Observation of a transition state resonance in the integral cross section of the F+HD reaction

Odyssey in the Wonderland of Chemical Dynamics

This is a recollection of my scientific trajectory. When I look back, I consider myself to be very fortunate for being able to do something I love and on topics of my own will. I am not a competitive person and tend to shy away from the limelight. Nonetheless, I survived in my profession and eventually made some modest contributions, which are beyond what I would have expected. We often forget about the human aspect of scientific endeavor. After all, science is done by individuals; humans have emotions and make mistakes. The frustrations of failures, the joys of finding problems and solutions to them, and the passion for fulfilling curiosity are all parts of this endeavor. Throughout the years, many people-mentors, students, postdocs, collaborators, and colleagues-have accompanied me in this exciting and fruitful journey, for which I am deeply grateful and feel very lucky to have them.

A Transition State Resonance Radically Reshapes Angular Distributions of the F + H 2 → FH(v f = 3) + H Reaction in the 62-102 meV Energy Range

Reactive angular distributions of the benchmark F + H 2(v i = 0) → FH(v f = 3) + H reaction show unusual propensity toward small scattering angles, a subject of a long debate in the literature. We use Regge trajectories to quantify the resonance contributions to state-to-state differential cross sections. Conversion to complex energy poles allows us to attribute the effect almost exclusively to a transition state resonance, long known to exist in the F + H 2 system and its isotopic variant F + HD. For our detailed analysis of angular scattering we employ the package DCS_Regge, recently developed for the purpose [Akhmatskaya E.; Sokolovski D.Comput. Phys. Commun.2022, 277, 108370].

The F + HD (v = 0, 1; j = 1) reaction: angular momentum correlations in the low (<1 meV) collision energy regime

A detailed analysis of the low collision energy (0.03-10 meV) integral reaction cross-section has been carried out for the F + HD (v = 0, 1; j = 1)→ HF(DF) + D(H) reaction using accurate, fully converged time-independent hyperspherical quantum dynamics. Particular attention has been paid to the shape (orbiting) resonances and their assignment to the orbital (L) and total (J) angular momenta as well as to the product's state resolved cross-sections at the energies of the resonances. As in previous works, it has been found that the energy position of the resonances depends on the initial state, but is essentially the same for the two exit channels and the product's rovibrational states. The analysis in terms of the orbital and total angular momenta showed that each resonance is characterised by a given value of L but is contributed by several J. The main resonances are due to L = 3 and L = 5 for both F + HD (v = 0, j = 1) and F + HD (v = 1, j = 1) reactions, although they appear at different collision energies. The product's vibrationally resolved excitation functions are found to follow the same pattern as the integral cross-section summed over all final states. A more detailed analysis has been made for the rotationally resolved integral cross-sections associated with L = 3, which gives rise to the main resonance for the two reactions and both product channels, for different final j' states, showing similar behaviour for all j' states except for j' = 0 due to parity conservation. The joint analysis of the final rotational and orbital angular momenta shows that L' and j' tend to have an antiparallel orientation.

Feshbach resonances in the F + CHD3 → HF + CD3 reaction

The signature of dynamics resonances was observed in the benchmark polyatomic F + CH₄/CHD₃ reactions more than a decade ago; however, the dynamical origin of the resonances is still not clear due to the lack of reliable quantum dynamics studies on accurate potential energy surfaces. Here, we report a six-dimensional state-to-state quantum dynamics study on the F + CHD₃ → HF + CD₃ reaction on a highly accurate potential energy surface. Pronounced oscillatory structures are observed in the total and product rovibrational-state-resolved reaction probabilities. Detailed analysis reveals that these oscillating features originate from the Feshbach resonance states trapped in the peculiar well on the HF(v' = 3)-CD₃ vibrationally adiabatic potential caused by HF chemical bond softening. Most of the resonance structures on the reaction probabilities are washed out in the well converged integral cross sections (ICS), leaving only one distinct peak at low collision energy. The calculated HF vibrational state-resolved ICS for CD₃(v = 0) agrees quantitatively with the experimental results, especially the branching ratio, but the theoretical CD₃ umbrella vibration state distribution is found to be much hotter than the experiment.

