State-to-State Dynamics of Elementary Bimolecular Reactions

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.

Imaging Resonance Effects in C + H2 Collisions Using a Zeeman Decelerator

An intriguing phenomenon in molecular collisions is the occurrence of scattering resonances, which originate from bound and quasi-bound states supported by the interaction potential at low collision energies. The resonance effects in the scattering behavior are extraordinarily sensitive to the interaction potential, and their observation provides one of the most stringent tests for theoretical models. We present high-resolution measurements of state-resolved angular scattering distributions for inelastic collisions between Zeeman-decelerated C(3P1) atoms and para-H2 molecules at collision energies ranging from 77 cm-1 down to 0.5 cm-1. Rapid variations in the angular distributions were observed, which can be attributed to the consecutive reduction of contributing partial waves and effects of scattering resonances. The measurements showed excellent agreement with distributions predicted by ab initio quantum scattering calculations. However, discrepancies were found at specific collision energies, which most likely originate from an incorrectly predicted quasi-bound state. These observations provide exciting prospects for further high-precision and low-energy investigations of scattering processes that involve paramagnetic species.

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.

Electronic nonadiabatic effects in the state-to-state dynamics of the H + H2 → H2 + H exchange reaction with a vibrationally excited reagent

Out of the many major breakthroughs that the hydrogen-exchange reaction has led to, electronic nonadiabatic effects that are mainly due to the geometric phase has intrigued many. In this work we investigate such effects in the state-to-state dynamics of the H + H2 (v = 3, 4, j = 0) → H2 (v', j') + H reaction with a vibrationally excited reagent at energies corresponding to thermal conditions. The dynamical calculations are performed by a time-dependent quantum mechanical method both on the lower adiabatic potential energy surface (PES) and also using a two-states coupled diabatic theoretical model to explicitly include all the nonadiabatic couplings present in the 1E' ground electronic manifold of the H3 system. The nonadiabatic couplings are considered here up to the quadratic term; however, the effect of the latter on the reaction dynamics is found to be very small. Adiabatic population analysis showed a minimal participation of the upper adiabatic surface even for the vibrationally excited reagent. A strong nonadiabatic effect appears in the state-to-state reaction probabilities and differential cross sections (DCSs). This effect is manifested as "out-of-phase" oscillations in the DCSs between the results of the uncoupled and coupled surface situations. The oscillations persist as a function of both scattering angle and collision energy in both the backward and forward scattering regions. The origins of these oscillations are examined in detail. The oscillations that appear in the forward direction are found to be different from those due to glory scattering, where the latter showed a negligibly small nonadiabatic effect. The nonadiabatic effects are reduced to a large extent when summed over all product quantum states, in addition to the cancellation due to integration over the scattering angle and partial wave summation.

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.

Imaging of the charge-transfer reaction of spin-orbit state-selected Ar+(2P3/2) with N2 reveals vibrational-state-specific mechanisms

Charge-transfer reactions are ubiquitous and play important roles in various gaseous environments, but, despite a long history of extensive research, our understanding of their dynamics at the quantum state-to-state level is still lacking. Here we report quantum-state-resolved experiments for the paradigmatic charge-transfer reaction Ar+ + N2 → Ar + N2+ using a three-dimensional velocity-map imaging crossed-beam apparatus with the Ar+ beam prepared exclusively in the spin-orbit state 2P3/2. High-resolution scattering images show strong dependence of rotational and angular distributions on the vibrational quantum number of the N2+ product. Trajectory surface-hopping calculations, which semi-quantitatively reproduce the experimental observations, support the existence of two distinct charge-transfer mechanisms. One of these, in the dominant N2+(v' = 1) channel, is the well-known long-distance harpooning mechanism. However, the highly rotationally excited products in the forward direction are attributed to a hard-collision glory scattering mechanism, which occurs on account of the strong attraction between the collisional partners counterbalanced by the short-range repulsive interaction.

Vibrational control of the reaction pathway in the H + CHD3 → H2 + CD3 reaction

An accurate full-dimensional quantum state-to-state simulation of the six-atom title reaction based on first-principles theory is reported. Counterintuitive effects are found: Increasing the energy in the reactant's CD₃ umbrella vibration reduces the energy in the corresponding product vibration. An in-depth analysis reveals the crucial role of the effective dynamical transition state: Its geometry is controlled by the vibrational states of the reactants and subsequently controls the quantum state distribution of the products. This finding enables generalizing the concept of transition state control of chemical reactions to the quantum state-specific level.

