An improved coupled-states approximation including the nearest neighbor Coriolis couplings for diatom-diatom inelastic collision

An effective approximation of Coriolis coupling in reactive scattering: application to the time-dependent wave packet calculations

Coriolis coupling plays a crucial role in reactive scattering, but dynamics calculations including the complete Coriolis coupling significantly increase the difficulty of numerical evolution due to the corresponding expensive matrix processing. The coupled state approximation that completely ignores the off-diagonal Coriolis coupling saves computational cost significantly but its error is usually unacceptable. In this paper, an improved coupled state approximation inspired by recently published results [D. Yang, X. Hu, D. H. Zhang and D. Xie, J. Chem. Phys., 2018, 148, 084101.] of the inelastic scattering problem is extended to deal with the reactive scattering. The calculations using the time-dependent wave packet method reveal that the new method can accurately reproduce the rigorous results of the H + HD (j0 < 3) → D + H2 reaction and immensely improve the computational efficiency. Additionally, we extend the new method to the non-adiabatic Li(2p) + H2 (v0 = 0, j0 = 0, 1) → H + LiH reaction, showcasing its advantages of low computational cost and high accuracy.

ABC+D: A time-independent coupled-channel quantum dynamics program for elastic and ro-vibrational inelastic scattering between atoms and triatomic molecules in full dimensionality

We discuss the details of a time-independent quantum mechanical method and its implementation for full-dimensional non-reactive scattering between a closed-shell triatomic molecule and a closed-shell atom. By solving the time-independent Schrödinger equation within the coupled-channel framework using a log-derivative method, the state-to-state scattering matrix (S-matrix) can be determined for inelastic scattering involving both the rotational and vibrational modes of the molecule. Various approximations are also implemented. The ABC+D code provides an important platform for understanding an array of physical phenomena involving collisions between atoms and molecules.

Recent advances in quantum theory on ro-vibrationally inelastic scattering

Molecular collisions are of fundamental importance in understanding intermolecular interaction and dynamics. Its importance is accentuated in cold and ultra-cold collisions because of the dominant quantum mechanical nature of the scattering. We review recent advances in the time-independent approach to quantum mechanical characterization of non-reactive scattering in tetratomic systems, which is ideally suited for large collisional de Broglie wavelengths characteristic in cold and ultracold conditions. We discuss quantum scattering algorithms between two diatoms and between a triatom and an atom and their implementation, as well as various approximate schemes. They not only enable the characterization of collision dynamics in realistic systems but also serve as benchmarks for developing more approximate methods.

Full-Dimensional Quantum Dynamics Studies of Ro-vibrationally Inelastic Scattering of H2O with Ar: A Benchmark Test of the Rigid-Rotor Approximation

While the rigid-rotor (RR) approximation is usually considered to be accurate for describing pure rotationally inelastic scattering involving diatoms in their ground or low-lying vibrational states, its validity in scattering involving polyatomic molecules has not been fully examined. The existence of soft/anharmonic vibrational modes in polyatomic molecules could make rotational-vibrational energy transfer rather efficient, thus undermining the premise of the RR approximation. In this work, we conduct a benchmark test of the RR approximation in the rotationally inelastic scattering of the H₂O(v₂ = 0, 1) + Ar system by comparing with full-dimensional quantum scattering calculations. We demonstrate that the error in the RR rate coefficient for v₂ = 0 is less than 5%, while it can reach up to 20% for some initial states within the v₂ = 1 manifold. These results indicate that the RR approximation gradually deteriorates with increasing quantum number v₂. Vibrational relaxation dynamics of this system was also studied, and it is found that transitions from initial states with a large rotational quantum number of projection on the a principal axis are more efficient. These results shed valuable light on ro-vibrationally inelastic scattering involving polyatomic molecules.

Efficient computational methods for rovibrational transition rates in molecular collisions

Astrophysical modeling of processes in environments that are not in local thermal equilibrium requires the knowledge of state-to-state rate coefficients of rovibrational transitions in molecular collisions. These rate coefficients can be obtained from coupled-channel (CC) quantum scattering calculations which are very demanding, however. Here we present various approximate, but more efficient methods based on the coupled-states approximation (CSA) which neglects the off-diagonal Coriolis coupling in the scattering Hamiltonian in body-fixed coordinates. In particular, we investigated a method called NNCC (nearest-neighbor Coriolis coupling) [D. Yang, X. Hu, D.H. Zhang, and D. Xie, J. Chem. Phys. 148, 084101 (2018)] that includes Coriolis coupling to first order. The NNCC method is more demanding than the common CSA method, but still much more efficient than full CC calculations, and it is substantially more accurate than CSA. All of this is illustrated by showing state-to-state cross sections and rate coefficients of rovibrational transitions induced in CO2 by collisions with He atoms. It is also shown that a further reduction of CPU time, practically without loss of accuracy, can be obtained by combining the NNCC method with the multi-channel distorted-wave Born approximation (MC-DWBA) that we applied in full CC calculations in a previous paper.

