Optical Control of Reactions between Water and Laser-Cooled Be+ Ions

Preparation of High Vibrational States in the Entire Molecular Beam

Preparing highly excited molecules is of great interest in chemistry, but it has long been a challenge due to the high laser power required within the narrow line width to excite a weak transition. We present a cavity-enhanced infrared excitation scheme using a milliwatt laser. As a demonstration, about 35% of CO molecules in a ground-state rotational level were excited to the highly excited v = 3 state in the entire pulsed supersonic beam, as confirmed by the depletion of molecules in the ground state. The method was also applied to excite HD molecules to the v = 2 state with a continuous-wave diode laser. This work provides a universal approach to prepare molecules in a specific quantum state, paving the way to study the chemical reaction dynamics of highly excited molecules.

A Neural Network Potential Energy Surface and Quantum Dynamics Study of Ca(1S) + H2(v 0 = 0, j 0 = 0) → CaH + H Reaction

The reactive collision between Ca and H2 molecules has attracted great interest experimentally due to the key role of the product CaH molecule in the field of astrophysics and cold molecules. However, quantum dynamics calculations for this system have not been reported due to the lack of a global potential energy surface (PES). Herein, a globally accurate PES of the ground-state CaH2 is developed by combining 11365 high-level ab initio points and permutation invariant polynomial neural network method. Based on the newly constructed PES, the state-to-state quantum dynamics calculations for the Ca(1S) + H2 (v 0 = 0, j 0 = 0) → CaH + H reaction are carried out using the time-dependent wave packet method. The dynamic results reveal that the reaction follows the complex-forming mechanism near the reactive threshold, whereas both the indirect insertion mechanism and direct abstraction mechanism have effects at higher collision energies. The newly constructed PES can be used to further study the influence of isotope substitution, rovibrational excitation, and spatial orientation of reactant molecules on reaction dynamics.

Accurate diabatization based on combined-hyperbolic-inverse-power-representation: 1,2 2A' states of BeH2

A diabatic potential energy matrix (DPEM) for the two lowest states of BeH2+ has been constructed using the combined-hyperbolic-inverse-power-representation (CHIPR) method. By imposing symmetry constraints on the coefficients of polynomials, the complete nuclear permutation inversion symmetry is correctly preserved in the CHIPR functional form. The symmetrized CHIPR functional form is then used in the diabatization by ansatz procedure. The ab initio energies are reproduced with satisfactory accuracy. In addition, the CHIPR-based DPEM also reproduces the local topology of a conical intersection. Future work will focus on a complete four-state diabatic representation with emphasis on the long-range interactions and spin-orbit couplings, which will enable accurate quantum scattering calculations for the Be+(2P) + H2 → BeH+(X1Σ+) + H(2S) reaction.

Non-IRC Mechanism of Bimolecular Reactions with Submerged Barriers: A Case Study of Si+ + H2O Reaction

Chemical reactions with submerged barriers may feature interesting dynamic behaviors that are distinct from those with substantial barriers or those entirely dominated by capture. The Si+ + H2O reaction is a prototypical example, involving even two submerged saddle points along the reaction path: one for the direct dissociation of H (H-dissociation SP) and another for H migration from the O-side to the Si-side (H-migration SP). We investigated the intricacies of this process by employing quasi-classical trajectory calculations on an accurate, full-dimensional ab initio potential energy surface. Through careful trajectory analysis, an interesting nonintrinsic reaction coordinate mechanism was found to play an important role in producing SiOH+ and H. This new pathway is featured as that the H atoms do not form HSiOH+ complexes along the minimum-energy path but directly dissociate into the products after passing through the H-migration SP. Furthermore, based on artificially scaled potential energy surfaces (PESs), the impact of barrier height on the reaction is also explored. This work provides new insights into the dynamics of the Si+ + H2O reaction and enriches our understanding of reactions with submerged barriers.

