A hierarchical construction scheme for accurate potential energy surface generation: An application to the F+H2 reaction

A Transition State Resonance Radically Reshapes Angular Distributions of the F + H 2 → FH(v f = 3) + H Reaction in the 62-102 meV Energy Range

Reactive angular distributions of the benchmark F + H 2(v i = 0) → FH(v f = 3) + H reaction show unusual propensity toward small scattering angles, a subject of a long debate in the literature. We use Regge trajectories to quantify the resonance contributions to state-to-state differential cross sections. Conversion to complex energy poles allows us to attribute the effect almost exclusively to a transition state resonance, long known to exist in the F + H 2 system and its isotopic variant F + HD. For our detailed analysis of angular scattering we employ the package DCS_Regge, recently developed for the purpose [Akhmatskaya E.; Sokolovski D.Comput. Phys. Commun.2022, 277, 108370].

The F + HD (v = 0, 1; j = 1) reaction: angular momentum correlations in the low (<1 meV) collision energy regime

A detailed analysis of the low collision energy (0.03-10 meV) integral reaction cross-section has been carried out for the F + HD (v = 0, 1; j = 1)→ HF(DF) + D(H) reaction using accurate, fully converged time-independent hyperspherical quantum dynamics. Particular attention has been paid to the shape (orbiting) resonances and their assignment to the orbital (L) and total (J) angular momenta as well as to the product's state resolved cross-sections at the energies of the resonances. As in previous works, it has been found that the energy position of the resonances depends on the initial state, but is essentially the same for the two exit channels and the product's rovibrational states. The analysis in terms of the orbital and total angular momenta showed that each resonance is characterised by a given value of L but is contributed by several J. The main resonances are due to L = 3 and L = 5 for both F + HD (v = 0, j = 1) and F + HD (v = 1, j = 1) reactions, although they appear at different collision energies. The product's vibrationally resolved excitation functions are found to follow the same pattern as the integral cross-section summed over all final states. A more detailed analysis has been made for the rotationally resolved integral cross-sections associated with L = 3, which gives rise to the main resonance for the two reactions and both product channels, for different final j' states, showing similar behaviour for all j' states except for j' = 0 due to parity conservation. The joint analysis of the final rotational and orbital angular momenta shows that L' and j' tend to have an antiparallel orientation.

HF Trimer: A New Full-Dimensional Potential Energy Surface and Rigorous 12D Quantum Calculations of Vibrational States

HF trimer, as the smallest and the lightest cyclic hydrogen-bonded (HB) cluster, has long been a favorite prototype system for spectroscopic and theoretical investigations of the structure, energetics, spectroscopy, and dynamics of hydrogen-bond networks. Recently, rigorous quantum 12D calculations of the coupled intra- and intermolecular vibrations of this fundamental HB trimer (J. Chem. Phys. 2023, 158, 234109) were performed, employing an older ab initio-based many-body potential energy surface (PES). While the theoretical results were found to be in reasonably good agreement with the available spectroscopic data, it was also evident that it is highly desirable to develop a more accurate 12D PES of HF trimer. Motivated by this, here we report a new, and the first fully ab initio 12D PES of this paradigmatic system. Approximately 42,540 geometries were sampled and calculated at the level of CCSD(T)-F12a/AVTZ. The permutationally invariant polynomial-neural network based Δ-machine learning approach (J. Phys. Chem. Lett. 2022, 13, 4729) was employed to perform cost-efficient calculations of the basis-set-superposition error (BSSE) correction. By strategically selecting data points, this approach facilitated the construction of a high-precision PES with BSSE correction, while requiring only a minimal number of BSSE value computations. The fitting error of the final PES is only 0.035 kcal/mol. To assess its performance, the 12D fully coupled quantum calculations of excited intra- and intermolecular vibrational states of HF trimer are carried out using the rigorous methodology developed by us earlier. The results are found to be in a significantly better agreement with the available spectroscopic data than those obtained with the previously existing semiempirical 12D PES.