Wave Packet Approach to Adiabatic and Nonadiabatic Dynamics of Cold Inelastic Scatterings

Due to the extremely large de Broglie wavelength of cold molecules, cold inelastic scattering is always characterized by the time-independent close-coupling (TICC) method. However, the TICC method is difficult to apply to collisions of large molecular systems. Here, we present a new strategy for characterizing cold inelastic scattering using wave packet (WP) method. In order to deal with the long de Broglie wavelength of cold molecules, the total wave function is divided into interaction, asymptotic and long-range regions (IALR). The three regions use different numbers of ro-vibrational basis functions, especially the long-range region, which uses only one function corresponding to the initial ro-vibrational state. Thus, a very large grid range can be used to characterize long de Broglie wavelengths in scattering coordinates. Due to its better numerical scaling law, the IALR-WP method has great potential in studying the inelastic scatterings of larger collision systems at cold and ultracold regimes.

A Time-Independent Quantum Approach to Ro-vibrationally Inelastic Scattering between Atoms and Triatomic Molecules

A full-dimensional time-independent quantum mechanical theory for ro-vibrationally inelastic scattering of triatomic molecules with atoms is formulated. The Jacobi-Radau coordinate system used in the calculation allows not only a near perfect description of the vibrational problem but also the adaptation of the exchange symmetry for A₂B type triatoms. The S-matrix elements are obtained by solving the close-coupling equations with contracted basis using the log-derivative method. This method is applied to the inelastic scattering of the water molecule by a chlorine atom, which sheds light on the energy gap law in energy transfer in atom-triatom collisions.

Efficient Method for an Approximate Treatment of the Coriolis Effect in Calculations of Quantum Dynamics and Spectroscopy, with Application to Scattering Resonances in Ozone

A numerical approach is developed to capture the effect of rotation-vibration coupling in a practically affordable way. In this approach only a limited number of adjacent rotational components are considered to be coupled, while the couplings to other rotational components are neglected. This partially coupled (PC) approach permits to reduce the size of Hamiltonian matrix significantly, which enables the calculations of ro-vibrational states above dissociation threshold (scattering resonances) for large values of total angular momentum. This method is employed here to reveal the role of the Coriolis effect in the ozone formation reaction at room temperature, dominated by large values of total angular momentum states, on the order of J = 24 and 28. We found that, overall, the effect of ro-vibrational coupling is not minor for large J. Compared to the results of symmetric top rotor approximation, where the ro-vibrational coupling is neglected, we found that the widths of scattering resonances, responsible for the lifetimes of metastable ozone states, remain nearly the same (on average), but the number of these states increases by as much as 20%. We also found that these changes are nearly the same in symmetric and asymmetric ozone isotopomers ¹⁶O¹⁸O¹⁶O and ¹⁶O¹⁶O¹⁸O. Therefore, based on the results of these calculations, the Coriolis coupling does not seem to favor the formation of asymmetric ozone molecules and thus cannot be responsible for symmetry-driven mass-independent fractionation of oxygen isotopes.

Quantum dynamics of the energy transfer for vibrationally excited HF (v = 7) colliding with D2 (v = 0): Theory assessing experiment

It is still challenging to accurately qualify the rate coefficients for vibrationally excited molecules in experiment. In particular, for the energy transfer between HF (v = 7) and D₂ (v = 0), which is a prototype for near resonant collisional transfer of vibrational excitation from one molecule to the other, the two available experimental results of rate coefficients contradict each other by a factor of nearly 20. In order to benchmark these data, in this work, the rate coefficients of vibration-vibration energy transfer processes of this system at temperatures ranging from 100 to 1500 K were calculated by employing the coupled-states approximation based on our recently developed full-dimensional ab initio intermolecular potential energy surface. The state-to-state rate coefficients were found to follow the general energy gap law. The calculated total vibration-vibration energy transfer rate coefficients decrease with the increase in the angular momentum of HF at most temperatures. The vibrational relaxation rate coefficient decreases monotonously with the temperature, and the calculated result of 8.1 × 10^-11 cm³ mol^-1 s^-1 at room temperature is in very good agreement with the experimental value reported by Dzelzkalns and Kaufman [J. Chem. Phys. 77, 3508 (1982)].