Cold Ion-Molecule Reactions in the Extreme Environment of a Coulomb Crystal

Coulomb crystals provide a unique environment in which to study ion-neutral gas-phase reactions. In these cold, trapped ensembles, we are able to study the kinetics and dynamics of small molecular systems. These measurements have connections to chemistry in the Interstellar Medium (ISM) and planetary atmospheres. This Feature Article will describe recent work in our laboratory that uses Coulomb crystals to study translationally cold, ion-neutral reactions. We provide a description of how the various affordances of our experimental system allow for detailed studies of the reaction mechanisms and the corresponding products. In particular, we will describe quantum-state resolved reactions, isomer-dependent reactions, and reactions with a rarely studied, astrophysically relevant ion, CCl+.

Enhanced Total Vibrational Excitation Yield in a Slow Narrow-Pulsed Hydrogen Molecular Beam

High-efficiency excitation of a molecular beam is critical for investigating state-selected chemistry. However, achieving vibrational excitation of the entire beam for Raman-active molecules such as H2 proves extremely challenging, primarily because laser pulses are much shorter than the molecular beam. In this study, we achieve a total excitation efficiency of over 20% by employing stimulated Raman pumping (SRP) in a slow, narrow-pulsed molecular beam. Through optimizing the intensity and spot shape of the SRP lasers, we attain saturated excitation within the laser crossing region. Furthermore, by reducing the beam velocity and narrowing the beam pulse using a cold valve and a fast chopper, we significantly enhance the total excitation yield. COMSOL simulation and a newly developed model reveal that a critical velocity allows the chopper to block unexcited molecules and reserve most of the excited ones from the beam, resulting in the highest overall excitation yield. This innovative setup opens new possibilities for state-selected experiments in surface science and ion-molecule reaction dynamics, particularly involving weak transitions and pulsed lasers.

Theoretical studies on the kinetics and dynamics of the BeH+ + H2O reaction: comparison with the experiment

The reaction of BeH+ with background gaseous H2O may play a role in qubit loss for quantum information processing with Be+ as trapped ions, and yet its reaction mechanism has not been well understood until now. In this work, a globally accurate, full-dimensional ground-state potential energy surface (PES) for the BeH+ + H2O reaction was constructed by fitting a total of 170 438 ab initio energy points at the level of RCCSD(T)-F12/aug-cc-pVTZ using the fundamental invariant-neural network method. The total root-mean-square error of the final PES was 0.178 kcal mol-1. For comparison, quasi-classical trajectory calculations were carried out on the PES at an experimental temperature of 150 K. The obtained thermal rate constant and product branching ratio of the BeD+ + H2O reaction agreed quite well with experimental results. In addition, the vibrational state distributions and energy disposals of the products were calculated and rationalized using the sudden vector projection model.

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

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

Electronically Nonadiabatic Effects on the Quantum Dynamics of the Ha + BeHb+ → Be+ + HaHb; Hb + BeHa+ Reactions

Nonadiabatic effects are ubiquitous and play an important role in many chemical processes. Here, the adiabatic and nonadiabatic quantum scattering calculations of the H + BeH⁺ reaction are performed using the time-dependent wave packet method based on an accurate diabatic potential energy matrix that includes the lowest two electronic states and their couplings. The resulting integral cross sections reveal that the nonadiabatic effect significantly inhibits the reactivity of the BeH⁺-depletion channel but enhances that of the H-exchange channel. The vibrational excitation is suppressed, but the translational excitation is promoted for the H₂ product in the BeH⁺-depletion channel when the nonadiabatic coupling is included. However, the nonadiabatic coupling has a mild effect on the H-exchange product-state distribution. When the nonadiabatic effect is considered, the differential cross sections of the H₂ product become less polarized because of the formation of an excited-state complex, whereas the corresponding results of the H-exchange channel only present an increase in the magnitude at the backward region.

