules: translational energy is more efficient than vibrational energy in enhancing a reaction with an early barrier. The recent sudden vector projection model is then applied to rationalize the observed mode specificity, which, however, shows that the translational mode vector has a larger coupling with the reaction coordinate than the stretching vector of the active bond, implying a reversed relative efficacy on promoting the reaction as well. In contrast, the mode and bond specificity for the exchange channel is not as strong as for the abstraction channel due to the regulation of the shallow well along the reaction path.

Chemical Activation of Water Molecule by Collision with Spin-Orbit-State-Selected Vanadium Cation: Quantum-Electronic-State Control of Chemical Reactivity

We have obtained absolute integral cross sections (σ's) for the reactions of spin-orbit-state-selected vanadium cations, V⁺[a⁵D_J(J = 0, 2), a⁵F_J(J = 1, 2), and a³F_J(J = 2, 3)], with a water molecule (H₂O) in the center-of-mass collision energy range E_cm = 0.1-10.0 eV. On the basis of these state-selected σ curves (σ versus E_cm plots) observed, three reaction product channels, VO⁺ + H₂, VH⁺ + OH, and VOH⁺ + H, from the V⁺ + H₂O reaction are unambiguously identified. Contrary to the previous guided ion beam study of the V⁺(a⁵D_J) + D₂O reaction, we have observed the formation of the VO⁺ + H₂ channel from the V⁺(a⁵D_J) + H₂O ground reactant state at low E_cm's (<3.0 eV). No spin-orbit J-state dependences for the σ curves of individual electronic states are discernible, indicating that spin-orbit interactions are weak with little effect on chemical reactivity of the titled reaction. For the three product channels identified, the triplet σ(a³F_J) values are overwhelmingly higher than the quintet σ(a⁵D_J) and σ(a⁵F_J) values, showing that the reaction is governed by a "weak quintet-triplet spin crossing" mechanism, favoring the conservation of total electron spins. The σ curves for exothermic product channels are found to exhibit a rapid decreasing profile as E_cm is increased, an observation consistent with the prediction of the charge-dipole and induced-dipole orbiting model. This experiment shows that the V⁺ + H₂O reaction can be controlled effectively to produce predominantly the VO⁺ + H₂ channel via the V⁺(a³F_J) + H₂O reaction at low E_cm's (≤0.1 eV) and that the ion-molecule reaction dynamics can be altered readily by selecting the electronic state of V⁺ cation. On the basis of the measured E_cm thresholds for the σ(a⁵D_J, a⁵F_J, and a³F_J: VH⁺) and σ(a⁵D_J, a⁵F_J, and a³F_J: VOH⁺) curves, we have deduced upper bound values of 2.6 ± 0.2 and 4.3 ± 0.3 eV for the 0 K bond dissociation energies, D₀(V⁺-H) and D₀(V⁺-OH), respectively. After correcting for the kinetic energy distribution resulting from the Doppler broadening effect of the H₂O molecule, we obtain D₀(V⁺-H) = 2.2 ± 0.2 eV and D₀(V⁺-OH) = 4.0 ± 0.3 eV, which are in agreement with D₀ determinations obtained by σ curve simulations.

Quantitative Dynamics of the N2O + C2H2 → Oxadiazole Reaction: A Model for 1,3-Dipolar Cycloadditions

The reaction N₂O + C₂H₂ → oxadiazole has been considered as a prototype for 1,3-dipolar cycloadditions. Here, we report a comprehensive dynamical study of this important reaction on a full-dimensional potential energy surface, which is fitted to about 64 000 high-level ab initio data by a machine learning approach. Comprehensive dynamical simulations are carried out to provide quantitative chemical insight into its reaction dynamics. In addition to confirming the enhancement effect of the N₂O bending mode on the reactivity, intricate mode specificity effects of other vibrational modes in reactants are revealed for the first time. The asymmetric stretching mode of N₂O and the C-C-H bending mode of C₂H₂ show no effect. All remaining modes can enhance the reactivity. In particular, the vibrational excitation of the N₂O symmetric stretching mode shows similar enhancement effect on the title reaction, compared to its bending mode excitation. Detailed analysis reveals that the concerted mechanism dominates with the reactants propelled sufficiently close to each other to yield product. This study advances our understanding of the chemical dynamics of the title reaction.