Δ-Machine Learning to Elevate DFT-Based Potentials and a Force Field to the CCSD(T) Level Illustrated for Ethanol

Progress in machine learning has facilitated the development of potentials that offer both the accuracy of first-principles techniques and vast increases in the speed of evaluation. Recently, Δ-machine learning has been used to elevate the quality of a potential energy surface (PES) based on low-level, e.g., density functional theory (DFT) energies and gradients to close to the gold-standard coupled cluster level of accuracy. We have demonstrated the success of this approach for molecules, ranging in size from H3O+ to 15-atom acetyl-acetone and tropolone. These were all done using the B3LYP functional. Here, we investigate the generality of this approach for the PBE, M06, M06-2X, and PBE0 + MBD functionals, using ethanol as the example molecule. Linear regression with permutationally invariant polynomials is used to fit both low-level and correction PESs. These PESs are employed for standard RMSE analysis for training and test data sets, and then general fidelity tests such as energetics of stationary points, normal-mode frequencies, and torsional potentials are examined. We achieve similar improvements in all cases. Interestingly, we obtained significant improvement over DFT gradients where coupled cluster gradients were not used to correct the low-level PES. Finally, we present some results for correcting a recent molecular mechanics force field for ethanol and comment on the possible generality of this approach.

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.

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.

A single resonance Regge pole dominates the forward-angle scattering of the state-to-state F + H2 → FH + H reaction at Etrans = 62.09 meV

The aim of the present paper is to bring clarity, through simplicity, to the important and long-standing problem: does a resonance contribute to the forward-angle scattering of the F + H2 reaction? We reduce the problem to its essentials and present a well-defined, yet rigorous and unambiguous, investigation of structure in the differential cross sections (DCSs) of the following three state-to-state reactions at a translational energy of 62.09 meV: F + H2(vi = 0, ji = 0, mi = 0) → FH(vf = 3, jf = 0, 1, 2, mf = 0) + H, where vi, ji, mi and vf, jf, mf are the initial and final vibrational, rotational and helicity quantum numbers respectively. Firstly, we carry out quantum-scattering calculations for the Fu-Xu-Zhang potential energy surface, obtaining accurate numerical scattering matrix elements for indistinguishable H2. The calculations use a time-independent method, with hyperspherical coordinates and an enhanced Numerov method. Secondly, the following theoretical techniques are employed to analyse structures in the DCSs: (a) full and Nearside-Farside (NF) partial wave series (PWS) and local angular momentum theory, including resummations of the full PWS up to second order. (b) The recently introduced "CoroGlo" test, which lets us distinguish between glory and corona scattering at forward angles for a Legendre PWS. (c) Six asymptotic (semiclassical) forward-angle glory theories and three asymptotic farside rainbow theories, valid for rainbows at sideward-scattering angles. (d) Complex angular momentum (CAM) theories of forward and backward scattering, with the Regge pole positions and residues computed by Thiele rational interpolation. Thirdly, our conclusions for the three PWS DCSs are: (a) the forward-angle peaks arise from glory scattering. (b) A broad (hidden) farside rainbow is present at sideward angles. (c) A single Regge pole contributes to the DCS across the whole angular range, being most prominent at forward angles. This proves that a resonance contributes to the DCSs for the three transitions. (d) The diffraction oscillations in the DCSs arise from NF interference, in particular, interference between the Regge pole and direct subamplitudes.

A Gaussian Process Based Δ-Machine Learning Approach to Reactive Potential Energy Surfaces

The Gaussian process (GP) is an efficient nonparametric machine learning (ML) method. A distinct advantage of the GP is its ability to provide an estimate of statistical uncertainties. This is particularly useful in constructing high-dimensional potential energy surfaces (PESs) from ab initio data as it offers an optimal way to add new geometries to reduce the overall error. In this work, GP is employed in the context of Δ-machine learning (Δ-ML), in which a correction PES to an inaccurate low-level PES is constructed using a small number of high-level ab initio calculations. This new method is tested in three prototypical reactive systems, namely, the H + H2 → H + H2, OH + H2 → H2O + H, and H + CH4 → H2 + CH3 reactions. The results show that the GP-based Δ-ML approach is more efficient than its direct application in constructing high-level PESs. We also compare the new method to a previously proposed neural-network-based Δ-ML approach [Liu and Li J. Phys. Chem. Lett. 2022, 13, 4729-4738]. The results indicate that the two Δ-ML methods have comparable efficiencies in constructing accurate PESs.

