Perspective: Vibrational-induced steric effects in bimolecular reactions

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.

Quantum-Controlled Collisions of H2 Molecules

The amount of information that can be obtained from a scattering experiment depends upon the precision with which the quantum states are defined in the incoming channel. By precisely defining the incoming states and measuring the outgoing states in a scattering experiment, we set up the boundary condition for experimentally solving the Schrödinger equation. In this Perspective we discuss cold inelastic scattering experiments using the most theoretically tractable H₂ and its isotopologues as the target. We prepare the target in a precisely defined rovibrational (v, j, m) quantum state using a special coherent optical technique called the Stark-induced adiabatic Raman passage (SARP). v and j represent the quantum numbers of the vibrational and rotational energy levels, and m refers to the projection of the rotational angular momentum vector j on a suitable quantization axis in the laboratory frame. Selection of the m quantum numbers defines the alignment of the molecular frame, which is necessary to probe the anisotropic interactions. For us to achieve the collision temperature in the range of a few degrees Kelvin, we co-expand the colliding partners in a mixed supersonic beam that is collimated to define a direction for the collision velocity. When the bond axis is aligned with respect to a well-defined collision velocity, SARP achieves stereodynamic control at the quantum scale. Through various examples of rotationally inelastic cold scattering experiments, we show how SARP coherently controls the dynamics of anisotropic interactions by preparing quantum superpositions of the orientational m states within a single rovibrational (v, j) energy state. A partial wave analysis, which has been developed for the cold scattering experiments, shows dominance of a resonant orbital that leaves its mark in the scattering angular distribution. These highly controlled cold collision experiments at the single partial wave limit allow the most direct comparison with the results of theoretical computations, necessary for accurate modeling of the molecular interaction potential.

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 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.

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.

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.

Benchmark ab initio stationary-point characterization of the complex potential energy surface of the multi-channel Cl + CH3NH2 reaction

We characterize the exothermic low/submerged-barrier hydrogen-abstraction (HCl + CH2NH2/CH3NH) as well as, for the first time, the endothermic high-barrier amino-substitution (CH3Cl + NH2), methyl-substitution (NH2Cl + CH3), and hydrogen-substitution (CH2ClNH2/CH3NHCl + H) pathways of the Cl + CH3NH2 reaction using an accurate composite ab initio approach. The computations reveal a CH3NH2Cl complex in the entrance channel, nine transition states corresponding to different abstractions, Walden-inversion substitution, and configuration-retaining front-side attack substitution pathways, as well as nine post-reaction complexes. The global minima of the electronic and vibrationally adiabatic potential energy surfaces correspond to the pre-reaction CH3NH2Cl and post-reaction CH2NH2HCl complexes, respectively. The benchmark composite energies of the stationary points are obtained by considering basis-set effects up to the correlation-consistent polarized valence quadruple-zeta basis augmented with diffuse functions (aug-cc-pVQZ) using the explicitly-correlated coupled-cluster singles, doubles, and perturbative triples CCSD(T)-F12b method, post-(T) correlation up to CCSDT(Q) including full triples and perturbative quadruples, core correlation, and scalar relativistic and spin-orbit effects, as well as harmonic zero-point energy corrections.

Advances and New Challenges to Bimolecular Reaction Dynamics Theory

Dynamics of bimolecular reactions in the gas phase are of foundational importance in combustion, atmospheric chemistry, interstellar chemistry, and plasma chemistry. These collision-induced chemical transformations are a sensitive probe of the underlying potential energy surface(s). Despite tremendous progress in past decades, our understanding is still not complete. In this Perspective, we survey the recent advances in theoretical characterization of bimolecular reaction dynamics, stimulated by new experimental observations, and identify key new challenges.

Vibrational Excitation Hindering an Ion-Molecule Reaction: The c-C_{3}H_{2}^{+}-H_{2} Collision Complex

Experiments within a cryogenic 22-pole ion trap have revealed an interesting reaction dynamic phenomenon, where rovibrational excitation of an ionic molecule slows down a reaction with a neutral partner. This is demonstrated for the low-temperature hydrogen abstraction reaction c-C_{3}H_{2}^{+}+H_{2}, where excitation of the ion into the ν_{7} antisymmetric C-H stretching mode decreased the reaction rate coefficient toward the products c-C_{3}H_{3}^{+}+H. Supported by high-level quantum-chemical calculations, this observation is explained by the reaction proceeding through a c-C_{3}H_{2}^{+}-H_{2} collision complex in the entrance channel, in which the hydrogen molecule is loosely bound to the hydrogen atom of the c-C_{3}H_{2}^{+} ion. This discovery enables high-resolution vibrational action spectroscopy for c-C_{3}H_{2}^{+} and other molecular ions with similar reaction pathways. Moreover, a detailed kinetic model relating the extent of the observed product depletion signal to the rate coefficients of inelastic collisions reveals that rotational relaxation of the vibrationally excited ions is significantly faster than the rovibrational relaxation, allowing for a large fraction of the ions to be vibrationally excited. This result provides fundamental insight into the mechanism for an important class of chemical reactions, and is capable of probing the inelastic collisional dynamics of molecular ions.

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.

