Full-dimensional quantum dynamics of CO in collision with H2

Ab Initio Potential Energy Surface for NaCl-H2 with Correct Long-Range Behavior

We report a full dimensional ab initio potential energy surface for NaCl-H2 based on precise fitting of a large data set of CCSD(T)/aug-cc-pVTZ energies. A major goal of this fit is to describe the very long-range interaction accurately. This is done in this instance via the dipole-quadrupole interaction. The NaCl dipole and the H2 quadrupole are available through previous works over a large range of internuclear distances. We use these to obtain exact effect charges on each atom. Diffusion Monte Carlo calculations are done for the ground vibrational state using the new potential.

Quantum stereodynamics of cold molecular collisions

Advances in quantum state preparations combined with molecular cooling and trapping technologies have enabled unprecedented control of molecular collision dynamics. This progress, achieved over the last two decades, has dramatically improved our understanding of molecular phenomena in the extreme quantum regime characterized by translational temperatures well below a kelvin. In this regime, collision outcomes are dominated by isolated partial waves, quantum threshold and quantum statistics effects, tiny energy splitting at the spin and hyperfine levels, and long-range forces. Collision outcomes are influenced not only by the quantum state preparation of the initial molecular states but also by the polarization of their rotational angular momentum, i.e., stereodynamics of molecular collisions. The Stark-induced adiabatic Raman passage technique developed in the last several years has become a versatile tool to study the stereodynamics of light molecular collisions in which alignment of the molecular bond axis relative to initial collision velocity can be fully controlled. Landmark experiments reported by Zare and coworkers have motivated new theoretical developments, including formalisms to describe four-vector correlations in molecular collisions that are revealed by the experiments. In this Feature article, we provide an overview of recent theoretical developments for the description of stereodynamics of cold molecular collisions and their implications to cold controlled chemistry.

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 studies of vibrational energy transfer dynamics between H2O and Ar: theory assessing experiment

We report the first full-dimensional quantum mechanical calculations of the ro-vibrational inelastic scattering dynamics between water molecules and argon atoms on an accurate potential energy surface, using a recently developed time-independent quantum method based on the close-coupling approach. The state-to-state integral cross-sections and rate coefficients show strong observance of gap laws. The calculated thermal rate coefficients for the relaxation of the stretching fundamental states of H₂O are in good agreement with experimental values, while those for the bending overtone state are approximately five times smaller than the values extracted through a previous kinetic modeling of fluorescence decay data. Our state-specific quantum scattering results suggest the need to reassess the kinetic modeling of the experimental data. This work advanced our understanding of the quantum dynamics of vibrationally inelastic energy transfer processes involving polyatomic molecules.

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.

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.

Evidence of Nonrigidity Effects in the Description of Low-Energy Anisotropic Molecular Collisions of Hydrogen Molecules with Excited Metastable Helium Atoms

Cold collisions serve as a sensitive probe of the interaction potential. In the recent study of Klein et al. (Nature Phys.2017, 13, 35–38), the one-parameter scaling of the interaction potential was necessary to obtain agreement between theoretical and observed patterns of the orbiting resonances for excited metastable helium atoms colliding with hydrogen molecules. Here, we show that the effect of nonrigidity of the H₂ molecule on the resonant structure, absent in the previous study, is critical to predict the correct positions of the resonances in that case. We have complemented the theoretical description of the interaction potential and revised reaction rate coefficients by proper inclusion of the flexibility of the molecule. The calculated reaction rate coefficients are in remarkable agreement with the experimental data without empirical adjustment of the interaction potential. We have shown that even state-of-the-art calculations of the interaction energy cannot ensure agreement with the experiment if such an important physical effect as flexibility of the interacting molecule is neglected. Our findings about the significance of the nonrigidity effects can be especially crucial in cold chemistry, where the quantum nature of molecules is pronounced.

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.

