Interference of quantized transition-state pathways in the H + D2 -> D + HD chemical reaction

Spiers Memorial Lecture: New directions in molecular scattering

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

High-Resolution Crossed-Beam Dynamics Studies of the D + Para-H2 → HD + H Reaction at 1.21 eV

Understanding kinetic isotope effects is important in the study of the reaction dynamics of elementary chemical reactions, particularly those involving hydrogen atoms and molecules. As one of the isotopic variants of the hydrogen exchange reaction, the D + para-H2 reaction has attracted much attention. However, experimental studies of this reaction have been limited primarily due to its strong experimental background noise. In this study, by using the velocity map ion imaging method and the near-threshold ionization technique, together with improvements on the vacuum condition in the vicinity of the collision zone, background noise was reduced significantly, and quantum state-resolved differential cross sections (DCSs) for the D + para-H2 reaction at a collision energy of 1.21 eV were acquired in a crossed molecular beams experiment. Interestingly, clear rotational state-dependent angular distributions were noticed in the quantum state-resolved DCSs. The most intense peak's positions for HD (v', j') products shift to different scattering directions as the product's ro-vibrational quantum number increases. Two different microscopic reaction mechanisms are found to be involved in this reaction for HD products in different vibrational states. The results show a direct correlation between the scattering angle and the product's rotational quantum number, revealing that the contributions of impact parameters are strongly influenced by the corresponding centrifugal barrier.

Strong Angular Oscillation of Rotationally Resolved Differential Cross Section in the H + HD → H2 + D Reaction at the Collision Energy of 2.07 eV: Evidence of Geometric Phase Effects

Geometric phase (GP) effects in chemical reactions are subtle quantum phenomena that are challenging to identify. In this work, we report a joint experimental and theoretical study of the H + HD → H2 + D reaction at a collision energy of 2.07 eV, which is far below the energy of the conical intersection of 2.53 eV. The rotationally state-resolved differential cross sections were measured by a crossed-beam experiment with the scheme of D-atom Rydberg tagging time-of-flight detection. Experimental angular distributions of three rotational states of H2 products exhibit notable variation near the backward scattering direction. Time-dependent quantum mechanics calculations (TDQMs) were carried out at the same collision energy, with and without the inclusion of GP. The experimental angular distributions are in good agreement with TDQM results with the inclusion of GP but do not agree with TDQM results without the inclusion of GP. This work demonstrates the existence of GP effects at energy far below the conical intersection.

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.

Research Progress on the Pathogenesis of Knee Osteoarthritis

Knee osteoarthritis (KOA) is a chronic joint bone disease characterized by inflammatory destruction and hyperplasia of bone. Its main clinical symptoms are joint mobility difficulties and pain, severe cases can lead to limb paralysis, which poses major pressure to the quality of life and mental health of patients, but also brings serious economic burden to society. The occurrence and development of KOA is influenced by many factors, including systemic factors and local factors. The joint biomechanical changes caused by aging, trauma and obesity, abnormal bone metabolism caused by metabolic syndrome, the effects of cytokines and related enzymes, genetic and biochemical abnormalities caused by plasma adiponectin, etc. all directly or indirectly lead to the occurrence of KOA. However, there is little literature that systematically and comprehensively integrates macro- and microscopic KOA pathogenesis. Therefore, it is necessary to comprehensively and systematically summarize the pathogenesis of KOA in order to provide a better theoretical basis for clinical treatment.

Theoretical Simulations of Kinetic Isotope Effects on Decarboxylation of 3-Carboxybenzisoxazole

Kinetic isotope effect values on the decarboxylation of 3-carboxybenzisoxazole have been computed using the second-order Kleinert's variational perturbation theory in the framework of Feynman's path integrals along with the potential energy surface obtained at the MP2/6-31+G(d) level. Good agreement with the experimental data was obtained, demonstrating that this novel computational approach for computing KIE values of organic reaction is a viable alternative to the traditional method employing the Bigeleisen equation and harmonic vibrational frequencies. Compared with the experimental measurements, consideration of anharmonicity and tunneling effects can significantly improve the calculated KIE values, reducing the root-mean-square deviation from 1.19 % for traditional method to 0.20 % for path-integral method.

