Rovibrational States Research Articles

Emission of high rovibrational hydrogen molecules under detached plasma conditions by recycling on the tungsten wall

Abstract It is well known that the rate coefficient of molecular-assisted recombination (MAR) varies by several orders of magnitude depending on the rovibrational states of the hydrogen molecules. A molecular dynamics simulation is performed to estimate the rovibrational states of recycled hydrogen molecules at the divertor in the JA-DEMO reactor under detached plasma conditions. The simulation results reveal that molecules in high rovibrational states are released even with low incident energy, which will be the dominant condition under detached plasma conditions. Molecules generated in this way can strongly affect the formation of the detached plasma via a molecular assisted-process such as MAR.

ExoMol line lists – LXII. Ro-vibrational energy levels and line strengths for the propadienediylidene (C3) in its ground electronic state

ABSTRACT Improved opacities are needed for modelling the atmospheres and evolution of cool carbon-rich stars and extra-solar planets; in particular, contributions made by the astrophysically important propadienediylidene (${\mathrm{C}}_{3}$) molecule need, at a minimum, to be determined using a line list which includes all significant transitions in the energy range of interest. We report variational calculations giving ro-vibrational energy levels and corresponding line strengths for $^{12}{\mathrm{C}}_3$, $^{12}{\mathrm{C}}^{13}{\mathrm{C}}^{12}{\mathrm{C}}$, and $^{12}{\mathrm{C}}^{12}{\mathrm{C}}^{13}{\mathrm{C}}$. In the $^{12}{\mathrm{C}}_3$ case, we obtain 2166 503 ro-vibrational state energies $\leqslant$2000 cm−1 for the electronic $\tilde{X}{\, }^{1}{\Sigma _{\rm g}}^{+}$ ground state. Comparison with experiment indicates a maximum error of $\pm 0.03$ ${\rm cm}^{-1}$ in calculated positions of lines involving an upper state energy $\lessapprox$4000 cm−1. For lines with upper state energies $\gtrapprox$4000 cm−1 to have comparable line-position accuracies, conical intersections would need to be accounted for in an adopted potential energy surface. Line lists and associated opacities are provided in the ExoMol data base (http://www.exomol.com).

Relativistic Correction from the Four-Body Nonadiabatic Exponential Wave Function.

We present a method for calculating the relativistic correction in hydrogen molecules that significantly exceeds the accuracy of all the previous literature results. This method utilizes the explicitly correlated nonadiabatic exponential wave function, and thus treats electrons and nuclei equivalently. The proposed method can be applied to any rovibrational state, including highly excited ones. The numerical precision of the relativistic correction reaches several kHz (∼10-7 cm-1), which is below the best experimental accuracy.

Atomic momentum distributions in polyatomic molecules in rotational-vibrational eigenstates.

We report a quantum mechanical method for calculating the momentum distributions of constituent atoms of polyatomic molecules in rotational-vibrational eigenstates. Application of the present theory to triatomic molecules in the rovibrational ground state revealed that oscillatory changes appear on the proton momentum distribution in the nonlinear H2O molecule, while no such modulation is present in the case of an oxygen atom in the linear CO2 molecule. The atomic momentum distributions were analyzed in detail by means of a rigid rotor model, and it was found that the oscillation originates from the quantum-mechanical delocalization of the target atom with respect to the other atoms.

Non-relativistic energy spectra of and diatomic molecules confined in a modified Scarf potential via supersymmetric WKB approach

In this research, the energy equation of the Schrodinger equation with the modified Scarf potential has been obtained using the supersymmetric WKB (SWKB) approach. The Pekeris approximation has been applied to enable the analytical solution. The energy equation was applied to determine the rovibrational states of two diatomic molecules such as O 2 + ( X 2 Π g ) and N 2 ( X 1 Σ g + ) . The average kinetic and potential energies were computed via the Hellman-Feynman theorem. The analytical result of the energy equation obtained coincides with the work reported in earlier literature where the authors had applied a different approach. The energy eigenvalues for the studied molecules were found to agree with the ones obtained using the Teitz-Hua molecular potential, the deformed modified Rosen-Morse (DMRM) potential, the Morse potential and the Rydberg-Klein-Rees data points. For the energy spectra, we found average absolute deviations of 0.129515% for O 2 + ( X 2 Π g ) and 1.834993% for N 2 ( X 1 Σ g + ) molecules respectively. The energy spectra increase as the quantum numbers increase up to the dissociation limit before decreasing. For the molecules, the atoms were found to possess an oscillatory-type motion where an increase in the mean kinetic energy resulted in a decrease in mean potential energy and vice-visa.