Inelastic vibrational dynamics of CS in collision with H2 using a full-dimensional potential energy surface

We report a six-dimensional (6D) potential energy surface (PES) for the CS-H2 system computed using high-level electronic structure theory and fitted using a hybrid invariant polynomial method. Full-dimensional quantum close-coupling scattering calculations have been carried out using this potential for rotational and, for the first time, vibrational quenching transitions of CS induced by H2. State-to-state cross sections and rate coefficients for rotational transitions in CS from rotational levels j1 = 0-5 in the ground vibrational state are compared with previous theoretical results obtained using a rigid-rotor approximation. For vibrational quenching, state-to-state and total cross sections and rate coefficients were calculated for the vibrational transitions in CS(v1 = 1,j1) + H2(v2 = 0,j2) → CS(v1' = 0,j1') + H2(v2' = 0,j2') collisions, for j1 = 0-5. Cross sections for collision energies in the range 1 to 3000 cm-1 and rate coefficients in the temperature range of 5 to 600 K are obtained for both para-H2 (j2 = 0) and ortho-H2 (j2 = 1) collision partners. Application of the computed results in astrophysics is also discussed.

A general variational approach for computing rovibrational resonances of polyatomic molecules. Application to the weakly bound H2He+ and H2⋅CO systems

The quasi-variational quantum chemical protocol and code GENIUSH [E. Mátyus et al., J. Chem. Phys. 130, 134112 (2009) and C. Fábri et al., J. Chem. Phys. 134, 074105 (2011)] has been augmented with the complex absorbing potential (CAP) technique, yielding a method for the determination of rovibrational resonance states. Due to the effective implementation of the CAP technique within GENIUSH, the GENIUSH-CAP code is a powerful tool for the study of important dynamical features of arbitrary-sized molecular systems with arbitrary composition above their first dissociation limit. The GENIUSH-CAP code has been tested and validated on the H₂He⁺ cation: the computed resonance energies and lifetimes are compared to those obtained with a previously developed triatomic rovibrational resonance-computing code, D²FOPI-CCS [T. Szidarovszky and A. G. Császár Mol. Phys. 111, 2131 (2013)], utilizing the complex coordinate scaling method. A unique feature of the GENIUSH-CAP protocol is that it allows the simple implementation of reduced-dimensional dynamical models. To prove this, resonance energies and lifetimes of the H₂⋅CO van der Waals complex have been computed utilizing a four-dimensional model (freezing the two monomer stretches), and a related potential energy surface, of the complex.

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.

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

Solving the time-independent close coupling equations of a diatom-diatom inelastic collision system by using the rigorous close-coupling approach is numerically difficult because of its expensive matrix manipulation. The coupled-states approximation decouples the centrifugal matrix by neglecting the important Coriolis couplings completely. In this work, a new approximation method based on the coupled-states approximation is presented and applied to time-independent quantum dynamic calculations. This approach only considers the most important Coriolis coupling with the nearest neighbors and ignores weaker Coriolis couplings with farther K channels. As a result, it reduces the computational costs without a significant loss of accuracy. Numerical tests for para-H₂+ortho-H₂ and para-H₂+HD inelastic collision were carried out and the results showed that the improved method dramatically reduces the errors due to the neglect of the Coriolis couplings in the coupled-states approximation. This strategy should be useful in quantum dynamics of other systems.

All-dimensional H2-CO potential: Validation with fully quantum second virial coefficients

We use a new high-accuracy all-dimensional potential to compute the cross second virial coefficient B₁₂(T) between molecular hydrogen and carbon monoxide. The path-integral method is used to fully account for quantum effects. Values are calculated from 10 K to 2000 K and the uncertainty of the potential is propagated into uncertainties of B₁₂. Our calculated B₁₂(T) are in excellent agreement with most of the limited experimental data available, but cover a much wider range of temperatures and have lower uncertainties. Similar to recently reported findings from scattering calculations, we find that the reduced-dimensionality potential obtained by averaging over the rovibrational motion of the monomers gives results that are a good approximation to those obtained when flexibility is fully taken into account. Also, the four-dimensional approximation with monomers taken at their vibrationally averaged bond lengths works well. This finding is important, since full-dimensional potentials are difficult to develop even for triatomic monomers and are not currently possible to obtain for larger molecules. Likewise, most types of accurate quantum mechanical calculations, e.g., spectral or scattering, are severely limited in the number of dimensions that can be handled.