Accurate Calculation of Rate Constant and Isotope Effect for the F + H2 Reaction by the Coupled 3D Time-Dependent Wave Packet Method on the Newly Constructed Ab Initio Ground Potential Energy Surface

We employ coupled three-dimensional (3D) time dependent wave packet formalism in hyperspherical coordinates for reactive scattering problem on the newly constructed ab initio calculated ground adiabatic potential energy surface for the F + H₂/D₂ reaction. The convergence profiles for various reactive channels are depicted at low collision energy regimes with respect to the total angular momentum (J) quantum numbers. For two different reactant diatomic molecules (H₂ and D₂) initially at their respective ground roto-vibrational state (v = 0, j = 0), calculated state-to-state as well as total integral cross sections as a function of collision energy, temperature dependent rate constants, and the kinetic isotope effect for various reactivity profiles of F + H₂ and F + D₂ reactions are presented along with previous theoretical and experimental results.

Strong non-Arrhenius behavior at low temperatures in the OH + HCl → H2O + Cl reaction due to resonance induced quantum tunneling

The OH + HCl reaction possesses many Feshbach resonances trapped in the hydrogen bond well in the entrance channel, which substantially enhance the reaction rates at low temperatures.

The F + HD(v = 0, 1; j = 0, 1) reactions: stereodynamical properties of orbiting resonances

The excitation functions (reaction cross-section as a function of collision energy) of the F + HD(v = 0, 1; j = 0, 1) benchmark system have been calculated in the 0.01-6 meV collision energy interval using a time-independent hyperspherical quantum dynamics methodology. Special attention has been paid to orbiting resonances, which bring about detailed information on the three-atom interaction during the reactive encounter. The location of the resonances depends on the rovibrational state of the reactants HD(v,j), but is the same for the two product channels HF + D and DF + H, as expected for these resonances that are linked to the van der Waals well at the entrance. The resonance intensities depend both on the entrance and on the exit channels. The peak intensities for the HF + D channel are systematically larger than those for DF + H. Vibrational excitation leads to an increase of the peak intensity by more than an order of magnitude, but rotational excitation has a less drastic effect. It deceases the resonance intensity of the F + HD(v = 1) reaction, but increases somewhat that of F + HD(v = 0). Polarization of the rotational angular momentum with respect to the initial velocity reveals intrinsic directional preferences in the F + HD(v = 0, 1; j = 1) reactions that are manifested in the resonance patterns. The helicities (Ω = 0, Ω = ±1) possible for j = 1 contribute to the resonances, but that from Ω± 1 is, in general, dominant and in some cases exclusive. It corresponds to a preferential alignment of the HD internuclear axis perpendicular to the initial direction of approach and, thus, to side-on collisions. This work also shows that external preparation of the reactants, following the intrinsic preferences, would allow the enhancement or reduction of specific resonance features, and would be of great help for their eventual experimental detection.

Determining the nature of quantum resonances by probing elastic and reactive scattering in cold collisions

Scattering resonances play a central role in collision processes in physics and chemistry. They help build an intuitive understanding of the collision dynamics due to the spatial localization of the scattering wavefunctions. For resonances that are localized in the reaction region, located at short separation behind the centrifugal barrier, sharp peaks in the reaction rates are the characteristic signature, observed recently with state-of-the-art experiments in low-energy collisions. If, however, the localization occurs outside of the reaction region, mostly the elastic scattering is modified. This may occur due to above-barrier resonances, the quantum analogue of classical orbiting. By probing both elastic and inelastic scattering of metastable helium with deuterium molecules in merged-beam experiments, we differentiate between the nature of quantum resonances-tunnelling resonances versus above-barrier resonances-and corroborate our findings by calculating the corresponding scattering wavefunctions.

