Direct mapping of the angle-dependent barrier to reaction for Cl + CHD3 using polarized scattering data

Benchmark ab initio characterization of the multi-channel Cl + CH3X [X = F, Cl, Br, I] reactive potential energy surfaces

We determine benchmark geometries and relative energies for the stationary points of the Cl + CH3X [X = F, Cl, Br, I] reactions. We consider four possible reaction pathways: hydrogen abstraction, hydrogen substitution, halogen abstraction, and halogen substitution, where the substitution processes can proceed via either Walden inversion or front-side attack. We perform geometry optimizations and obtain harmonic vibrational frequencies at the explicitly-correlated UCCSD(T)-F12b/aug-cc-pVTZ level of theory, followed by UCCSD(T)-F12b/aug-cc-pVQZ single-point computations to make finite-basis-set error negligible. To reach chemical (<1 kcal mol-1), or even subchemical (<0.5 kcal mol-1) accuracy, we include core-correlation, scalar relativistic, post-(T), spin-orbit-splitting and zero-point-energy contributions, as well, in the relative energies of all the stationary points. Our benchmark 0 K reaction enthalpies are compared to available experimental results and show good agreement. The stationary-point structures and energetics are interpreted in terms of Hammond's postulate and used to make predictions related to the dynamical behavior of these reactive systems.

First-principles mode-specific reaction dynamics

Controlling the outcome of chemical reactions by exciting specific vibrational and/or rotational modes of the reactants is one of the major goals of modern reaction dynamics studies. In the present Perspective, we focus on first-principles vibrational and rotational mode-specific dynamics computations on reactions of neutral and anionic systems beyond six atoms such as X + C2H6 [X = F, Cl, OH], HX + C2H5 [X = Br, I], OH- + CH3I, and F- + CH3CH2Cl. The dynamics simulations utilize high-level ab initio analytical potential energy surfaces and the quasi-classical trajectory method. Besides initial state specificity and the validity of the Polanyi rules, mode-specific vibrational-state assignment for polyatomic product species using normal-mode analysis and Gaussian binning is also discussed and compared with experiment.

Accurate Quantum Dynamics Calculations for the Cl + CH4/CHD3/CD4 Reaction Rates

Full-dimensional quantum dynamics simulations of the reaction of Cl with methane and its isotopomers are reported. Thermal rate constants are computed for the Cl + CH4 → HCl + CH3, Cl + CHD3 → HCl + CD3, and Cl + CD4 → DCl + CD3 reactions. Temperatures between 200 and 500 K are considered. In this temperature range, excellent agreement with the experiment is obtained. A detailed analysis of the kinetic isotope effect reveals the crucial importance of the CH3/CD3 umbrella motion. Comparison with approximate ring-polymer molecular dynamics simulations shows significant differences depending on the isotope studied.

Enhancing reactivity of SiO+ ions by controlled excitation to extreme rotational states

Optical pumping of molecules provides unique opportunities for control of chemical reactions at a wide range of rotational energies. This work reports a chemical reaction with extreme rotational excitation of a reactant and its kinetic characterization. We investigate the chemical reactivity for the hydrogen abstraction reaction SiO⁺ + H₂ → SiOH⁺ + H in an ion trap. The SiO⁺ cations are prepared in a narrow rotational state distribution, including super-rotor states with rotational quantum number (j) as high as 170, using a broad-band optical pumping method. We show that the super-rotor states of SiO⁺ substantially enhance the reaction rate, a trend reproduced by complementary theoretical studies. We reveal the mechanism for the rotational enhancement of the reactivity to be a strong coupling of the SiO⁺ rotational mode with the reaction coordinate at the transition state on the dominant dynamical pathway.

