Quantum interference between spin-orbit split partial waves in the F + HD → HF + D reaction

Quantum state tracking and control of a single molecular ion in a thermal environment

Understanding molecular state evolution is central to many disciplines, including molecular dynamics, precision measurement, and molecule-based quantum technology. Details of the evolution are obscured when observing a statistical ensemble of molecules. Here, we report real-time observations of thermal radiation-driven transitions between individual states ("jumps") of a single molecule. We reversed these "jumps" through microwave-driven transitions, resulting in a twentyfold improvement in the time the molecule dwells in a chosen state. The measured transition rates showed anisotropy in the thermal environment, pointing to the possibility of using single molecules as in-situ probes for the strengths of ambient fields. Our approaches for state detection and manipulation could apply to a wide range of species, facilitating their uses in fields including quantum science, molecular physics, and ion-neutral chemistry.

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.

Quantum interference in atom-exchange reactions

Chemical reactions, where bonds break and form, are highly dynamic quantum processes. A fundamental question is whether coherence can be preserved in chemical reactions and then harnessed to generate entangled products. Here we investigated this question by studying the 2KRb → K2 + Rb2 reaction at 500 nK, focusing on the nuclear spin degrees of freedom. We prepared the initial nuclear spins in KRb in an entangled state by lowering the magnetic field to where the spin-spin interaction dominates and characterized the preserved coherence in nuclear spin wavefunction after the reaction. We observed an interference pattern that is consistent with full coherence at the end of the reaction, suggesting that entanglement prepared within the reactants could be redistributed through the atom-exchange process.

Development of the Time-Independent Methods for the Cl + H2/F + HD Reaction Using Hyper-Spherical Coordinates Including (Full) Spin-Orbit Characteristics

Recently, a combined study of high-resolution molecular crossed beam experiment and accurate full-dimensional time-dependent theory, including full spin-orbit characteristics on the effect of electronic spin and orbital angular momenta in the F + HD reaction, was reported by some of us, focusing on the partial wave resonance phenomenon (Science 2021, 371, 936-940). It revealed that the time-dependent theory could explain all of the details observed in the high-resolution experiment. Here, we develop two time-independent close-coupling methods using hyperspherical coordinates, including the two-state model, where only a part of the spin-orbit characteristics is considered, and the six-state model, where the full spin-orbit characteristics is considered. With these two newly developed theoretical models and the adiabatic theoretical model, the detailed reaction dynamics of the F + HD (v = 0, j = 0) reaction and the Cl + H2 (v = 0, j = 0) reaction are investigated and compared. Some of the results are compared with the time-dependent quantum wave packet theory and the experimental observations, and good agreements have been obtained, which suggests the validity of the pure-procession approximation in the six-state model using different theoretical methods. This work demonstrates the ability of the reactive scattering theory including full spin-orbit characteristics for describing the reactions of a halogen atom plus hydrogen molecule and its isotopologues.

Significant Isotope Effects from the Nonadiabatic Couplings in the Cl(2P) + HD(v = 0, j = 0) Reaction

The impact of non-Born-Oppenheimer couplings on the isotopic effects in the reaction of the Cl(2P) atom with the HD (v = 0, j = 0) molecule is investigated with our recently developed nonadiabatic time-independent quantum scattering methods, where the full open-shell characteristics are included in the six-state model, and also with the recently developed two-state model solving by time-independent methods, where part of the open-shell characteristic is included. The same reaction is also calculated with the simple adiabatic model using the lowest adiabatic potential energy surface. Compared with the results from different models, it is found that the reactivity of the Cl + HD → HCl + D channel is significantly overestimated in the adiabatic model. In contrast, the reactivity of the other channel agrees well with the nonadiabatic models. This is due to the van der Waals well in the reactant channel being changed a lot by including the nonadiabatic couplings. These quantum dynamics calculations suggest that sometimes the adiabatic model should be used with caution; otherwise, it may result in significant deviations for some reactions.

Vibration to Vibration: Product Energy Distribution of F + HD Crossed Molecular Beam Experiments

We investigated the F + HD(v = 1, j = 0) → HF + D reaction using the crossed molecular beam technique combined with the D atom Rydberg tagging time-of-flight spectroscopy. By detecting the products at various scattering angles for different collision energies in the range of 0.8-1.2 kcal/mol, we observed the forward-scattering products of HF(v' = 4) and determined the threshold energy for the opening of this reaction channel. Similar experiments were conducted for the F + HD(v = 0, j = 0) → HF + D reaction within the range of 1.1-1.6 kcal/mol, where forward-scattering products of HF(v' = 3) were observed, and the threshold energy for this reaction channel was determined as well. Furthermore, we measured the differential cross-sections for the F + HD → HF + D reaction in both the vibrational ground state and the excited state of HD and analyzed the vibrational quantum-state distribution of the HF products. It was found that the population of vibrational quantum states of the HF products increases synchronously with the excitation of the reactant HD vibrationally.