Proton transfer dynamics modified by CH-stretching excitation

Gaining insight how specific rovibrational states influence reaction kinetics and dynamics is a fundamental goal of physical chemistry. Purely statistical approaches often fail to predict the influence of a specific state on the reaction outcome, evident in a great number of both experimental and theoretical studies. Most detailed insight in atomistic reaction mechanisms is achieved using accurate collision experiments and high level dynamics calculations. For ion-molecule reactions such experiments are scarce. Here we show the influence of symmetric CH-stretching vibration on the rate and dynamics of proton transfer in the reaction of F- + CH3I. We find a pronounced shift in the reaction dynamics for excited reactions from indirect to preferred direct dynamics at higher collision energy. Moreover, excited reactions occur at larger impact parameters. Finally, we compare vibrational excitation with collision energy and find that vibration is overall more efficient in promoting reactivity, which agrees with recent theoretical calculations.

Influence of Vibrational Excitation on the Reaction of F- with CH3I: Spectator Mode Behavior, Enhancement, and Suppression

Detailed insight into chemical reaction dynamics can be obtained by probing the effect of mode-specific vibrational excitation. Suppression or enhancement of reactivity is possible as is already known from the Polanyi rules. In the reaction F- + CH3I, we found vibrational enhancement, suppression, and spectator mode dynamics in the four different reaction channels. For this system we have probed the influence of symmetric CH-stretching vibration over a collision energy range of 0.7-2.3 eV. Proton transfer is significantly enhanced, while for the nucleophilic substitution channel the spectator mode dynamics at lower collision energies unexpectedly move toward enhancement at higher collision energies. In contrast, for two halide abstraction channels, forming FI- and FHI-, we found an overall suppression, which stems mainly from a suppression of the FHI- product. We compare these results to quasiclassical trajectory calculations and with the sudden vector projection model.

Active stereo-control of the Cl + CH4(ν3 = 1) reaction: a three-dimensional perspective

The transition state in Cl + CH4 is of Cl-H-C collinear geometry. As the reactant CH4 is vibrationally excited by a linearly polarized infrared (IR) light to the antisymmetric-stretching state of ν3 = 1, all four C-H bonds are collectively excited and any one of the H-atoms can be reactive. Yet, a strong alignment of the excited CH4(ν3 = 1), as evidenced from the striking stereo-specificity in the Cl + CH4 reaction, was clearly revealed in a previous, exploratory study. Reported here is the full account of that investigation at two collisional energies of Ec = 4.8 and 2.7 kcal mol-1, using a crossed molecular-beam, product-imaging approach. By active control of the polarization direction of an IR laser under judiciously chosen beam-geometries, a complete set of polarization-dependent differential cross sections is disentangled from the CH3(00) product images. To our surprise, the quantitative results appear nearly identical to those obtained for the isotope-substituted reaction of Cl + CHD3(ν1 = 1) → HCl(ν) + CD3(00). A detailed discussion is presented to elucidate the underlying physics for such an intriguing similarity in stereo-reactivity between a spherical-top and a symmetric-top reactant.

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.

Modification of Enzyme Activity by Vibrational Strong Coupling of Water

Vibrational strong coupling (VSC) has recently emerged as a completely new tool for influencing chemical reactivity. It harnesses electromagnetic vacuum fluctuations through the creation of hybrid states of light and matter, called polaritonic states, in an optical cavity resonant to a molecular absorption band. Here, we investigate the effect of vibrational strong coupling of water on the enzymatic activity of pepsin, where a water molecule is directly involved in the enzyme's chemical mechanism. We observe an approximately 4.5-fold decrease of the apparent second-order rate constant kcat /Km when coupling the water stretching vibration, whereas no effect was detected for the strong coupling of the bending vibration. The possibility of modifying enzymatic activity by coupling water demonstrates the potential of VSC as a new tool to study biochemical reactivity.