Imaging Frontside and Backside Attack in Radical Ion-Molecule Reactive Scattering

We report on the reactive scattering of methyl iodide, CH₃I, with atomic oxygen anions O^-. This radical ion-molecule reaction can produce different ionic products depending on the angle of attack of the nucleophile O^- on the target molecule. We present results on the backside and frontside attack of O^- on CH₃I, which can lead to I^- and IO^- products, respectively. We combine crossed-beam velocity map imaging with quantum chemical calculations to unravel the chemical reaction dynamics. Energy-dependent scattering experiments in the range of 0.3-2.0 eV relative collision energy revealed that three different reaction pathways can lead to I^- products, making it the predominant observed product. Backside attack occurs via a hydrogen-bonded complex with observed indirect, forward, and sideways scattered iodide products. Halide abstraction via frontside attack produces IO^-, which mainly shows isotropic and backward scattered products at low energies. IO^- is observed to dissociate further to I^- + O at a certain energy threshold and favors more direct dynamics at higher collision energies.

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.

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.

Benchmark Ab Initio Characterization of the Abstraction and Substitution Pathways of the Cl + CH3CN Reaction

We investigate the reaction pathways of the Cl + CH₃CN system: hydrogen abstraction, methyl substitution, hydrogen substitution, and cyanide substitution, leading to HCl + CH₂CN, ClCN/CNCl + CH₃, ClCH₂CN + H, and CH₃Cl + CN, respectively. Hydrogen abstraction is exothermic and has a low barrier, whereas the other channels are endothermic with high barriers. The latter two can proceed via a Walden inversion or front-side attack mechanism, and the front-side attack barriers are always higher. The C-side methyl substitution has a lower barrier and also a lower endothermicity than the N-side reaction. The computations utilize an accurate composite ab initio approach and the explicitly correlated CCSD(T)-F12b method. The benchmark classical and vibrationally adiabatic energies of the stationary points are determined with the most accurate CCSD(T)-F12b/aug-cc-pVQZ energies adding further contributions of the post-(T) and core correlation, scalar relativistic effects, spin–orbit coupling, and zero-point energy corrections. These contributions are found to be non-negligible to reach subchemical accuracy.

Chemistry of a Light Impurity in a Bose-Einstein Condensate

Similar to an electron in a solid, an impurity in an atomic Bose-Einstein condensate (BEC) is dressed by excitations from the medium, forming a polaron quasiparticle with modified properties. This impurity can also undergo chemical recombination with atoms from the BEC, a process resonantly enhanced when universal three-body Efimov bound states cross the continuum. To study the interplay between these phenomena, we use a Gaussian state variational method able to describe both Efimov physics and arbitrarily many excitations of the BEC. We show that the polaron cloud contributes to bound state formation, leading to a shift of the Efimov resonance to smaller interaction strengths. This shifted scattering resonance marks the onset of a polaronic instability towards the decay into large Efimov clusters and fast recombination, offering a remarkable example of chemistry in a quantum medium.

First-Principles Theory for the Reaction of Chlorine with Methane

A full-dimensional quantum dynamics simulation of the Cl + CH₄ → HCl + CH₃ reaction based on first-principles theory is reported. Accurate thermal rate constants are calculated, and perfect agreement with experiment is obtained. Despite the heavy atoms present in both reactants, the passage of the reaction barrier is found to occur within only a few tens of femtoseconds. This surprisingly short time scale results from correlated motion of the transferring hydrogen atom and the hydrogen atoms in the methyl fragment which facilitates irreversible barrier passage without relevant participation of heavy atoms. Resonance effects resulting from the heavy-light-heavy characteristics of the reaction system, which were observed in reactive scattering studies, do not affect the thermal rate constant.

Controlling the Spin-Orbit Branching Fraction in Molecular Collisions

The collision geometry, that is, the relative orientation of reactants before interaction, can have a large effect on how a collision or reaction proceeds. Certain geometries may prevent access to a given product channel, while others might enhance it. In this Letter, we demonstrate how the initial orientation of NO molecules relative to approaching Ar atoms determines the branching between the spin-orbit changing and the spin-orbit conserving rotational product channels. We use a recently developed quantum treatment to calculate differential and integral branching fractions, at any arbitrary orientation, from theoretical and experimental data points. Our results show that a substantial degree of control over the final spin-orbit state of the scattering products can be achieved by tuning the initial collision geometry.