Benchmarking of machine learning interatomic potentials for reactive hydrogen dynamics at metal surfaces

Simulations of chemical reaction probabilities in gas surface dynamics require the calculation of ensemble averages over many tens of thousands of reaction events to predict dynamical observables that can be compared to experiments. At the same time, the energy landscapes need to be accurately mapped, as small errors in barriers can lead to large deviations in reaction probabilities. This brings a particularly interesting challenge for machine learning interatomic potentials, which are becoming well-established tools to accelerate molecular dynamics simulations. We compare state-of-the-art machine learning interatomic potentials with a particular focus on their inference performance on CPUs and suitability for high throughput simulation of reactive chemistry at surfaces. The considered models include polarizable atom interaction neural networks (PaiNN), recursively embedded atom neural networks (REANN), the MACE equivariant graph neural network, and atomic cluster expansion potentials (ACE). The models are applied to a dataset on reactive molecular hydrogen scattering on low-index surface facets of copper. All models are assessed for their accuracy, time-to-solution, and ability to simulate reactive sticking probabilities as a function of the rovibrational initial state and kinetic incidence energy of the molecule. REANN and MACE models provide the best balance between accuracy and time-to-solution and can be considered the current state-of-the-art in gas-surface dynamics. PaiNN models require many features for the best accuracy, which causes significant losses in computational efficiency. ACE models provide the fastest time-to-solution, however, models trained on the existing dataset were not able to achieve sufficiently accurate predictions in all cases.

Spectroscopy and dynamics of isolated anions: Versatile instrumentation for photodetachment and photoelectron spectroscopy.

Molecular anions are appealing targets for study because, compared with their neutral and cationic counterparts, they can be probed with conventional laboratory lasers without the need for multiphoton ionization schemes, and they provide spectroscopic details on the corresponding neutral molecules. Here, we describe a section of a modular instrument designed to perform high-throughput photoelectron and photodetachment spectroscopy of gas-phase anions, with future provision for time-resolved and isomer-selective spectroscopy. The instrument framework allows for the incorporation and adaptation of several ion sources, as demonstrated here with plasma (electric) discharge sources providing variable hard to soft ion generation conditions. The generated anions are separated according to their mass-to-charge ratio through time-of-flight mass spectrometry (m/zΔm/z = 500-600) and are focused into a set of perpendicular velocity-map imaging electrodes (ΔEE≈4%), where mass-selected anions are probed using laser light and the ejected electrons are velocity-map imaged. Instrument performance is demonstrated through the acquisition of photodetachment and photoelectron spectra for CH2CN-, showing sharp resonances in the vicinity of the detachment threshold assigned to rovibrational states of a dipole-bound anion and broader lifetime-limited spectral features at photon energies well above the threshold assigned to prompt autodetachment from a temporary anion resonance. Similar measurements could be performed on any molecular anions generated in the sources.

Hydrogen isotope effects on recombination dominant plasmas in NAGDIS-II

The detachment processes of the hydrogen (H) and deuterium (D) plasmas are comparatively investigated in the linear plasma device NAGDIS-II. The laser Thomson scattering measurements demonstrate that the recombination rate of the H plasma is greater than that of the D plasma as the neutral pressure increases in the molecular activated recombination (MAR) dominant detachment phase. As the recombination process by MAR is strongly dependent on the vibrational and rotationally excited states of the molecule, the rovibrational quantum state populations of the H and D molecules are measured using the Fulcher-α band spectroscopy. The results indicate that the vibrational temperature in the electronic ground state is considerably higher than the rotational temperature during detachment. The reaction rate coefficients for MARs due to charge exchange chains (CX-MAR) and dissociative attachment chains (DA-MAR) are calculated by the collision-radiation model under the measured temperature conditions. It can be observed that the CX-MAR is larger than the DA-MAR for both H and D, and that the CX-MAR of H is larger than the CX-MAR of D at electron temperatures T e above 1 eV. In consideration of the experimentally observed vibrational and rotational excitation temperatures, the reaction rate coefficients of CX-MAR and DA-MAR are increasing in the low T e region. These calculations are in accordance with the experimental results, which indicate that recombination processes due to MAR are more predominant in the H plasma compared to the D plasma. Furthermore, a transition from MAR to electron–ion recombination processes is observed in the D plasma at T e below 0.5 eV.