Capture Theory Models: An overview of their development, experimental verification, and applications to ion-molecule reactions

Since Arrhenius first proposed an equation to account for the behaviour of thermally activated reactions in 1889, significant progress has been made in our understanding of chemical reactivity. A number of capture theory models have been developed over the past several decades to predict the rate coefficients for reactions between ions and molecules-ranging from the Langevin equation (for reactions between ions and non-polar molecules) to more recent fully quantum theories (for reactions at ultra-cold temperatures). A number of different capture theory methods are discussed, with the key assumptions underpinning each approach clearly set out. The strengths and limitations of these capture theory methods are examined through detailed comparisons between low-temperature experimental measurements and capture theory predictions. Guidance is provided on the selection of an appropriate capture theory method for a given class of ion-molecule reaction and set of experimental conditions-identifying when a capture-based model is likely to provide an accurate prediction. Finally, the impact of capture theories on fields such as astrochemical modelling is noted, with some potential future directions of capture-based approaches outlined.

Charge Transfer Reactions between Water Isotopologues and Kr+ ions

Astrochemical models often adopt capture theories to predict the behavior of experimentally unmeasured ion-molecule reactions. Here, reaction rate coefficients are reported for the charge transfer reactions of H2O and D2O molecules with cold, trapped Kr+ ions. Classical capture theory predictions are found to be in excellent agreement with the experimental findings. A crossing point identified between the reactant and product potential energy surfaces, constructed from high-level ab initio calculations, further supports a capture-driven mechanism of charge transfer. However, ion-molecule reactions do not always agree with predictions from capture theory models. The appropriateness of using capture theory-based models in the absence of detailed experimental or theoretical studies is discussed, alongside an analysis of why capture theory is appropriate for describing the likelihood of charge transfer between Kr+ and the two water isotopologues.

Neural network potential energy surface and quantum dynamics studies for the Ca+(2S) + H2 → CaH+ + H reaction

Reactive collisions of Ca+ ion with H2 molecule play a crucial role in ultracold chemistry, quantum information and other cutting-edge fields, and have been widely concerned experimentally, but the corresponding...

Representing Globally Accurate Reactive Potential Energy Surfaces with Complex Topography by Combining Gaussian Process Regression and Neural Network

There has been increasing attention in using machine learning technologies, such as neural network (NN) and Gaussian process regression (GPR), to model multidimensional potential energy surfaces (PESs). NN PES features...

Velocity-tunable beam of continuously decelerated polar molecules for cold ion-molecule reaction studies

Producing high densities of molecules is a fundamental challenge for low-temperature, ion-molecule reaction studies. Traveling-wave Stark decelerators promise to deliver high density beams of cold, polar molecules but require non-trivial control of high-voltage potentials. We have overcome this experimental challenge and demonstrate continuous deceleration of ND₃ from 385 to 10 m/s, while driving the decelerator electrodes with a 10 kV amplitude sinewave. In addition, we test an alternative slowing scheme, which increases the time delay between decelerated packets of ND₃ and non-decelerated molecules, allowing for better energy resolution of subsequent reaction studies. We characterize this source of neutral, polar molecules suitable for energy-resolved reaction studies with trapped ions at cold translational temperatures. We also propose a combined apparatus consisting of the traveling-wave decelerator and a linear ion trap with a time-of-flight mass spectrometer and discuss to what extent it may achieve cold, energy-resolved, ion-neutral reactions.

Quantum Dynamics Studies of the Significant Intramolecular Isotope Effects on the Nonadiabatic Be+(2P) + HD → BeH+/BeD+ + D/H Reaction

Quantum time-dependent wave packet dynamics studies on the nonadiabatic Be⁺(²P) + HD → BeH⁺/BeD⁺ + D/H reaction are performed for the first time employing recently constructed diabatic potential energy surfaces. Strong intramolecular isotope effects and unusual results are presented, which are attributed to the dynamic effects of shallow wells induced by avoided crossing on the diagonal V₂₂^d surface. The BeH⁺ + D and BeD⁺ + H channels are dominated by high-J and low-J partial waves, respectively. The BeD⁺/BeH⁺ branching ratio is larger than 10 at low energy and gradually decreases with increasing collision energy. The BeH⁺ product is primarily distributed at low vibrational states, whereas there exists an obvious population inversion of vibrational states on the BeD⁺ product. The results of differential cross sections suggest that the formation of the BeH⁺ + D channel favors a direct reaction process, while the BeD⁺ + H channel is mainly generated by the complex-forming mechanism.