From Reactive Rainbow to Dynamic Resonance Well

Scattering resonance is a fascinating phenomenon which manifests as a peak or a dip in an observable as a function of collisional energy (E_c). Its occurrence requires a potential well to support the resonance states. In this regard, reactive resonance is unusual in that it can exist in a reaction with unbound Born-Oppenheimer potential energy surface, on which the quasi-bound states are dynamically trapped-meaning that some energy is temporarily tied to the other degrees of freedom than the reaction coordinate. The concept of vibrational adiabaticity has been the cornerstone in understanding this phenomenon, for which the vibrationally adiabatic well depth is of primary concern. Recent studies on the F + CH₃D reaction have accumulated compelling evidence for a dominant resonance-mediated pathway at low E_c as well as for a rainbow feature in pair-correlated angular distribution at higher E_c. Here, we report an in-depth study to not only substantiate both claims but also, more importantly, make the first attempt to quantify the vibrationally adiabatic well depth directly from the observed rainbow structure and then compare with the theoretical prediction.

Probing the location of the unpaired electron in spin-orbit changing collisions of NO with Ar

Understanding the molecular forces that drive a reaction or scattering process lies at the heart of molecular dynamics. Here, we present a combined experimental and theoretical study of the spin-orbit changing scattering dynamics of oriented NO molecules with Ar atoms. Using our crossed molecular beam apparatus, we have recorded velocity-map ion images and extracted differential and integral cross sections of the scattering process in the side-on geometry. We observe an overall preference for collisions close to the N atom in the spin-orbit changing manifold, which is a direct consequence of the location of the unpaired electron on the potential energy surface. In addition, a prominent forward scattered feature is observed for intermediate, even rotational transitions when the atom approaches the molecule from the O-end. The appearance of this peak originates from an attractive well on the A' potential energy surface, which efficiently directs high impact parameter trajectories towards the region of high unpaired electron density near the N-end of the molecule. The ability to orient molecules prior to collision, both experimentally and theoretically, allows us to sample different regions of the potential energy surface(s) and unveil the associated collision pathways.

Investigation of the low-energy stereodynamics in the Ne(3P2) + N2, CO reactions

We report on an experimental investigation of the low-energy stereodynamics of the energy transfer reactions Ne(³P₂) + X, producing Ne(¹S) + X⁺ and [Ne-X]⁺ (X = N₂ or CO). Collision energies in the range 0.2 K-700 K are obtained by using the merged beam technique. Two kinds of product ions are generated by Penning and associative ionization, respectively. The intermediate product [Ne-X]⁺ in vibrationally excited states can predissociate into bare ions (X⁺). The experimental ratio of the NeX⁺ and X⁺ product ion yields is similar for both molecules at high collision energies but diverge at collision energies below 100 K. This difference is explained by the first excited electronic state of the product ions, which is accessible in the case of CO but lies too high in energy in the case of N₂.

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

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

Mapping the emergence of molecular vibrations mediating bond formation

Fundamental studies of chemical reactions often consider the molecular dynamics along a reaction coordinate using a calculated or suggested potential energy surface^1-5. But fully mapping such dynamics experimentally, by following all nuclear motions in a time-resolved manner-that is, the motions of wavepackets-is challenging and has not yet been realized even for the simple stereotypical bimolecular reaction^6-8: A-B + C → A + B-C. Here we track the trajectories of these vibrational wavepackets during photoinduced bond formation of the gold trimer complex [Au(CN)₂^-]₃ in an aqueous monomer solution, using femtosecond X-ray liquidography^9-12 with X-ray free-electron lasers^13,14. In the complex, which forms when three monomers A, B and C cluster together through non-covalent interactions^15,16, the distance between A and B is shorter than that between B and C. Tracking the wavepacket in three-dimensional nuclear coordinates reveals that within the first 60 femtoseconds after photoexcitation, a covalent bond forms between A and B to give A-B + C. The second covalent bond, between B and C, subsequently forms within 360 femtoseconds to give a linear and covalently bonded trimer complex A-B-C. The trimer exhibits harmonic vibrations that we map and unambiguously assign to specific normal modes using only the experimental data. In principle, more intense X-rays could visualize the motion not only of highly scattering atoms such as gold but also of lighter atoms such as carbon and nitrogen, which will open the door to the direct tracking of the atomic motions involved in many chemical reactions.