Rovibrational Transitions in HCl due to Collisions with H2: Spin-free and Hyperfine-resolved Transitions

Hydrogen chloride (HCl) is a key repository of chlorine in the interstellar medium. Accurate determinations of its abundance are critical to assessing the chlorine elemental abundance and constraining stellar nucleosynthesis models. To aid in modeling recent and future observations of HCl rovibrational spectra, we present cross sections and rate coefficients for collisions between HCl and molecular hydrogen. Transitions between rovibrational states of HCl are considered for temperatures ranging from 10 to 3000 K. Cross sections are computed using a full dimensional quantum close-coupling (CC) method and a reduced dimensionality coupled-states (CS) approach. The CS results, benchmarked against the CC results, are used with a recoupling approach to calculate hyperfine-resolved rate coefficients for rovibrational transitions of HCl induced by H2. The rate coefficients will allow for a better determination of the HCl abundance in the interstellar medium and an improved understanding of interstellar chlorine chemistry. We demonstrate the utility of the new rate coefficients in a nonthermodynamic equilibrium radiative transfer model applied to observations of HCl rovibrational transitions in a circumstellar shell.

High-Resolution Imaging Study on Photodissociation of OCS+ [A2ΠΩ=1/2,3/2 (ν1 0 ν3)

The development of the velocity map ion imaging (VMI) technique has greatly advanced the study of photodissociation dynamics. The high-resolution imaging study of the photodissociation allows for the acquisition of precise and detailed information on the fragments. This information can further provide more insight into the energy partition and potential pathways involved in the photodissociation process. In this study, we report the investigation on the photodissociation of OCS+ via the A2ΠΩ=1/2,3/2 states following the excitation of A2Π (ν1 0 ν3) ← X2Π (0 0 0) by using time-sliced VMI techniques in the ultraviolet region. Our investigation revealed significant mode-dependent recoil anisotropies and branching ratios of two product channels for both Ω = 1/2 and Ω = 3/2. The photolysis products also exhibited dramatic deviation in angular distributions and generally comparable kinetic energy distributions following the excitation to the same vibrational modes of A2ΠΩ states with two separate spin-orbit components. According to the observation in this study and previously reported photodissociation mechanisms of the OCS+ cations, the decay from the A2Π3/2 state was more likely via the internal conversion to high rovibrational states of the X2Π state, in comparison to the A2Π1/2 state.

Quantum Dynamics Studies of the Li + Na2 (V = 0, j = 0) → Na + NaLi Reaction on a New Neural Network Potential Energy Surface.

The ultracold reaction offers a unique opportunity to elucidate the intricate microscopic mechanism of chemical reactions, and the Na2Li system serves as a pivotal reaction system in the investigation of ultracold reactions. In this work, a high-precision potential energy surface (PES) of the Na2Li system is constructed based on high-level ab initio energy points and the neural network (NN) method, and a proper asymptotic functional form is adopted for the long-range interaction, which is suitable for the study of cold or ultracold collisions. Based on the new NN PES, the dynamics of the Li + Na2 (v = 0, j = 0) → Na + NaLi reaction are studied in the collision energy range of 10-7 to 80 cm-1. In the high collision energy range of 8 to 80 cm-1, the dynamics of the reaction is studied using the time-dependent wave packet method and the statistical quantum mechanical (SQM) method. Comparing the results of the two methods, it is found that the SQM method provides a rough description of the product ro-vibrational state distribution but overestimates the integral cross-section values. With the decrease of collision energy, the reaction differential cross section gradually changes from forward-backward symmetric scattering to predominant forward scattering. In the low collision energy range from 10-7 to 8 cm-1, the SQM method is used to study the reaction dynamics, and the rate constant in the Wigner threshold region is estimated to be 2.87 × 10-10 cm3/s.