Imaging the Ion-Molecule Reaction Dynamics of O- + CD4

While neutral reactions involved in methane oxidation have been intensively studied, much less information is known about the reaction dynamics of the oxygen radical anion with methane. Here, we study the scattering dynamics of this anion-molecule reaction using crossed-beam velocity map imaging with deuterated methane. Differential scattering cross sections for the deuterium abstraction channel have been determined at relative collision energies between 0.2 and 1.5 eV and ab initio calculations of the important stationary points along the reaction pathway have been performed. At lower collision energies, direct backscattering and indirect complex-mediated reaction dynamics are observed, whereas at higher energies, sideways deuterium stripping dominates the reaction. Above 0.7 eV collision energy, a suppressed cross section is observed at low product ion velocities, which is likely caused by the endoergic pathway of combined deuteron/deuterium transfer, forming heavy water. The measured product internal energy is attributed mainly to the low-lying deformation and out-of-plane bending vibrations of the methyl radical product. The results are compared with a previous crossed-beam result for the reaction of oxygen anions with nondeuterated ̧methane and with the related neutral-neutral reactions, showing similar dynamics and qualitative agreement.

Theoretical Development of the Interaction-Asymptotic Region Decomposition Method for Tetratomic Reactive Scattering

An accurate and efficient time-dependent wave packet method is proposed for solving the product state-resolved reaction probabilities of the tetratomic reactive system. In this method, the entire scattering process is divided into the interaction region and multiple asymptotic regions, sharing the same spirit as the interaction-asymptotic region decomposition (IARD) approach in a triatomic reactive scattering process. The hyperspherical coordinate is adopted in the interaction region, while the corresponding Jacobi coordinate is employed in each asymptotic region. Therefore, in this IARD method, the "coordinate problem", the difficulty of expressing the wave function in the entire region using a single coordinate system, can be effectively avoided, and only a very small number of the grid points (or the basis functions) are required. For the numerical illustration, the typical tetratomic reaction H2 + OH with zero total angular momentum is calculated, and compared with other quantum wave packet methods. Our proposed IARD method for the tetratomic reactive system is much more efficient and accurate.

Unveiling Quantum Interference in the D+ + H2 Nonadiabatic Reaction Dynamics at Low Collision Energies

Fully converged nonadiabatic dynamics calculations of the D+ + H2 → H+ + HD reaction are performed at low temperatures using the time-dependent wave packet approach based on a set of precise 3 × 3 diabatic potential energy surfaces (PESs) ( Phys. Chem. Chem. Phys., 2021, 23, 7735-7747, DOI: 10.1039/D0CP04100A). The D+ + H2 reaction is mediated by a dense manifold of resonances associated with the deep potential well on the ground-state PES. The calculated results show that the nonadiabatic coupling can affect the resonance positions, deviating from the expectation based solely on adiabatic considerations. Furthermore, significant forward-backward asymmetry in total differential cross sections (DCSs) is revealed, which is markedly influenced by nonadiabatic effects. The nonadiabatic effects not only affect the contribution of partial waves in the reaction but also make the interference patterns in the DCSs change significantly.

Correlation Study of the Spin-Orbit State-Resolved Scattering of Al(2P) in Oxidation Reaction and Nonreactive Collision

Spin-orbit coupling plays an important role in chemical reactivity, especially in reactions that require the change of electron spin states. However, it is difficult to measure and analyze the reaction dynamics between spin-orbit splitting states, particularly for splitting states with a small energy difference. In this study, we find that nonreactive scattering of spin-orbit splitting states can provide complementary information that is overlooked in chemical reaction studies. Here, the oxidation reactivities of spin-orbit Al(2P1/2,3/2) states with small energy difference of 112 cm-1 are clearly distinguished in the high rotational AlO(v = 0 and 1, N) products at low collision energy of 507 cm-1 using a laser ablation crossed-beam and time-sliced ion velocity mapping technique, in conjunction with state-selected nonreactive scattering studies. For both the AlO(v = 0 and 1) channels, the spin-orbit relative reactivity σ3/2/σ1/2 increases with the increase of rotational level N of AlO products. However, for AlO(v = 0), the reactivity of the Al(2P3/2) excited state is consistently lower than that of the Al(2P1/2) ground state, whereas for AlO(v = 1), the reactivity of Al(2P3/2) is higher than that of Al(2P1/2) at a higher rotational state. The relative reactivity of spin-orbit split Al(2P) states at different scattering angles shows a more pronounced enhancement of forward scattering relative to side and backward scattering for Al(2P3/2) when a higher rotationally excited AlO is produced. Nonreactive scattering studies of Al(2P) suggest that the Al(2P3/2) state is deexcited to the ground Al(2P1/2) state at the sideways and backward scattering directions, and the deexcitation is supposed to reduce the reactivity of the excited Al(2P3/2) at the corresponding direction.