Theory Finally Agrees with Experiment for the Dynamics of the Cl + C2H6 Reaction

Since the pioneering reaction dynamics studies of H + H2 in the 1970s, theory increased the system size by one atom in every decade arriving to six-atom reactions in the early 2010s. Here, we take a significant step forward by reporting accurate dynamics simulations for the nine-atom Cl + ethane (C2H6) reaction using a new high-quality spin-orbit-ground-state ab initio potential energy surface. Quasi-classical trajectory simulations on this surface cool the rotational distribution of the HCl product molecules, thereby providing unprecedented agreement with experiment after several previous failed attempts of theory. Unlike Cl + CH4, the Cl + C2H6 reaction is exothermic with an adiabatically submerged transition state, allowing testing of the validity of the Polanyi rules for a negative-barrier reaction.

Vibrational overtone excitation of D2 in a molecular beam with a high-energy, narrow-bandwidth, nanosecond optical parametric oscillator/amplifier

We have built a high-energy, narrow-bandwidth, nanosecond light source for efficient preparation of vibrationally excited molecules in a molecular beam. It consists of an injection-seeded optical parametric oscillator and two optical parametric amplifiers. Pumped by the second harmonic of a commercial injection-seeded Nd:YAG laser, it can generate pulse energies up to 377 mJ at 655 nm with a bandwidth smaller than 200 MHz. Its stability is excellent, with a standard deviation of pulse energy of 5.2 mJ and a wavelength stability of 0.001 cm^-1. We demonstrated this light source in a crossed-molecular-beam experiment of the H + D₂ (v = 2, j = 0) → HD + D reaction, in which it was used for overtone excitation of D₂ molecules from (v = 0, j = 0) to (v = 2, j = 0) with an overall excitation efficiency of 2.5%.

Experimental and Theoretical Study of the Vibrationally Excited Reaction Cl + D2 (v = 1, j = 0) → DCl + D

Vibrationally excited reaction of Cl + D₂ (v = 1, j = 0) → DCl + D was investigated by a high-resolution crossed beam experiment, with D₂ molecules in the vibrationally excited state prepared by the scheme of stimulated Raman pumping. Differential cross sections (DCSs) were obtained at three collision energies of 4.03, 4.93, and 5.68 kcal/mol. Backward scattering is dominant for both DCl (v' = 0) and DCl (v' = 1) products, and no forward scattering signal was observed at these three collision energies. Collision-energy-dependent DCS in the backward scattering direction was measured at collision energies between 3.62 and 5.97 kcal/mol. Comparing with the DCSs from the vibrational ground state, it is found that the vibrational excitation of D₂ molecules significantly enhances the reactivity because of the later barrier nature of the reaction. No obvious oscillatory structure was found in the collision-energy-dependent DCS in the backward scattering direction, suggesting that the title reaction proceeds via a direct abstraction mechanism.

Benchmark ab initio and dynamical characterization of the stationary points of reactive atom + alkane and SN2 potential energy surfaces

We review composite ab initio and dynamical methods and their applications to characterize stationary points of atom/ion + molecule reactions.

Universal crossed beam imaging studies of polyatomic reaction dynamics

Crossed-beam imaging studies of polyatomic reactions show surprising dynamics not anticipated by extrapolation from smaller model systems.

An accurate potential energy surface and ring polymer molecular dynamics study of the Cl + CH4→ HCl + CH3reaction

Thermal rate coefficients for the Cl + CH₄/CD₄reactions were studied on a new full-dimensional accurate potential energy surface with the spin–orbit corrections considered in the entrance channel.