Neural network potentials for chemistry: concepts, applications and prospects

Artificial Neural Networks (NN) are already heavily involved in methods and applications for frequent tasks in the field of computational chemistry such as representation of potential energy surfaces (PES) and spectroscopic predictions. This perspective provides an overview of the foundations of neural network-based full-dimensional potential energy surfaces, their architectures, underlying concepts, their representation and applications to chemical systems. Methods for data generation and training procedures for PES construction are discussed and means for error assessment and refinement through transfer learning are presented. A selection of recent results illustrates the latest improvements regarding accuracy of PES representations and system size limitations in dynamics simulations, but also NN application enabling direct prediction of physical results without dynamics simulations. The aim is to provide an overview for the current state-of-the-art NN approaches in computational chemistry and also to point out the current challenges in enhancing reliability and applicability of NN methods on a larger scale.

Δ-Machine Learned Potential Energy Surfaces and Force Fields

There has been great progress in developing machine-learned potential energy surfaces (PESs) for molecules and clusters with more than 10 atoms. Unfortunately, this number of atoms generally limits the level of electronic structure theory to less than the "gold standard" CCSD(T) level. Indeed, for the well-known MD17 dataset for molecules with 9-20 atoms, all of the energies and forces were obtained with DFT calculations (PBE). This Perspective is focused on a Δ-machine learning method that we recently proposed and applied to bring DFT-based PESs to close to CCSD(T) accuracy. This is demonstrated for hydronium, N-methylacetamide, acetyl acetone, and ethanol. For 15-atom tropolone, it appears that special approaches (e.g., molecular tailoring, local CCSD(T)) are needed to obtain the CCSD(T) energies. A new aspect of this approach is the extension of Δ-machine learning to force fields. The approach is based on many-body corrections to polarizable force field potentials. This is examined in detail using the TTM2.1 water potential. The corrections make use of our recent CCSD(T) datasets for 2-b, 3-b, and 4-b interactions for water. These datasets were used to develop a new fully ab initio potential for water, termed q-AQUA.

Permutation-Invariant-Polynomial Neural-Network-Based Δ-Machine Learning Approach: A Case for the HO2 Self-Reaction and Its Dynamics Study

Δ-machine learning, or the hierarchical construction scheme, is a highly cost-effective method, as only a small number of high-level ab initio energies are required to improve a potential energy surface (PES) fit to a large number of low-level points. However, there is no efficient and systematic way to select as few points as possible from the low-level data set. We here propose a permutation-invariant-polynomial neural-network (PIP-NN)-based Δ-machine learning approach to construct full-dimensional accurate PESs of complicated reactions efficiently. Particularly, the high flexibility of the NN is exploited to efficiently sample points from the low-level data set. This approach is applied to the challenging case of a HO₂ self-reaction with a large configuration space. Only 14% of the DFT data set is used to successfully bring a newly fitted DFT PES to the UCCSD(T)-F12a/AVTZ quality. Then, the quasiclassical trajectory (QCT) calculations are performed to study its dynamics, particularly the mode specificity.

Accurate Calculation of Rate Constant and Isotope Effect for the F + H2 Reaction by the Coupled 3D Time-Dependent Wave Packet Method on the Newly Constructed Ab Initio Ground Potential Energy Surface

We employ coupled three-dimensional (3D) time dependent wave packet formalism in hyperspherical coordinates for reactive scattering problem on the newly constructed ab initio calculated ground adiabatic potential energy surface for the F + H₂/D₂ reaction. The convergence profiles for various reactive channels are depicted at low collision energy regimes with respect to the total angular momentum (J) quantum numbers. For two different reactant diatomic molecules (H₂ and D₂) initially at their respective ground roto-vibrational state (v = 0, j = 0), calculated state-to-state as well as total integral cross sections as a function of collision energy, temperature dependent rate constants, and the kinetic isotope effect for various reactivity profiles of F + H₂ and F + D₂ reactions are presented along with previous theoretical and experimental results.