Chemical reaction thresholds according to classical-limit quantum dynamics

Classical-limit quantum dynamics is used to explain the origin of the quantum thresholds of chemical reactions from their classical dynamics when these are vibrationally nonadiabatic across the interaction region. This study is performed within the framework of an elementary model of chemical reaction that mimics the passage from the free rotation of the reagents to the bending vibration at the transition state to the free rotation of the products.

Constructive Quantum Interference in Photochemical Reactions

Interferences emerge when multiple pathways coexist together, leading toward the same result. Here, we report a theoretical study for a reaction scheme that leads to constructive quantum interference in a photoassociation (PA) reaction of a ⁸⁷Rb Bose-Einstein condensate where the reactant spin state is prepared in a coherent superposition of multiple bare spin states. This is achieved by changing the reactive scattering channel in the PA reaction. As the origin of coherent control comes from the spin part of the wavefunction, we show that it is sufficient to use radio frequency (RF) coupling to achieve the superposition state. We simulate the RF coupling on a quantum processor (IBMQ Lima), and our results show that interferences can be used as a resource for the coherent control of photochemical reactions. The approach is general and can be employed to study a wide spectrum of chemical reactions in the ultracold regime.

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.

A molecular double-slit experiment

[Figure: see text].

Inelastic Scattering of H Atoms from Surfaces

We have developed an instrument that uses photolysis of hydrogen halides to produce nearly monoenergetic hydrogen atom beams and Rydberg atom tagging to obtain accurate angle-resolved time-of-flight distributions of atoms scattered from surfaces. The surfaces are prepared under strict ultrahigh vacuum conditions. Data from these experiments can provide excellent benchmarks for theory, from which it is possible to obtain an atomic scale understanding of the underlying dynamical processes governing H atom adsorption. In this way, the mechanism of adsorption on metals is revealed, showing a penetration-resurfacing mechanism that relies on electronic excitation of the metal by the H atom to succeed. Contrasting this, when H atoms collide at graphene surfaces, the dynamics of bond formation involving at least four carbon atoms govern adsorption. Future perspectives of H atom scattering from surfaces are also outlined.

Non-unitary quantum electronics: Novel functions from the edge of the quantum world

Novel categories of electronic devices and quantum materials are obtained by pipelining the unitary evolution of electron quantum states as described by Schrödinger’s equation with non-unitary processes that interrupt the coherent propagation of electrons. These devices and materials reside in the fascinating transition regime between quantum mechanics and classical physics. The devices are designed such that a nonreciprocal unitary state evolution, achieved by means of a broken inversion symmetry, is interrupted by individual inelastic scattering events caused by defects coupled to an environment. Two-terminal non-unitary quantum devices, for example, feature nonreciprocal conductance in linear response. Thus, they are exemptions to Onsager’s reciprocal relation, and they challenge the second law of thermodynamics. Furthermore, materials and metamaterials featuring such functionalities may be realized by embedding such nanostructures into their unit cells.

Time-dependent quantum mechanical wave packet dynamics

Starting from a model study of the collinear (H, H₂) exchange reaction in 1959, the time-dependent quantum mechanical wave packet (TDQMWP) method has come a long way in dealing with systems as large as Cl + CH₄. The fast Fourier transform method for evaluating the second order spatial derivative of the wave function and split-operator method or Chebyshev polynomial expansion for determining the time evolution of the wave function for the system have made the approach highly accurate from a practical point of view. The TDQMWP methodology has been able to predict state-to-state differential and integral reaction cross sections accurately, in agreement with available experimental results for three dimensional (H, H₂) collisions, and identify reactive scattering resonances too. It has become a practical computational tool in predicting the observables for many A + BC exchange reactions in three dimensions and a number of larger systems. It is equally amenable to determining the bound and quasi-bound states for a variety of molecular systems. Just as it is able to deal with dissociative processes (without involving basis set expansion), it is able to deal with multi-mode nonadiabatic dynamics in multiple electronic states with equal ease. We present an overview of the method and its strength and limitations, citing examples largely from our own research groups.