Globally Accurate Full-Dimensional Potential Energy Surface for H2 + HCl Inelastic Scattering

A globally accurate full-dimensional potential energy surface (PES) for the inelastic scattering between H₂ and HCl is developed on the basis of a large number of points calculated at the coupled-cluster singles, doubles, and perturbative triples level of theory. The machine-learned PES is trained with 42 417 ab initio points using the permutation invariant polynomial-neural network method, resulting in a root-mean-square fitting error of 5.6 cm^-1. Both full- and reduced-dimensional quantum calculations for rotationally inelastic scattering are performed on this new PES and good agreement is obtained with previous quantum dynamical results on a reduced-dimensional model. Furthermore, strong resonances are identified at collision energies below 100 K, including cold conditions. This new PES provides a reliable platform for future studies of scattering dynamics with vibrationally excited collision partners in a wide range of collision energies extending to cold and ultracold conditions.

Stereodynamical control of product branching in multi-channel barrierless hydrogen abstraction of CH3OH by F

Comprehensive dynamical simulations of a prototypical multi-channel reaction on a globally accurate potential energy surface show that the non-statistical product branching is dictated by unique stereodynamics in the entrance channels.

Hydrogen abstraction from methanol (CH₃OH) by F atoms presents an ideal proving ground to investigate dynamics of multi-channel reactions, because two types of hydrogen can be abstracted from the methanol molecule leading to the HF + CH₃O and HF + CH₂OH products. Using the quasi-classical trajectory approach on a globally accurate potential energy surface based on high-level ab initio calculations, this work reports a comprehensive dynamical investigation of this multi-channel reaction, yielding measurable attributes including integral and differential cross sections, as well as branching ratios. It is shown that while complex-forming and direct mechanisms coexist at low collision energies, these barrierless reaction channels are dominated at high energies by the direct mechanism, in which the reaction is only possible for trajectories entering into the respective dynamical cones of acceptance. Perhaps more importantly, the non-statistical product branching is found to be dictated by unique stereodynamics in the entrance channels.

Imaging pair-correlated reaction cross sections in F + CH3D(νb = 0, 1) → CH2D(ν4 = 1) + HF(ν)

The title reactions were studied in a crossed-beam experiment at collisional energies (Ec) from 0.5 to 4.7 kcal mol-1. The νb (ν4) vibrational mode denotes the bending (umbrella) motion of the CH3D reactant (CH2D product). Using a time-sliced, velocity-map imaging technique, we extracted the state-specific, pair-correlated integral and differential cross sections. As with other isotopically analogous ground-state reactions, an inverted vibrational population of the HF coproduct was observed. Both the step-like excitation function near the threshold and the oscillatory forward-backward peakings in the Ec-evolution of the two dominant pair-correlated angular distributions at lower Ec suggest a resonance-mediated, time-delay mechanism. As Ec increases, the angular distribution of the HF(ν = 2) product evolves into a smooth and broad swath in the backward hemisphere, indicative of a direct rebound mechanism. One quantum excitation of the bending modes of CH3D(νb = 1) promotes the reaction rate by two- to three-fold up to Ec = 2.1 kcal mol-1. Broadly speaking, all major findings are qualitatively in line with previous results in the reactions of the F atom with other isotopologues. However, the rainbow feature recently observed in the CH2D(00) + HF(ν = 3) product channel is entirely absent. A possible rationale is put forward, which reinforces the previous reactive rainbow conjecture and calls for future theoretical investigations.

Dynamics in reactions on metal surfaces: A theoretical perspective

Recent advances in theoretical characterization of reaction dynamics on metal surfaces are reviewed. It is shown that the widely available density functional theory of metals and their interactions with molecules have enabled first principles theoretical models for treating surface reaction dynamics. The new theoretical tools include methods to construct high-dimensional adiabatic potential energy surfaces, to characterize nonadiabatic processes within the electronic friction models, and to describe dynamics both quantum mechanically and classically. Three prototypical surface reactions, namely, dissociative chemisorption, Eley-Rideal reactions, and recombinative desorption, are surveyed with a focus on some representative examples. While principles governing gas phase reaction dynamics may still be applicable, the presence of the surface introduces a higher level of complexity due to strong interaction between the molecular species and metal substrate. Furthermore, most of these reactive processes are impacted by energy exchange with surface phonons and/or electron-hole pair excitations. These theoretical studies help to interpret and rationalize experimental observations and, in some cases, guide experimental explorations. Knowledge acquired in these fundamental studies is expected to impact many practical problems in a wide range of interfacial processes.