The role of electron-nuclear coupling on multi-state photoelectron spectra, scattering processes and phase transitions

We present first principle based beyond Born-Oppenheimer (BBO) theory and its applications on various models as well as realistic spectroscopic and scattering processes, where the Jahn-Teller (JT) theory is brought in conjunction with the BBO approach on the phase transition of lanthanide complexes. Over one and half decades, our development of BBO theory is demonstrated with ab initio calculations on representative molecules of spectroscopic interest (NO2 radical, Na3 and K3 clusters, NO3 radical, C6H6+ and 1,3,5-C6H3F3+ radical cations) as well as triatomic reactive scattering processes (H+ + H2 and F + H2). Such an approach exhibits the effect of JT, Renner-Teller (RT) and pseudo Jahn-Teller (PJT) type of interactions. While implementing the BBO theory, we generate highly accurate diabatic potential energy surfaces (PESs) to carry out quantum dynamics calculation and find excellent agreement with experimental photoelectron spectra of spectroscopic systems and cross-sections/rate constants of scattering processes. On the other hand, such electron-nuclear couplings incorporated through JT theory play a crucial role in dictating higher energy satellite transitions in the dielectric function spectra of the LaMnO3 complex. Overall, this article thoroughly sketches the current perspective of the BBO approach and its connection with JT theory with various applications on physical and chemical processes.

Beyond Born-Oppenheimer constructed diabatic potential energy surfaces for F + H2 reaction

First principles based beyond Born-Oppenheimer theory has been implemented on the F + H₂ system for constructing multistate global diabatic Potential Energy Surfaces (PESs) through the incorporation of Nonadiabatic Coupling Terms (NACTs) explicitly. The spin-orbit (SO) coupling effect on the collision process of the F + H₂ reaction has been included as a perturbation to the non-relativistic electronic Hamiltonian. Adiabatic PESs and NACTs for the lowest three electronic states (1²A', 2²A', and 1²A″) are determined in hyperspherical coordinates as functions of hyperangles for a grid of fixed values of the hyperradius. Jahn-Teller (JT) type conical intersections between the two A' states translate along C_2v and linear geometries in F + H₂. In addition, A' and A″ states undergo Renner-Teller (RT) interaction at collinear configurations of this system. Both JT and RT couplings are validated by integrating NACTs along properly chosen contours. Subsequently, we have solved adiabatic-to-diabatic transformation (ADT) equations to evaluate the ADT angles for constructing the diabatic potential matrix of F + H₂, including the SO coupling terms. The newly calculated diabatic PESs are found to be smooth, single-valued, continuous, and symmetric and can be invoked for performing accurate scattering calculations on the F + H₂ system.

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.

Dynamics study on the non-adiabatic Na(3p) + HD → NaH/NaD + D/H reaction: insertion-abstraction mechanism

Time-dependent wave packet calculations are carried out for two reaction channels of the non-adiabatic Na(3p) + HD → NaH/NaD + D/H reaction. The potential well on the excited state potential energy surface makes the reaction preferable to proceed through the insertion reaction path. The dominance of the NaD + H reaction channel and product rotational state distributions are found to be in agreement with the characteristics of typical adiabatic insertion reactions. However, significant forward scattering peaks in the differential cross sections (DCS) are found to be inconsistent with the forward-backward symmetric scattering characteristic of typical adiabatic insertion reactions, which indicate that the Na(3p) + HD reaction is dominated by a direct reaction mechanism. The comparison between adiabatic and non-adiabatic calculated DCSs reveals that the non-adiabatic couplings in the reaction could reduce the lifetime of the intermediate complex. Finally, the insertion-abstraction mechanism is put forward for the non-adiabatic Na(3p) + HD reaction.

Benchmark Quantum Kinetics at Low Temperatures toward Absolute Zero and Role of Entrance Channel Wells on Tunneling, Virtual States, and Resonances: The F + HD Reaction

This paper reports a study of the quantum reaction dynamics and kinetics of the F + HD reaction at low and ultralow temperatures, focusing on the range from the Wigner limit up to 50 K. Close coupling time-independent quantum reactive scattering calculations for the production of HF and DF molecules have been carried out on two potential energy surfaces differing in the description of the reaction entrance channel. This case is computationally more demanding than the cases of F with H₂ and D₂ ( De Fazio et al. Frontiers in Chemistry 2019 , 7 , 328 ) but offers a wider phenomenology regarding the roles of quantum mechanical effects of tunneling, of virtual states, and of resonances. The results show that at the temperatures in the cold and ultracold regimes small changes in the entrance channel long-range interaction induce surprising near threshold features. The presence of a virtual state close to the reactive threshold gives rise to a marked anti-Arrhenius behavior of the rate constants below 100 mK. This effect enhances reaction rates by about 2 orders of magnitude, making them of the same order as those at room temperature and confining the onset of the Wigner regime in the microkelvin region.