Towards chemistry at absolute zero

The prospect of cooling matter down to temperatures that are close to absolute zero raises intriguing questions about how chemical reactivity changes under these extreme conditions. Although some types of chemical reaction still occur at 1 μK, they can no longer adhere to the conventional picture of reactants passing over an activation energy barrier to become products. Indeed, at ultracold temperatures, the system enters a fully quantum regime, and quantum mechanics replaces the classical picture of colliding particles. In this Review, we discuss recent experimental and theoretical developments that allow us to explore chemical reactions at temperatures that range from 100 K to 500 nK. Although the field is still in its infancy, exceptional control has already been demonstrated over reactivity at low temperatures.

Isomer-specific kinetics of the C+ + H2O reaction at the temperature of interstellar clouds

The reaction C⁺ + H₂O → HCO⁺/HOC⁺ + H is one of the most important astrophysical sources of HOC⁺ ions, considered a marker for interstellar molecular clouds exposed to intense ultraviolet or x-ray radiation. Despite much study, there is no consensus on rate constants for formation of the formyl ion isomers in this reaction. This is largely due to difficulties in laboratory study of ion-molecule reactions under relevant conditions. Here, we use a novel experimental platform combining a cryogenic buffer-gas beam with an integrated, laser-cooled ion trap and high-resolution time-of-flight mass spectrometer to probe this reaction at the temperature of cold interstellar clouds. We report a reaction rate constant of k = 7.7(6) × 10^-9 cm³ s^-1 and a branching ratio of formation η = HOC⁺/HCO⁺ = 2.1(4). Theoretical calculations suggest that this branching ratio is due to the predominant formation of HOC⁺ followed by isomerization of products with internal energy over the isomerization barrier.

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.

Final-State-Resolved Dynamics of the H3+ + CO → H2 +HCO+/HOC+ Reaction: A Quasi-Classical Trajectory Study

The ion-molecule reaction H₃⁺ + CO → H₂ + HCO⁺/HOC⁺, which initiates the formation of crucial organic molecules, plays a key role in interstellar and circumstellar environments. In this work, the quasi-classical trajectory method is employed to study the reaction dynamics on a recently developed full-dimensional global potential energy surface (PES). The calculated product internal energy distributions and relative internal excited fractions agree reasonably well with the experimental measurements. For the two reaction channels, most of the available energy flows into the vibrational modes of HCO⁺ or HOC⁺ at low collision energies, followed by the translational mode and the rotational modes of HCO⁺ or HOC⁺. As the collision energy increases, the proportion of the product translational energy increases while the proportion of the product vibrational energy decreases. Furthermore, the CH and CO stretching modes and their combination bands are effectively excited for the product HCO⁺ while the bending mode is remarkably excited for the product HOC⁺.

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

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

Two Cycling Centers in One Molecule: Communication by Through-Bond Interactions and Entanglement of the Unpaired Electrons

Many applications in quantum information science (QIS) rely on the ability to laser-cool molecules. The scope of applications can be expanded if laser-coolable molecules possess two or more cycling centers, i.e., moieties capable of scattering photons via multiple absorption-emission events. Here we employ the equation-of-motion coupled-cluster method for double electron attachment (EOM-DEA-CCSD) to study the electronic structure of hypermetallic molecules with two alkaline-earth metals connected by an acetylene linker. The electronic structure of the molecules is similar to that of two separated alkali metals; however, the interaction between the two electrons is weak and largely dominated by through-bond interactions. The communication between the two cycling centers is quantified by the extent of the entanglement of the two unpaired electrons associated with the two cycling centers. This contribution highlights the rich electronic structure of hypermetallic molecules that may advance various applications in QIS and beyond.

Quasi-classical trajectory analysis with isometric feature mapping and locally linear embedding: deep insights into the multichannel reaction on an NH3+(4A) potential energy surface

Two manifold learning methods, isometric feature mapping and locally linear embedding, are applied to the analysis of quasi-classical trajectories for multi-channel reaction NH⁺ + H₂ → N + H₃⁺/NH₂⁺ + H.

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.