Benchmark ab initio characterization of the abstraction and substitution pathways of the OH + CH4/C2H6 reactions

We report benchmark ab initio stationary-point properties for the hydrogen-abstraction, hydrogen-substitution, and methyl-substitution pathways of the OH + CH₄/C₂H₆ reactions.

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.

Stark-induced adiabatic Raman passage examined through the preparation of D2 (v = 2, j = 0) and D2 (v = 2, j = 2, m = 0)

We study the conditions that must be met for successful preparation of a large ensemble in a specific target quantum state using Stark-induced adiabatic Raman passage (SARP). In particular, we show that the threshold condition depends on the relative magnitudes of the Raman polarizability (r_0v) and the difference of the optical polarizabilities (Δα_00→vj) of the initial (v = 0, j = 0) and the target (v, j) rovibrational levels. Here, v and j are the vibrational and rotational quantum numbers, respectively. To illustrate how the operation of SARP is controlled by these two parameters, we experimentally prepared D₂ (v = 2, j = 0) and D₂ (v = 2, j = 2, m = 0) in a beam of D₂ (v = 0, j = 0) molecules using a sequence of partially overlapping pump and Stokes laser pulses. By comparing theory and experiment, we were able to determine the Raman polarizability r₀₂ ≈ 0.3 × 10^-41 Cm/(V/m) and the difference polarizabilities Δα_00→20 ≈ 1.4 × 10^-41 Cm/(V/m) and Δα_00→22 ≈ 3.4 × 10^-41 Cm/(V/m) for the two Raman transitions. Our experimental data and theoretical calculations show that because the ratio r/Δα is larger for the (0,0) → (2,0) transition than the (0,0) → (2,2) transition, much less optical power is required to transfer a large population to the (v = 2, j = 0) level. Nonetheless, our experiment demonstrates that substantial population transfer to both the D₂ (v = 2, j = 0) and D₂ (v = 2, j = 2, m = 0) is achieved using appropriate laser fluences. Our derived threshold condition demonstrates that with increasing vibrational quantum number, it becomes more difficult to achieve large amounts of population transfer.

Detailed benchmark ab initio mapping of the potential energy surfaces of the X + C2H6 [X = F, Cl, Br, I] reactions

We provide benchmark relative energies for the stationary points of three different channels of the halogen atom + ethane reactions.

Cold quantum-controlled rotationally inelastic scattering of HD with H2 and D2 reveals collisional partner reorientation

Molecular interactions are best probed by scattering experiments. Interpretation of these studies has been limited by lack of control over the quantum states of the incoming collision partners. We report here the rotationally inelastic collisions of quantum-state prepared deuterium hydride (HD) with H₂ and D₂ using a method that provides an improved control over the input states. HD was coexpanded with its partner in a single supersonic beam, which reduced the collision temperature to 0-5 K, and thereby restricted the involved incoming partial waves to s and p. By preparing HD with its bond axis preferentially aligned parallel and perpendicular to the relative velocity of the colliding partners, we observed that the rotational relaxation of HD depends strongly on the initial bond-axis orientation. We developed a partial-wave analysis that conclusively demonstrates that the scattering mechanism involves the exchange of internal angular momentum between the colliding partners. The striking differences between H₂/HD and D₂/HD scattering suggest the presence of anisotropically sensitive resonances.

Crossed beam polyatomic reaction dynamics: recent advances and new insights

This review summarizes the developments in polyatomic reaction dynamics, focusing on reactions of unsaturated hydrocarbons with O-atoms and methane with atoms/radicals.

Control of chemical reactivity by transition-state and beyond

It has been long established that the transition state for an activated reaction controls the overall reactivity, serving as the bottleneck for reaction flux. However, the role of the transition state in regulating quantum state resolved reactivity has only been addressed more recently, thanks to advances in both experimental and theoretical techniques. In this perspective, we discuss some recent advances in understanding mode-specific reaction dynamics in bimolecular reactions, mainly focusing on the X + H2O/CH4 (X = H, F, Cl, and O(3P)) systems, extensively studied in our groups. These advances shed valuable light on the importance of the transition state in mode-specific and steric dynamics of these prototypical reactions. It is shown that many mode-specific phenomena can be understood in terms of a transition-state based model, which assumes in the sudden limit that the ability of a reactant mode for promoting the reaction stems from its coupling with the reaction coordinate at the transition state. Yet, in some cases the long-range anisotropic interactions in the entrance (or exit) valley, which govern how the trajectories reach (or leave) the transition state, also come into play, thus modifying the reactive outcomes.

Mode specific dynamics in the H2 + SH → H + H2S reaction

Full-dimensional quantum dynamics and quasi-classical trajectory studies indicate strong mode selectivity in the H₂ + SH reaction.

Quantum dynamics of polyatomic dissociative chemisorption on transition metal surfaces: mode specificity and bond selectivity

Recent advances in quantum dynamical characterization of polyatomic dissociative chemisorption on accurate global potential energy surfaces are critically reviewed.

A new perspective: imaging the stereochemistry of molecular collisions

The concept of the steric effect plays a central role in chemistry. This Perspective describes how the polarization of reactant molecules in space can be used to probe directly the steric effect, and highlights some of the new measurements that are made possible by coupling reactant orientation and alignment with ion imaging techniques.