Orbiting resonances in the F + HD (v = 0, 1) reaction at very low collision energies. A quantum dynamical study

Time-independent, fully converged, quantum dynamical calculations have been performed for the F + HD (v = 0, j = 0) and F + HD (v = 1, j = 0) reactions on an accurate potential energy surface down to collision energies of 0.01 meV. The two isotopic exit channels, HF + D and DF + H, have been investigated. The calculations reproduce satisfactorily the Feshbach resonance structures for collision energies between 10 and 40 meV, previously reported in the literature for the HF + D channel. Contrary to the results of a former literature work, vibrational excitation of HD is found to enhance reactivity in all cases down to the lowest collision energy investigated. Shape-type orbiting resonances are found for collision energies lower than 2 meV. The resonances appear as peaks in the reaction cross sections that are associated to specific values of the total angular momentum, J. In contrast with the Feshbach resonances at higher energies, the orbiting resonance structure, which is caused by the van der Waals well of the entrance channel, is identical for the HF + D and DF + H exit channels. The orbiting resonance peaks for F + HD (v = 0) are very small, but those for F + HD (v = 1) could be observed, in principle, with a combination of Raman pumping and merged beams methods.

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.

Imaging a Resonance-Dominant Polyatomic Reaction: F + CH3D → CH3(ν2 = 2) + DF(ν)

The title reaction was studied in a crossed-beam scattering experiment at the collisional energy ( E_c) ranging from 0.46 to 4.53 kcal mol^-1. Using a time-sliced velocity-imaging technique, both the pair-correlated integral and differential cross sections were measured. On the basis of the observed structures in state-specific excitation functions and the patterns in the E_c evolution of product angular distributions, we inferred that the title reaction proceeds predominantly via a resonance-mediated pathway, in contrast to the previous findings in the isotopically analogous reactions where the alternative direct abstraction pathway often dominates the reactivity. Despite the complexity of numerous scattering resonances involved in this six-atom reaction, extending our understanding of the isolated resonance in the analogous benchmark F + HD (H₂) reaction enables us to propose plausible mechanistic origins for the formation as well as the decay of the complicated overlapped resonances.

Slow Photoelectron Velocity-Map Imaging of Cryogenically Cooled Anions

Slow photoelectron velocity-map imaging spectroscopy of cryogenically cooled anions (cryo-SEVI) is a powerful technique for elucidating the vibrational and electronic structure of neutral radicals, clusters, and reaction transition states. SEVI is a high-resolution variant of anion photoelectron spectroscopy based on photoelectron imaging that yields spectra with energy resolution as high as 1-2 cm^-1. The preparation of cryogenically cold anions largely eliminates hot bands and dramatically narrows the rotational envelopes of spectral features, enabling the acquisition of well-resolved photoelectron spectra for complex and spectroscopically challenging species. We review the basis and history of the SEVI method, including recent experimental developments that have improved its resolution and versatility. We then survey recent SEVI studies to demonstrate the utility of this technique in the spectroscopy of aromatic radicals, metal and metal oxide clusters, nonadiabatic interactions between excited states of small molecules, and transition states of benchmark bimolecular reactions.

Spiers Memorial Lecture : Introductory lecture: quantum dynamics of chemical reactions

This Spiers Memorial Lecture discusses quantum effects that can be calculated and observed in the chemical reactions of small molecules.

Rainbows, supernumerary rainbows and interference effects in the angular scattering of chemical reactions: an investigation using Heisenberg's S matrix programme

Rainbow and supernumerary rainbow in the angular scattering of a state-to-state chemical reaction.

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.

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.

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.

Complex angular momentum theory of state-to-state integral cross sections: resonance effects in the F + HD → HF(v′ = 3) + D reaction

State-to-state reactive integral cross sections (ICSs) are often affected by quantum mechanical resonances, especially in the neighborhood of a reactive threshold.