Quantum Dynamics of Rotational Energy Transfer Processes for N2-HF and N2-DF Systems

The rate coefficients of rotationally inelastic collision processes for N₂-HF as well as N₂-DF systems were calculated by applying the recently developed coupled-states approximation including the nearest neighbor Coriolis couplings approach, based on the full-dimensional ab initio intermolecular potential energy surface. It was found that the energy gap law governs these energy transfer processes. For rotational quenching of N₂ (j₁ = 2-10) by the ground rotational state of HF, j₁ = 6 and 5 have the maximum quenching rate for ortho-N₂ and para-N₂, respectively. Quenching rate coefficients for initially excited HF and DF (j₂ = 1) in collisions with N₂ were also reported, where N₂-DF has a larger quenching rate than N₂-HF due to larger density of states of the N₂-DF system.

Breakdown of energy transfer gap laws revealed by full-dimensional quantum scattering between HF molecules

Inelastic collisions involving molecular species are key to energy transfer in gaseous environments. They are commonly governed by an energy gap law, which dictates that transitions are dominated by those between initial and final states with roughly the same ro-vibrational energy. Transitions involving rotational inelasticity are often further constrained by the rotational angular momentum. Here, we demonstrate using full-dimensional quantum scattering on an ab initio based global potential energy surface (PES) that HF-HF inelastic collisions do not obey the energy and angular momentum gap laws. Detailed analyses attribute the failure of gap laws to the exceedingly strong intermolecular interaction. On the other hand, vibrational state-resolved rate coefficients are in good agreement with existing experimental results, validating the accuracy of the PES. These new and surprising results are expected to extend our understanding of energy transfer and provide a quantitative basis for numerical simulations of hydrogen fluoride chemical lasers.

Globally Accurate Full-Dimensional Potential Energy Surface for H2 + HCl Inelastic Scattering

A globally accurate full-dimensional potential energy surface (PES) for the inelastic scattering between H₂ and HCl is developed on the basis of a large number of points calculated at the coupled-cluster singles, doubles, and perturbative triples level of theory. The machine-learned PES is trained with 42 417 ab initio points using the permutation invariant polynomial-neural network method, resulting in a root-mean-square fitting error of 5.6 cm^-1. Both full- and reduced-dimensional quantum calculations for rotationally inelastic scattering are performed on this new PES and good agreement is obtained with previous quantum dynamical results on a reduced-dimensional model. Furthermore, strong resonances are identified at collision energies below 100 K, including cold conditions. This new PES provides a reliable platform for future studies of scattering dynamics with vibrationally excited collision partners in a wide range of collision energies extending to cold and ultracold conditions.

Restricted basis set coupled-channel calculations on atom-molecule collisions in magnetic fields

Rigorous coupled-channel quantum scattering calculations on molecular collisions in external fields are computationally demanding due to the need to account for a large number of coupled channels and multiple total angular momenta J of the collision complex. We show that by restricting the total angular momentum basis to include only the states with helicities K ≤ K_max, it is possible to obtain accurate elastic and inelastic cross sections for low-temperature He + CaH, Li + CaH, and Li + SrOH collisions in the presence of an external magnetic field at a small fraction of the computational cost of the full coupled-channel calculations (where K is the projection of the molecular rotational angular momentum on the atom-diatom axis). The optimal size of the truncated helicity basis set depends on the mechanism of the inelastic process and on the magnitude of the external magnetic field, with the minimal basis set (K_max = 0) producing quantitatively accurate results for, e.g., ultracold Li + CaH and Li + SrOH scattering at low magnetic fields, leading to nearly 90-fold gain in computational efficiency. Larger basis sets are required to accurately describe the resonance structure in the magnetic field dependence of Li + CaH and Li + SrOH inelastic cross sections in the few partial wave-regime as well as indirect spin relaxation in He + CaH collisions. Our calculations indicate that the resonance structure is due to an interplay of the spin-rotation and Coriolis couplings between the basis states of different K and the couplings between the rotational states of the same K induced by the anisotropy of the interaction potential.

A full-dimensional potential energy surface and quantum dynamics of inelastic collision process for H2-HF

A full-dimensional ab initio potential energy surface for the H₂-HF van der Waals complex was constructed by employing the coupled-cluster singles and doubles with noniterative inclusion of connected triples with augmented correlation-consistent polarised valence quadruple-zeta basis set plus bond functions. Using the improved coupled-states approximation including the nearest neighbor Coriolis couplings, we calculated the state-to-state scattering dynamics for pure rotational and ro-vibrational energy transfer processes. For pure rotational energy transfer, our results showed a different dynamical behavior for para-H₂ and ortho-H₂ in collision with hydrogen fluoride (HF), which is consistent with the previous study. Interestingly, some strong resonant peaks were presented in the cross sections for ro-vibrational energy transfer. In addition, the calculated vibrational-resolved rate constant is in agreement with the experimental results reported by Bott et al. These dynamics data can be further applied to the numerical simulation of HF chemical lasers.