Ro-vibrational relativistic states for the q-deformed hyperbolic barrier potential

Ro-vibrational relativistic states for the q-deformed hyperbolic barrier potential

Enhanced Quantum Control of Individual Ultracold Molecules Using Optical Tweezer Arrays

Control over the quantum states of individual molecules is crucial in the quest to harness their rich internal structure and dipolar interactions for applications in quantum science. In this paper, we develop a toolbox of techniques for the control and readout of individually trapped polar molecules in an array of optical tweezers. Starting with arrays of up to eight Rb and eight Cs atoms, we assemble arrays of RbCs molecules in their rovibrational and hyperfine ground state with an overall efficiency of 48(2)%. We demonstrate global microwave control of multiple rotational states of the molecules and use an auxiliary tweezer array to implement site-resolved addressing and state control. We show how the rotational state of the molecule can be mapped onto the position of Rb atoms and use this capability to readout multiple rotational states in a single experimental run. Further, using a scheme for the midsequence detection of molecule formation errors, we perform rearrangement of assembled molecules to prepare small defect-free arrays. Finally, we discuss a feasible route to scaling to larger arrays of molecules. Published by the American Physical Society 2024

Rovibrational calculations without model Hamiltonians: The infrared and microwave spectra of thiopropynal

AbstractRovibrational configuration interaction theory has been used to study the rotational spectrum and low lying rovibrational states of thiopropynal, a molecule, which has recently been detected in an interstellar cloud. Geometrical parameters, fundamental vibrational transitions and spectroscopic constants are also provided. All calculations rely on an ‐mode representation of the multidimensional potential energy surface, which has been obtained from explicitly correlated coupled‐cluster approaches including core correlation effects and an approximate treatment of high‐order coupled‐cluster terms. Comparison with experimental data is provided for several properties and the agreement was found to be excellent in most cases.

Wavelength-Dependent Dynamics of the O(1D2) Channel in the 1Δu State Photodissociation of CO2.

The wavelength-dependent dynamics of the O(1D2) channel, formed by photoexcitation of CO2 to the 1Δu state at 143.53-153.03 nm, is investigated by using the time-sliced velocity-mapped ion imaging method. The measured ionic peaks of the O(1D2) images are analyzed to determine the total kinetic energy release (TKER) spectra and image anisotropy parameters. The structures observed in the TKER spectra can be directly assigned to the ro-vibrational state distributions of the counter CO photofragments. Compared to those observed at 157 and 155 nm, the highly rotationally excited CO photofragments still obviously appear in v = 0 and 1, but the fraction of rotational excitations is significantly reduced. Conversely, the CO photofragments exhibit substantially higher vibrational excitations, implying that the nearly linear 21A' state also contributes to dissociation in addition to the bend configuration. The image anisotropy parameters display an extremely slow decreasing trend with an increase of the CO ro-vibrational state besides those for the highest ro-vibrationally excited CO photofragments. Nevertheless, the nonaxial recoil effect, suggested in previous photodissociation studies of CO2 and other triatomic molecular systems, is still appropriate to explain the observations of internal energy dependences of image anisotropy parameters.

Information theoretic clustering for coarse-grained modeling of non-equilibrium gas dynamics

We present a new framework towards the objective of learning coarse-grained models based on the maximum entropy principle. We show that existing methods for assigning clusters using the maximum entropy approach are heuristic or sub-optimal. We propose a machine learning framework informed by rate-distortion theory to learn optimal cluster assignments, aiming to improve the effectiveness of the coarse-graining process. Our approach involves transforming the discrete optimization problem into a probabilistic and continuous form. Our inverse modeling approach involves the development of a fully differentiable, adjoint-driven dynamics solver for use with gradient-based optimization techniques. The entire framework is end-to-end differentiable, facilitating backward pass gradient computation to flow through the ODE solve and probabilistic coarse-graining to train a classifier. We demonstrate application in the evolution of particle quantum states in non-equilibrium conditions. The high dimensionality of these equations poses a significant challenge for efficient and accurate computations, even for seemingly simple chemical systems. Training is performed using a loss function informed by rate-distortion theory to cluster the rovibrational states of some molecule, effectively forming a reduced order model of the master equations. We also introduce variable transformations along with several ways of improving the tractability of the training process. These allow the framework to process the extremely high-dimensional discrete optimization problem successfully. Our method is general, and to demonstrate the effectiveness in a controlled setting, we apply it to a one-dimensional Gaussian source quantization problem for which an analytical solution is known, followed by the problem of isothermal relaxation of a ▪ system with O(104) degrees of freedom.