Observation of the geometric phase effect in the H+HD→H2+D reaction below the conical intersection

It has long been known that there is a conical intersection (CI) between the ground and first excited electronic state in the H₃ system. Its associated geometric phase (GP) effect has been theoretically predicted to exist below the CI since a long time. However, the experimental evidence has not been established yet and its dynamical origin is waiting to be elucidated. Here we report a combined crossed molecular beam and quantum reactive scattering dynamics study of the H+HD → H₂+D reaction at 2.28 eV, which is well below the CI. The GP effect is clearly identified by the observation of distinct oscillations in the differential cross section around the forward direction. Quantum dynamics theory reveals that the GP effect arises from the phase alteration of a small part of the wave function, which corresponds to an unusual roaming-like abstraction pathway, as revealed by quasi-classical trajectory calculations.

The geometric phase effect associated with a conical intersection between the ground and first excited electronic state has been predicted in the H₃ system below the conical intersection energy. The authors, by a crossed molecular beam technique and quantum dynamic calculations, provide experimental evidence and insight into its origin.

Prediction of a Feshbach Resonance in the Below-the-Barrier Reactive Scattering of Vibrationally Excited HD with H

Quantum reactive scattering calculations on the vibrational quenching of HD due to collisions with H were carried out employing an accurate potential energy surface. The state-to-state cross sections for the chemical reaction HD(v = 1, j = 0) + H → D + H₂(v' = 0, j') at collision energies between 1 and 10 000 cm^-1 are presented, and a Feshbach resonance in the low-energy regime, below the reaction barrier, is observed for the first time. The resonance is attributed to coupling with the vibrationally adiabatic potential correlating to the v = 1, j = 1 level of the HD molecule, and it is dominated by the contribution from a single partial wave. The properties of the resonance, such as its dynamic behavior, phase behavior, and lifetime, are discussed.

Quantum interference in H + HD → H2 + D between direct abstraction and roaming insertion pathways

Understanding quantum interferences is essential to the study of chemical reaction dynamics. Here, we provide an interesting case of quantum interference between two topologically distinct pathways in the H + HD → H2 + D reaction in the collision energy range between 1.94 and 2.21 eV, manifested as oscillations in the energy dependence of the differential cross section for the H2 (v′ = 2, j′ = 3) product (where v′ is the vibrational quantum number and j′ is the rotational quantum number) in the backward scattering direction. The notable oscillation patterns observed are attributed to the strong quantum interference between the direct abstraction pathway and an unusual roaming insertion pathway. More interestingly, the observed interference pattern also provides a sensitive probe of the geometric phase effect at an energy far below the conical intersection in this reaction, which resembles the Aharonov–Bohm effect in physics, clearly demonstrating the quantum nature of chemical reactivity.

Imaging the State-to-State Dynamics of the H + D2 → HD + D Reaction at 1.42 eV

High-resolution state-resolved differential cross sections (DCSs) are of great importance in understanding quantum reaction dynamics, and they are the most detailed observables that can be experimentally measured. Here we report a synergic crossed molecular beam and quantum reaction dynamics study on the H + D₂ reaction. With the time-sliced velocity map ion imaging (VMI) technique and the near-threshold ionization scheme, we acquired the product rovibrational state-resolved DCSs of the H + D₂ (v = 0, j = 0) → HD (v', j') + D reaction at a collision energy of 1.42 eV. For HD products with small j' quantum numbers, significant forward scattering with clear angular oscillations was observed. The forward scattering disappears for the rotational states with large j' quantum numbers. Interestingly, as the j' number increases, the peak of the DCS shifts from backward to sideways systematically. The experimental observation agrees very well with theoretical quantum mechanical dynamics results, which reveals that the systematic shift of the peak in the DCS from backward scattering to sideways scattering can be understood very well with the strong correlation between the product rotational quantum number j' and the specific partial waves (J = 3-12), whereas the forward angular oscillations are from the coherent summation of larger partial waves.