High-Resolution Imaging of C + He Collisions using Zeeman Deceleration and Vacuum-Ultraviolet Detection

High-resolution measurements of angular scattering distributions provide a sensitive test for theoretical descriptions of collision processes. Crossed beam experiments employing a decelerator and velocity map imaging have proven successful to probe collision cross sections with extraordinary resolution. However, a prerequisite to exploit these possibilities is the availability of a near-threshold state-selective ionization scheme to detect the collision products, which for many species is either absent or inefficient. We present the first implementation of recoil-free vacuum ultraviolet (VUV) based detection in scattering experiments involving a decelerator and velocity map imaging. This allowed for high-resolution measurements of state-resolved angular scattering distributions for inelastic collisions between Zeeman-decelerated carbon C(³P₁) atoms and helium atoms. We fully resolved diffraction oscillations in the angular distributions, which showed excellent agreement with the distributions predicted by quantum scattering calculations. Our approach offers exciting prospects to investigate a large range of scattering processes with unprecedented precision.

Bimolecular Chemistry in the Ultracold Regime

Advances in atomic, molecular, and optical physics techniques allowed the cooling of simple molecules down to the ultracold regime ([Formula: see text]1 mK) and opened opportunities to study chemical reactions with unprecedented levels of control. This review covers recent developments in studying bimolecular chemistry at ultralow temperatures. We begin with a brief overview of methods for producing, manipulating, and detecting ultracold molecules. We then survey experimental works that exploit the controllability of ultracold molecules to probe and modify their long-range interactions. Further combining the use of physical chemistry techniques such as mass spectrometry and ion imaging significantly improved the detection of ultracold reactions and enabled explorations of their dynamics in the short range. We discuss a series of studies on the reaction KRb + KRb → K₂ + Rb₂ initiated below 1 [Formula: see text]K, including the direct observation of a long-lived complex, the demonstration of product rotational state control via conserved nuclear spins, and a test of the statistical model using the complete quantum state distribution of the products. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Precision test of statistical dynamics with state-to-state ultracold chemistry

Chemical reactions represent a class of quantum problems that challenge both the current theoretical understanding and computational capabilities¹. Reactions that occur at ultralow temperatures provide an ideal testing ground for quantum chemistry and scattering theories, because they can be experimentally studied with unprecedented control², yet display dynamics that are highly complex³. Here we report the full product state distribution for the reaction 2KRb → K₂ + Rb₂. Ultracold preparation of the reactants allows us complete control over their initial quantum degrees of freedom, whereas state-resolved, coincident detection of both products enables the probability of scattering into each of the 57 allowed rotational state-pairs to be measured. Our results show an overall agreement with a state-counting model based on statistical theory^4-6, but also reveal several deviating state-pairs. In particular, we observe a strong suppression of population in the state-pair closest to the exoergicity limit as a result of the long-range potential inhibiting the escape of products. The completeness of our measurements provides a benchmark for quantum dynamics calculations beyond the current state of the art.

Nuclear spin conservation enables state-to-state control of ultracold molecular reactions

Quantum-state control of reactive systems has enabled microscopic probes of underlying interaction potentials and the alteration of reaction rates using quantum statistics. However, extending such control to the quantum states of reaction outcomes remains challenging. Here, we realize this goal by utilizing the conservation of nuclear spins throughout the reaction. Using resonance-enhanced multiphoton ionization spectroscopy to investigate the products formed in bimolecular reactions between ultracold KRb molecules we find that the system retains a near-perfect memory of the reactants' nuclear spins, manifested as a strong parity preference for the rotational states of the products. We leverage this effect to alter the occupation of these product states by changing the coherent superposition of initial nuclear spin states with an external magnetic field. In this way, we are able to control both the inputs and outputs of a reaction with quantum-state resolution. The techniques demonstrated here open up the possibilities to study quantum entanglement between reaction products and ultracold reaction dynamics at the state-to-state level.