Isotope-Dependent Rotational States Distributions Enhanced by Dynamic Resonance States: A Comparison Study of the F + HD → HF(vHF = 2) + D and F + H2 → HF(vHF = 2) + H Reaction

An interesting trimodal structure in the HF (v' = 2) rotational distribution produced by the F + HD (v = 0, j = 0) reaction, but monomodal structure in the HF (v' = 2) rotational distribution produced by the F + H2 (v = 0, j = 0) reaction, were observed using a high-resolution crossed molecular beam apparatus. The rotational states of product HF (v' = 2) are much hotter in the F + HD reaction. It is uncovered that the observations are due to the dominant role of the dynamical resonance states in these two isotopic reactions. The angular potential well in the region of the resonance state of the F + HD reaction is much deeper and supports wave function with high angular kinetic energy, which in turn comes from different H tunneling processes in the F + HD and F + H2 reaction.

Theoretical reaction kinetics astride the transition between moderate and deep tunneling regimes: the F + HD case

For the reaction between F and HD, giving HF + D and DF + H, the rate constants, obtained from rigorous quantum scattering calculations at temperatures ranging from 350 K down to 100 K, show deviations from the Arrhenius behavior that have been interpreted in terms of tunneling of either H or D atoms through a potential energy barrier. The interval of temperature investigated extends from above to below a crossover value Tc, a transition temperature separating the moderate and deep quantum tunneling regimes. Below Tc, the rate of the H or D exchange reaction is controlled by the prevalence of tunneling over the thermal activation mechanism. In this temperature range, Bell's early treatment of quantum tunneling, based on a semiclassical approximation for the barrier permeability, provides a reliable tool to quantitatively account for the contribution of the tunneling effect. This treatment is here applied for extracting from rate constants properties of the effective tunneling path, such as the activation barrier height and width. We show that this is a way of parametrizing the dependence of the apparent activation energy on temperature useful for both calculated and experimental rate constants in an ample interval of temperature, from above to below Tc, relevant for modelization of astrophysical and in general very low-temperature environments.

Accurate double many-body expansion potential energy surface by extrapolation to the complete basis set limit and dynamics calculations for ground state of NH2

An accurate single-sheeted double many-body expansion potential energy surface is reported for the title system. A switching function formalism has been used to warrant the correct behavior at the H2(X1Σg+)+N(2D) and NH (X3Σ-)+H(2S) dissociation channels involving nitrogen in the ground N(4S) and first excited N(2D) states. The topographical features of the novel global potential energy surface are examined in detail, and found to be in good agreement with those calculated directly from the raw ab initio energies, as well as previous calculations available in the literature. The novel surface can be using to treat well the Renner-Teller degeneracy of the 12A″ and 12A' states of NH 2. Such a work can both be recommended for dynamics studies of the N(2D)+H2 reaction and as building blocks for constructing the double many-body expansion potential energy surface of larger nitrogen/hydrogen-containing systems. In turn, a test theoretical study of the reaction N(2D)+H2(X1Σg+)(ν=0,j=0)→NH (X3Σ-)+H(2S) has been carried out with the method of quantum wave packet on the new potential energy surface. Reaction probabilities, integral cross sections, and differential cross sections have been calculated. Threshold exists because of the energy barrier (68.5 meV) along the minimum energy path. On the curve of reaction probability for total angular momentum J = 0, there are two sharp peaks just above threshold. The value of integral cross section increases quickly from zero to maximum with the increase of collision energy, and then stays stable with small oscillations. The differential cross section result shows that the reaction is a typical forward and backward scatter in agreement with experimental measurement result.

THEORETICAL STUDY ON PARTIAL POTENTIAL SURFACE AND SCATTERING RESONANCE STATE OF THE ASYMMETRICAL H EXCHANGING X + H2O → XH + OH (X = Cl, F, H) REACTIVE SYSTEM

In the course of an extensive investigation aimed at understanding the detailed mechanism of a prototypical polyatomic reaction, several remarkable observations were uncovered. To interpret these findings, we surmise the existence of a reactive resonance in this polyatomic reaction. The system of concern is X + H 2 O → XH + OH ( X = Cl, F, H ), and it belongs to a type of asymmetrical H exchanging reaction. Because the concerned electronic number is quite small, it is usually regarded as a template constructed the model of theory or experiment. In this paper, compared with the symmetrical systems, we constructed the partial potential surfaces of asymmetrical systems in order to research their resonance states. All results are in good agreement with previous theoretical and experimental works.