Opposite Effects of the Rotational and Translational Energy on the Rates of Ion-Molecule Reactions near 0 K: The D2++NH3 and D2++ND3 Reactions

The ion-molecule reactions D2++NH3 and D2++ND3 are studied at low collision energies (Ecoll from zero to approximately kB×50 K), with the D2+ ions in the ground rovibrational state and for different rotational temperatures of the ammonia molecules, using the Rydberg-Stark merged-beam approach. Two different rotational temperatures (approximately 15 K and approximately 40 K), measured by (2+1) resonance-enhanced multiphoton-ionization spectroscopy, are obtained by using a seeded supersonic expansion in He and a pure ammonia expansion, respectively. The experimental data reveal a strong enhancement of the rate coefficients at the lowest collision energies caused by the charge-dipole interaction. Calculations based on a rotationally adiabatic capture model accurately reproduce the observed kinetic-energy dependence of the rate coefficients. The rate coefficients increase with increasing rotational temperature of the ammonia molecules, which contradicts the expectation that rotational excitation should average the dipoles out. Moreover, these reactions exhibit a pronounced inverse kinetic isotope effect. The difference is caused by nuclear-spin-statistical factors and the smaller rotational constants and tunneling splittings in ND3. Published by the American Physical Society 2024

Time evolution of natural orbitals in abinitio molecular dynamics.

This work combines for the first time abinitio molecular dynamics (AIMD) within the Born-Oppenheimer approximation with a global natural orbital functional (GNOF), an approximate functional of the one-particle reduced density matrix. The most prominent feature of GNOF-AIMD is its ability to display the real-time evolution of natural orbitals, providing detailed information on the time-dependent electronic structure of complex systems and processes, including reactive collisions. The quartet ground-state reaction N(4S) + H2(1Σ) → NH(3Σ) + H(2S) is taken as a validation test. Collision energy influences on integral cross sections for different initial rovibrational states of H2 and rotational-state distributions of the NH product are discussed, showing a good agreement with previous high-quality theoretical results.

Coupled 3D (J ≥ 0) Time-Dependent Wave Packet Calculation for the F + H2 Reaction on Accurate Ab Initio Multi-State Diabatic Potential Energy Surfaces.

We had calculated adiabatic potential energy surfaces (PESs), nonadiabatic, and spin-orbit (SO) coupling terms among the lowest three electronic states (12A', 22A', and 12A″) of the F + H2 system using the multireference configuration interaction (MRCI) level of theory, and the adiabatic-to-diabatic transformation equations were solved to formulate the diabatic Hamiltonian matrix [J. Chem. Phys. 2020, 153, 174301] for the entire region of the nuclear configuration space. The accuracy of such diabatic PESs is explored by performing scattering calculations to evaluate integral cross sections (ICSs) and rate constants. The nonadiabatic and SO effects are studied by utilizing coupled 3D time-dependent wave packet formalism with zero and nonzero total angular momentum on multiple adiabatic/diabatic surfaces calculation. We depict the convergence profiles of reaction probabilities for the reactive as well as nonreactive processes on various electronic states at different collision energies with respect to total angular momentum including all helicity quantum numbers. Finally, total ICSs are calculated as functions of collision energies for the initial rovibrational state (v = 0, j = 0) of the H2 molecule along with the temperature-dependent rate coefficient, where those quantities are compared with previous theoretical and experimental results.

Highly efficient creation and detection of deeply bound molecules via invariant-based inverse engineering with feasible modified drivings.

Stimulated Raman Adiabatic Passage (STIRAP) and its variants, such as M-type chainwise-STIRAP, allow for efficiently transferring the populations in a multilevel system and have widely been used to prepare molecules in their rovibrational ground state. However, their transfer efficiencies are generally imperfect. The main obstacle is the presence of losses and the requirement to make the dynamics adiabatic. To this end, in the present paper, a new theoretical method is proposed for the efficient and robust creation and detection of deeply bound molecules in three-level Λ-type and five-level M-type systems via "Invariant-based shortcut-to-adiabaticity." In the regime of large detunings, we first reduce the dynamics of three- and five-level molecular systems to those of effective two- and three-level counterparts. By doing so, the major molecular losses from the excited states can be well suppressed. Consequently, the effective two-level counterpart can be directly compatible with two different "Invariant-based Inverse Engineering" protocols; the results show that both protocols give a comparable performance and have a good experimental feasibility. For the effective three-level counterpart, by considering a relation among the four incident pulses, we show that this model can be further generalized to an effective Λ-type one with the simplest resonant coupling. This generalized model permits us to borrow the "Invariant-based Inverse Engineering" protocol from a standard three-level Λ-type system to a five-level M-type system. Numerical calculations show that the weakly bound molecules can be efficiently transferred to their deeply bound states without strong laser pulses, and the stability against parameter variations is well preserved. Finally, the detection of ultracold deeply bound molecules is discussed.