Steric Effects in the Inelastic Scattering of NO(X) + Ar: Side-on Orientation

The rotationally inelastic collisions of NO(X) with Ar, in which the NO bond-axis is oriented side-on (i.e., perpendicular) to the incoming collision partner, are investigated experimentally and theoretically. The NO(X) molecules are selected in the |j = 0.5, Ω = 0.5, ε = -1, f⟩ state prior to bond-axis orientation in a static electric field. The scattered NO products are then state selectively detected using velocity-map ion imaging. The experimental bond-axis orientation resolved differential cross sections and integral steric asymmetries are compared with quantum mechanical calculations, and are shown to be in good agreement. The strength of the orientation field is shown to affect the structure observed in the differential cross sections, and to some extent also the steric preference, depending on the ratio of the initial e and f Λ-doublets in the superposition determined by the orientation field. Classical and quantum calculations are compared and used to rationalize the structures observed in the differential cross sections. It is found that these structures are due to quantum mechanical interference effects, which differ for the two possible orientations of the NO molecule due to the anisotropy of the potential energy surface probed in the side-on orientation. Side-on collisions are shown to maximize and afford a high degree of control over the scattering intensity at small scattering angles (θ < 90°), while end-on collisions are predicted to dominate in the backward scattered region (θ > 90°).

Direct observation of product-pair correlations in rotationally inelastic collisions of ND3 with D2

We present a combined experimental and theoretical study of state-to-state inelastic scattering of ND₃(j = 1₁^-) with D₂ (j = 0, 1, 2, 3) molecules at collision energies around 800 cm^-1. Using a crossed molecular beam apparatus which employs the combination of Stark deceleration and velocity map imaging, we observe the correlated rotational excitations of both collision partners. For D₂, both elastic (Δj_D2 = 0), inelastic excitation (j = 0 →j = 2) and inelastic de-excitation (j = 2 →j = 0) processes are observed. For a number of final ND₃ states, inelastic channels in which D₂ is rotationally excited or de-excited appear surprisingly strong. The experimental results are in excellent agreement with the predictions from quantum scattering calculations which are based on an ab initio ND₃-D₂ potential energy surface.

Quantum-state-controlled channel branching in cold Ne(3P2)+Ar chemi-ionization

A prerequisite to gain a complete understanding of the most basic aspects of chemical reactions is the ability to perform experiments with complete control over the reactant degrees of freedom. By controlling these, details of a reaction mechanism can be investigated and ultimately manipulated. Here, we present a study of chemi-ionization-a fundamental energy-transfer reaction-under completely controlled conditions. The collision energy of the reagents was tuned from 0.02 K to 1,000 K, with the orientation of the excited Ne atom relative to Ar fully specified by an external magnetic field. Chemi-ionization of Ne(³P₂) and Ar in these conditions enables a detailed investigation of how the reaction proceeds, and provides us with a means to control the branching ratio between the two possible reaction outcomes. The merged-beam experimental technique used here allows access to a low-energy regime in which the atoms dynamically reorient into a favourable configuration for reaction, irrespective of their initial orientations.

Stereodynamics of Ne(3P2) reacting with Ar, Kr, Xe, and N2

Stereodynamics experiments of Ne(³P₂) reacting with Ar, Kr, Xe, and N₂ leading to Penning and associative ionization have been performed in a crossed molecular beam apparatus. A curved magnetic hexapole was used to state-select and polarize Ne(³P₂) atoms which were then oriented in a rotatable magnetic field and crossed with a beam of Ar, Kr, Xe, or N₂. The ratio of associative to Penning ionization was recorded as a function of the magnetic field direction for collision energies between 320 cm^-1 and 500 cm^-1. Reactivities are obtained for individual states that differ only in Ω, the projection of the neon total angular momentum vector on the inter-particle axis. The results are rationalized on the basis of a model involving a long-range and a short-range reaction mechanism. Substantially lower probability for associative ionization was observed for N₂, suggesting that predissociation plays a critical role in the overall reaction pathway.

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.