CRISPR/Cas12a-Powered Competitive Immunosorbent Assay for Small Molecules

CRISPR/Cas systems are powerful tools for sensitive nucleic acid molecular diagnosis due to their specific nucleic acid recognition and high trans-cleavage activity and have also allowed for quantification of non-nucleic acid targets, relying on a strategy to convert the target detection to analysis of nucleic acids. Here, we describe a CRISPR/Cas12a-powered immunosorbent assay for sensitive small-molecule detection by using the antibody coated on the microplate to recognize the target and the small molecule-labeled active DNA (acDNA) to trigger the activity of CRISPR/Cas12a. In the absence of small-molecule targets, acDNA probes are captured by the antibody on the microplate and then activate Cas12a in catalytic trans-cleavage of fluorescent DNA reporters, generating strong fluorescence. The presence of small-molecule targets displaces the acDNA probes from the antibody, causing a decrease of acDNA probes on the microplate and reduction of activated Cas12a, so the fluorescence signal decreases, and small molecules can be detected by monitoring the fluorescence change. After systematically optimizing experimental conditions (e.g., Cas12a reaction), the proposed method achieved the detection of three model small molecules, biotin, digoxin, and folic acid, with low detection limits, and a flexible detection concentration range was obtained by simply changing the amount of acDNA probes and immobilized antibodies. The assay showed high selectivity and good applicability in complex media. The integration of the CRISPR/Cas12a system improves the analytical performance of immunoassay, broadening and facilitating its applications in rapid, simple, and sensitive small molecule analysis.

Incorporating Nuclear Quantum Effects in Molecular Dynamics with a Constrained Minimized Energy Surface

The accurate incorporation of nuclear quantum effects in large-scale molecular dynamics (MD) simulations remains a significant challenge. Recently, we combined constrained nuclear-electronic orbital (CNEO) theory with classical MD and obtained a new approach (CNEO-MD) that can accurately and efficiently incorporate nuclear quantum effects into classical simulations. In this Letter, we provide the theoretical foundation for CNEO-MD by developing an alternative formulation of the equations of motion for MD. In this new formulation, the expectation values of quantum nuclear positions evolve classically on an effective energy surface that is obtained from a constrained energy minimization procedure when solving for the quantum nuclear wave function, thus enabling the incorporation of nuclear quantum effects in classical MD simulations. For comparison with other existing approaches, we examined a series of model systems and found that this new MD approach is significantly more accurate than the conventional way of performing classical MD and generally outperforms centroid MD and ring-polymer MD in describing vibrations in these model systems.

Stereodynamics-Controlled Product Branching in the Nonadiabatic H + NaD → Na(3s, 3p) + HD Reaction at Low Temperatures

Nonadiabatic processes play an important role at energies near or higher than conical intersection of adiabatic potential energy surfaces in chemical reactions. In this work, dynamics of the nonadiabatic H + NaD reaction at low temperatures are studied by using the quantum wave packet method based on an improved L-shaped grid. The nonadiabatic H + NaD reaction has two exothermic reaction channels: Na(3s) + HD and Na(3p) + HD; the latter can only occur via nonadiabatic transition. The dynamics results show that the product branching of the H + NaD reaction at collision energies ranging from 20 to 80 cm^-1 is controlled by stereodynamics. The Na(3s) and Na(3p) reaction channels occur through collinear collision and side-on collision, respectively. When the collision energy is lower than 20 cm^-1, the resonance-mediated reaction mechanism is dominant in both the Na(3s) and Na(3p) reaction channels.

Low-temperature reaction dynamics of paramagnetic species in the gas phase

Radicals are abundant in a range of important gas-phase environments. They are prevalent in the atmosphere, in interstellar space, and in combustion processes. As such, understanding how radicals react is essential for the development of accurate models of the complex chemistry occurring in these gas-phase environments. By controlling the properties of the colliding reactants, we can also gain insights into how radical reactions occur on a fundamental level. Recent years have seen remarkable advances in the breadth of experimental methods successfully applied to the study of reaction dynamics involving paramagnetic species-from improvements to the well-known crossed molecular beams approach to newer techniques involving magnetically guided and decelerated beams. Coupled with ever-improving theoretical methods, quantum features are being observed and interesting insights into reaction dynamics are being uncovered in an increasingly diverse range of systems. In this highlight article, we explore some of the exciting recent developments in the study of chemical dynamics involving paramagnetic species. We focus on low-energy reactive collisions involving neutral radical species, where the reaction parameters are controlled. We conclude by identifying some of the limitations of current methods and exploring possible new directions for the field.

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.

Quantum interference between spin-orbit split partial waves in the F + HD → HF + D reaction

The effect of electron spin-orbit interactions on chemical reaction dynamics has been a topic of much research interest. Here we report a combined experimental and theoretical study on the effect of electron spin and orbital angular momentum in the F + HD → HF + D reaction. Using a high-resolution imaging technique, we observed a peculiar horseshoe-shaped pattern in the product rotational-state-resolved differential cross sections around the forward-scattering direction. The unusual dynamics pattern could only be explained properly by highly accurate quantum dynamics theory when full spin-orbit characteristics were considered. Theoretical analysis revealed that the horseshoe pattern was largely the result of quantum interference between spin-orbit split-partial-wave resonances with positive and negative parities, providing a distinctive example of how spin-orbit interaction can effectively influence reaction dynamics.