Isotope-selective chemistry in the Be+(2S1/2) + HOD → BeOD+/BeOH+ + H/D reaction

Low temperature reactions between laser-cooled Be+(2S1/2) ions and partially deuterated water (HOD) molecules have been investigated using an ion trap and interpreted with zero-point corrected quasi-classical trajectory calculations on a highly accurate global potential energy surface for the ground electronic state. Both product channels have been observed for the first time, and the branching to BeOD+ + H is found to be 0.58 ± 0.14. The experimental observation is reproduced by both quasi-classical trajectory and statistical calculations. Theoretical analyses reveal that the branching to the two product channels is largely due to the availability of open states in each channel.

Engineering Excited-State Interactions at Ultracold Temperatures

Using a recently developed method for precisely controlling collision energy, we observe a dramatic suppression of inelastic collisions between an atom and ion (Ca+Yb^{+}) at low collision energy. This suppression, which is expected to be a universal phenomenon, arises when the spontaneous emission lifetime of the excited state is comparable to or shorter than the collision complex lifetime. We develop a technique to remove this suppression and engineer excited-state interactions. By dressing the system with a strong catalyst laser, a significant fraction of the collision complexes can be excited at a specified atom-ion separation. This technique allows excited-state collisions to be studied, even at ultracold temperature, and provides a general method for engineering ultracold excited-state interactions.

Laser Cooling of Radium Ions

The unstable radium nucleus is appealing for probing new physics due to its high mass, octupole deformation, and energy level structure. Ion traps, with long hold times and low particle numbers, are excellent for work with radioactive species, such as radium and radium-based molecular ions, where low activity, and hence low total numbers, is desirable. We address the challenges associated with the lack of stable isotopes in a tabletop experiment with a low-activity (∼10  μCi) source where we laser-cool trapped radium ions. With a laser-cooled radium ion we measured the 7p^{2}P_{1/2}^{o} state's branching fractions to the ground state, 7s^{2}S_{1/2}, and a metastable excited state, 6d^{2}D_{3/2}, to be p=0.9104(7) and 0.0896(7), respectively. With a nearby tellurium reference line we measured the 7s^{2}S_{1/2}→7p^{2}P_{1/2}^{o} transition frequency, 640.096 63(6) THz.

Electronic and geometric structure analysis of neutral and anionic metal nitric chalcogens: The case of MNX series (M=Li, Na, Be and X=O, S, Se, Te)

Coupled cluster and multireference configuration approaches are employed to study the electronic and geometric structures of mono-coordinated complexes of lithium, sodium, and beryllium with nitric oxide and its isovalent NS, NSe, and NTe species. Ground and low-lying excited states were examined for both linear-bonded and side-bonded isomers. We show that the ionic M⁺ NX^- (M=Li, Na, Be and X=O, S, Se, Te) picture is a more natural representation and can account for the symmetry of the low-lying electronic states as Σ^- , Δ, and Σ⁺ , the smaller excitation energies and the larger binding energies for heavier X. An additional electron binds to the positively charged Li and Na terminal creating stable anions. The electron affinity (EA) of LiNX and NaNX species is in the 0.5-0.8 eV range. Despite the negative EA of beryllium and the very small EA of NO, the BeNO molecule has an EA of ~1.0 eV, which is increased to ~1.5 eV for the heavier BeNX species. This is attributed to the fact that the additional electron goes to the beryllium end for BeNO but to a π(MN)π*(NX) orbital of the rest species. Our accurate results contradict previous findings and serve as a guide for future experimental studies. © 2019 Wiley Periodicals, Inc.

Superatomic nature of alkaline earth metal–water complexes: the cases of Be(H2O)0,+4 and Mg(H2O)0,+6

Beryllium– and magnesium–water complexes are shown to accommodate peripheral electrons around their Be²⁺(H₂O)₄ and Mg²⁺(H₂O)₆ cores in hydrogenic type orbitals.

Towards a rational design of laser-coolable molecules: insights from equation-of-motion coupled-cluster calculations

Access to cold molecules is critical for quantum information science, design of new sensors, ultracold chemistry, and search of new phenomena.