Photoelectrons Are Not Always Quite Free

The photoelectron spectra of Sm₂O^- obtained over a range of photon energies exhibit anomalous changes in relative excited-state band intensities. Specifically, the excited-state transition intensities increase relative to the transition to the neutral ground state with decreasing photon energy, the opposite of what is expected from threshold effects. This phenomenon was previously observed in studies on several Sm-rich homo- and heterolanthanide oxides collected with two different harmonic outputs of a Nd:YAG (2.330 and 3.495 eV) [ J. Chem. Phys. 2017, 146, 194310]. We relate these anomalous intensities to populations of ground and excited anionic and neutrals states through the inspection of time-dependent perturbation theory within the adiabatic and sudden limits and for the first time show that transition intensities in photoelectron spectroscopy have a deep significance in gauging participation from excited states. We believe our results will have significance in the study of other electron-rich systems that have especially high density of accessible spin states.

Dynamical interference in the vibronic bond breaking reaction of HCO

First-principles treatments of quantum molecular reaction dynamics have reached the level of quantitative accuracy even in cases with strong non-Born-Oppenheimer effects. This achievement permits the interpretation of puzzling experimental phenomena related to dynamics governed by multiple coupled potential energy surfaces. We present a combined experimental and theoretical study of the photodissociation of formyl radical (HCO). Oscillations observed in the distribution of product states are found to arise from the interference of matter waves-a manifestation analogous to Young's double-slit experiment.

Observation of the geometric phase effect in the H + HD → H2+ D reaction

Theory has established the importance of geometric phase (GP) effects in the adiabatic dynamics of molecular systems with a conical intersection connecting the ground- and excited-state potential energy surfaces, but direct observation of their manifestation in chemical reactions remains a major challenge. Here, we report a high-resolution crossed molecular beams study of the H + HD → H2+ D reaction at a collision energy slightly above the conical intersection. Velocity map ion imaging revealed fast angular oscillations in product quantum state–resolved differential cross sections in the forward scattering direction for H2products at specific rovibrational levels. The experimental results agree with adiabatic quantum dynamical calculations only when the GP effect is included.

Angular momentum-scattering angle quantum correlation: a generalized deflection function

A natural generalization of the classical deflection function, the functional dependence of the deflection angle on the angular momentum (or the impact parameter), is the joint probability density function of these two quantities, revealing the correlation between them. It provides, at a glance, detailed information about the reaction mechanisms and how changes in the impact parameter affect the product angular distribution. It is also useful to predict the presence of quantum phenomena such as interference. However, the classical angular momentum-scattering angle correlation function has a limited use whenever quantum effects become important. Rigorously speaking, there is not a quantum equivalent of the classical joint distribution, as the differential cross section depends on the coherences between the different values of J caused by the cross terms in the expansion of partial waves. In this article, we present a simple method to calculate a quantum analog of this correlation, a generalized deflection function that can shed light onto the reaction mechanism using just quantum mechanical results. Our results show that there is a very good agreement between the quantum and classical correlation functions as long as quantum effects are not all relevant. When this is not the case, it will also be shown that the quantum correlation function is most useful to observe the extent of quantum effects such as interference among different reaction mechanisms.

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.