Effect of Reagent Vibration and Rotation on the State-to-State Dynamics of the Hydrogen Exchange Reaction, H + H2 → H2 + H

State-to-state dynamics of the benchmark hydrogen exchange reaction H + H₂ (v = 0-4, j = 0-3) → H₂ (v', j') + H is investigated with the aid of the real wave packet approach of Gray and Balint-Kurti (J. Chem. Phys. 1998, 108, 950-962) and electronic ground BKMP2 potential energy surface of Boothroyd et al. (J. Chem. Phys. 1996, 104, 7139-7152). Initial state-selected and product state-resolved reaction probabilities, integral cross section, and product diatom vibrational and rotational level populations at a few collision energies are reported to elucidate the energy disposal mechanism. State-specific thermal rate constants are also calculated and compared with the available literature results. Coriolis coupling terms of the nuclear Hamiltonian are included, and calculations are parallelized over the helicity quantum number, Ω'. Attempts are made, in particular, to study the effect of reagent vibrational and rotational excitations on the dynamical attributes. It is found that the calculations become computationally expensive with reagent vibrational and rotational excitation. Reagent vibrational excitation is found to enhance the reactivity and has significant impact on the energy disposal to the vibrational and rotational degrees of freedom of the product. The interplay of reagent translational and vibrational energy on the product vibrational distribution unfolds an important aspect of the energy disposal mechanism. The effect of reagent rotation on the state-to-state dynamics is found not to be very significant, and the weak effect turns out to be specific to v'.

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.

High-resolution imaging of molecular collisions using a Zeeman decelerator

We present the first crossed beam scattering experiment using a Zeeman decelerated molecular beam. The narrow velocity spreads of Zeeman decelerated NO (X²Π_3/2, j = 3/2) radicals result in high-resolution scattering images, thereby fully resolving quantum diffraction oscillations in the angular scattering distribution for inelastic NO-Ne collisions and product-pair correlations in the radial scattering distribution for inelastic NO-O₂ collisions. These measurements demonstrate similar resolution and sensitivity as in experiments using Stark decelerators, opening up possibilities for controlled and low-energy scattering experiments using chemically relevant species such as H and O atoms, O₂ molecules, or NH radicals.

Cold and controlled chemical reaction dynamics

State-to-state chemical reaction dynamics, with complete control over the reaction parameters, offers unparalleled insight into fundamental reactivity.

A global ab initio potential energy surface and dynamics of the proton-transfer reaction: OH− + D2 → HOD + D−

The reaction mechanisms of OH⁻ + D₂ → HOD + D⁻ were first revealed by theory, based on an accurate full-dimensional PES.

Hyperfine Magnetic Substate Resolved State-to-State Chemistry

We extend state-to-state chemistry to a realm where besides vibrational, rotational, and hyperfine quantum states magnetic quantum numbers are also resolved. For this, we make use of the Zeeman effect, which energetically splits levels of different magnetic quantum numbers. The chemical reaction which we choose to study is three-body recombination in an ultracold quantum gas of ^{87}Rb atoms forming weakly bound Rb_{2} molecules. Here, we find the propensity rule that the total m_{F} quantum number of the two atoms forming the molecule is conserved. Our method can be employed for many other reactions and inelastic collisions and will allow for novel insights into few-body processes.

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.

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.

Combined Experimental-Theoretical Study of the OH + CO → H + CO2 Reaction Dynamics

A combined experimental-theoretical study is performed to advance our understanding of the dynamics of the prototypical tetra-atom, complex-forming reaction OH + CO → H + CO₂, which is also of great practical relevance in combustion, Earth's atmosphere, and, potentially, Mars's atmosphere and interstellar chemistry. New crossed molecular beam experiments with mass spectrometric detection are analyzed together with the results from previous experiments and compared with quasi-classical trajectory (QCT) calculations on a new, full-dimensional potential energy surface (PES). Comparisons between experiment and theory are carried out both in the center-of-mass and laboratory frames. Good agreement is found between experiment and theory, both for product angular and translational energy distributions, leading to the conclusion that the new PES is the most accurate at present in elucidating the dynamics of this fundamental reaction. Yet, small deviations between experiment and theory remain and are presumably attributable to the QCT treatment of the scattering dynamics.