Oscillation of Branching Ratios Between the D(2s)+D(1s) and the D(2p)+D(1s) Channels in Direct Photodissociation of D_{2}

The direct photodissociation of D_{2} at excitation energies above 14.76 eV occurs via two channels, D(2s)+D(1s) and D(2p)+D(1s). The branching ratios between the two have been measured from the dissociation threshold to 3200 cm^{-1} above it, and it is found that they show cosine oscillations as a function of the fragment wave vector magnitudes. The oscillation is due to an interference effect and can be simulated using the phase difference between the wave functions of the two channels, analogous to Young's double-slit experiment. By fitting the measured branching ratios, we have determined the depths and widths of the effective spherical potential wells related to the two channels, which are in agreement with the effective depths and widths of the ab initio interaction potentials. The results of this Letter illustrate the importance of the relative phase between the fragments in controlling the branching ratios of the photodissociation channels.

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.

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.

Effects of reagent rotation on interferences in the product angular distributions of chemical reactions

Differential cross sections (DSCs) of the HD(v', j') product for the reaction of H atoms with supersonically cooled D2 molecules in a small number of initial rotational states have been measured at a collision energy of 1.97 eV. These DCSs show an oscillatory pattern that results from interferences caused by different dynamical scattering mechanisms leading to products scattered into the same solid angle. The interferences depend on the initial rotational state j of the D2(v = 0, j) reagent and diminish in strength with increasing rotation. We present here a detailed explanation for this behavior and how each dynamical scattering mechanism has a dependence on the helicity Ω, the projection of the initial rotational angular momentum j of the D2 reagent on the approach direction. Each helicity corresponds to a different internuclear axis distribution, with the consequence that the dependence on Ω reveals the preference of the different quasiclassical mechanisms as a function of approach direction. We believe that these results are general and will appear in any reaction for which several mechanisms are operative.

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.

Single-molecule chemical reaction reveals molecular reaction kinetics and dynamics

Understanding the microscopic elementary process of chemical reactions, especially in condensed phase, is highly desirable for improvement of efficiencies in industrial chemical processes. Here we show an approach to gaining new insights into elementary reactions in condensed phase by combining quantum chemical calculations with a single-molecule analysis. Elementary chemical reactions in liquid-phase, revealed from quantum chemical calculations, are studied by tracking the fluorescence of single dye molecules undergoing a reversible redox process. Statistical analyses of single-molecule trajectories reveal molecular reaction kinetics and dynamics of elementary reactions. The reactivity dynamic fluctuations of single molecules are evidenced and probably arise from either or both of the low-frequency approach of the molecule to the internal surface of the SiO2 nanosphere or the molecule diffusion-induced memory effect. This new approach could be applied to other chemical reactions in liquid phase to gain more insight into their molecular reaction kinetics and the dynamics of elementary steps.

Rate coefficients from quantum and quasi-classical cumulative reaction probabilities for the S(1D) + H2 reaction

Cumulative reaction probabilities (CRPs) at various total angular momenta have been calculated for the barrierless reaction S((1)D) + H(2) → SH + H at total energies up to 1.2 eV using three different theoretical approaches: time-independent quantum mechanics (QM), quasiclassical trajectories (QCT), and statistical quasiclassical trajectories (SQCT). The calculations have been carried out on the widely used potential energy surface (PES) by Ho et al. [J. Chem. Phys. 116, 4124 (2002)] as well as on the recent PES developed by Song et al. [J. Phys. Chem. A 113, 9213 (2009)]. The results show that the differences between these two PES are relatively minor and mostly related to the different topologies of the well. In addition, the agreement between the three theoretical methodologies is good, even for the highest total angular momenta and energies. In particular, the good accordance between the CRPs obtained with dynamical methods (QM and QCT) and the statistical model (SQCT) indicates that the reaction can be considered statistical in the whole range of energies in contrast with the findings for other prototypical barrierless reactions. In addition, total CRPs and rate coefficients in the range of 20-1000 K have been calculated using the QCT and SQCT methods and have been found somewhat smaller than the experimental total removal rates of S((1)D).