Quantum dynamics of ClH2O- photodetachment: Isotope effect and impact of anion vibrational excitation

Photodetachment of the ClH₂O^- anion is investigated using full-dimensional quantum mechanics on accurate potential energy surfaces of both the anion and neutral species. Detailed analysis of the photoelectron spectrum and the corresponding wavefunctions reveals that the photodetachment leads to, in the product channel of the exothermic HCl + OH → Cl + H₂O reaction, the formation of numerous Feshbach resonances due apparently to slow energy transfer from H₂O vibrational modes to the dissociation coordinate. These long-lived resonances can be grouped into two broad peaks in the low-resolution photoelectron spectrum, which is in good agreement with available experiments, and they are assigned to the ground and first excited OH stretching vibrational manifolds of H₂O complexed with Cl. In addition, effects of isotope substitution on the photoelectron spectrum were small. Finally, photodetachment of the vibrationally excited ClH₂O^- in the ionic hydrogen bond mode is found to lead to Feshbach resonances with higher stretching vibrational excitations in H₂O.

Dynamical resonances in chemical reactions

The transition state is a key concept in the field of chemistry and is important in the study of chemical kinetics and reaction dynamics.

Symmetry and the geometric phase in ultracold hydrogen-exchange reactions

Quantum reactive scattering calculations are reported for the ultracold hydrogen-exchange reaction and its non-reactive atom-exchange isotopic counterparts, proceeding from excited rotational states. It is shown that while the geometric phase (GP) does not necessarily control the reaction to all final states, one can always find final states where it does. For the isotopic counterpart reactions, these states can be used to make a measurement of the GP effect by separately measuring the even and odd symmetry contributions, which experimentally requires nuclear-spin final-state resolution. This follows from symmetry considerations that make the even and odd identical-particle exchange symmetry wavefunctions which include the GP locally equivalent to the opposite symmetry wavefunctions which do not. It is shown how this equivalence can be used to define a constant which quantifies the GP effect and can be obtained solely from experimentally observable rates. This equivalence reflects the important role that discrete symmetries play in ultracold chemistry and highlights the key role that ultracold reactions can play in understanding fundamental aspects of chemical reactivity more generally.

A review of dynamical resonances in A + BC chemical reactions

The concept of the transition state has played an important role in the field of chemical kinetics and reaction dynamics. Reactive resonances in the transition-state region can dramatically enhance the reaction probability; thus investigation of the reactive resonances has attracted great attention from chemical physicists for many decades. In this review, we mainly focus on the recent progress made in probing the elusive resonance phenomenon in the simple A  +  BC reaction and understanding its nature, especially in the benchmark F/Cl  +  H₂ and their isotopic variants. The signatures of reactive resonances in the integral cross section, differential cross section (DCS), forward- and backward-scattered DCS, and anion photodetachment spectroscopy are comprehensively presented in individual prototype reactions. The dynamical origins of reactive resonances are also discussed in this review, based on information on the wave function in the transition-state region obtained by time-dependent quantum wave-packet calculations.

Dynamics of transient speciesviaanion photodetachment

Recent experimental and theoretical advances in transient reaction dynamics probed by photodetachment of polyatomic anions are reviewed.

Recent advances in quantum scattering calculations on polyatomic bimolecular reactions

This review surveys quantum scattering calculations on chemical reactions of polyatomic molecules in the gas phase published in the last ten years.

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.

Recent Advances in Quantum Dynamics of Bimolecular Reactions

In this review, we survey the latest advances in theoretical understanding of bimolecular reaction dynamics in the past decade. The remarkable recent progress in this field has been driven by more accurate and efficient ab initio electronic structure theory, effective potential-energy surface fitting techniques, and novel quantum scattering algorithms. Quantum mechanical characterization of bimolecular reactions continues to uncover interesting dynamical phenomena in atom-diatom reactions and beyond, reaching an unprecedented level of sophistication. In tandem with experimental explorations, these theoretical developments have greatly advanced our understanding of key issues in reaction dynamics, such as microscopic reaction mechanisms, mode specificity, product energy disposal, influence of reactive resonances, and nonadiabatic effects.

Mechanisms of SN2 reactions: insights from a nearside/farside analysis

A nearside/farside analysis, performed for the first time for a complex-forming polyatomic reaction, reveals details of the reaction mechanism.

Molecular collisions coming into focus

Control over molecules in a Stark decelerator enables the measurement of diffraction oscillations in NO-atom scattering.

Is the simplest chemical reaction really so simple?

Modern computational methods have become so powerful for predicting the outcome for the H + H2 → H2 + H bimolecular exchange reaction that it might seem further experiments are not needed. Nevertheless, experiments have led the way to cause theorists to look more deeply into this simplest of all chemical reactions. The findings are less simple.