The F + HD(v = 0, 1; j = 0, 1) reactions: stereodynamical properties of orbiting resonances

The excitation functions (reaction cross-section as a function of collision energy) of the F + HD(v = 0, 1; j = 0, 1) benchmark system have been calculated in the 0.01-6 meV collision energy interval using a time-independent hyperspherical quantum dynamics methodology. Special attention has been paid to orbiting resonances, which bring about detailed information on the three-atom interaction during the reactive encounter. The location of the resonances depends on the rovibrational state of the reactants HD(v,j), but is the same for the two product channels HF + D and DF + H, as expected for these resonances that are linked to the van der Waals well at the entrance. The resonance intensities depend both on the entrance and on the exit channels. The peak intensities for the HF + D channel are systematically larger than those for DF + H. Vibrational excitation leads to an increase of the peak intensity by more than an order of magnitude, but rotational excitation has a less drastic effect. It deceases the resonance intensity of the F + HD(v = 1) reaction, but increases somewhat that of F + HD(v = 0). Polarization of the rotational angular momentum with respect to the initial velocity reveals intrinsic directional preferences in the F + HD(v = 0, 1; j = 1) reactions that are manifested in the resonance patterns. The helicities (Ω = 0, Ω = ±1) possible for j = 1 contribute to the resonances, but that from Ω± 1 is, in general, dominant and in some cases exclusive. It corresponds to a preferential alignment of the HD internuclear axis perpendicular to the initial direction of approach and, thus, to side-on collisions. This work also shows that external preparation of the reactants, following the intrinsic preferences, would allow the enhancement or reduction of specific resonance features, and would be of great help for their eventual experimental detection.

Benchmark Quantum Kinetics at Low Temperatures toward Absolute Zero and Role of Entrance Channel Wells on Tunneling, Virtual States, and Resonances: The F + HD Reaction

This paper reports a study of the quantum reaction dynamics and kinetics of the F + HD reaction at low and ultralow temperatures, focusing on the range from the Wigner limit up to 50 K. Close coupling time-independent quantum reactive scattering calculations for the production of HF and DF molecules have been carried out on two potential energy surfaces differing in the description of the reaction entrance channel. This case is computationally more demanding than the cases of F with H₂ and D₂ ( De Fazio et al. Frontiers in Chemistry 2019 , 7 , 328 ) but offers a wider phenomenology regarding the roles of quantum mechanical effects of tunneling, of virtual states, and of resonances. The results show that at the temperatures in the cold and ultracold regimes small changes in the entrance channel long-range interaction induce surprising near threshold features. The presence of a virtual state close to the reactive threshold gives rise to a marked anti-Arrhenius behavior of the rate constants below 100 mK. This effect enhances reaction rates by about 2 orders of magnitude, making them of the same order as those at room temperature and confining the onset of the Wigner regime in the microkelvin region.

Application of the Partial Wave QP Decomposition to the Angular Scattering of the State-to-State F + H2 Reaction at Etrans = 0.04088 eV

We analyze the physical content of structures present in the product differential cross sections (DCSs) of the benchmark F + H₂(v_i, j_i, m_i) → FH(v_f, j_f, m_f) + H reaction, where v, j, and m are the vibrational, rotational, and helicity quantum numbers, respectively, for the initial and final states. We analyze three state-to-state transitions: 000 → 300, 000 → 310, and 000 → 320. Accurate quantum S matrix elements are employed at a translational energy of 0.04088 eV for the Fu-Xu-Zhang potential energy surface. Our analysis of the DCSs uses a new technique called the QP decomposition; it makes an exact decomposition of the scattering (S) matrix into a Q part and a P part. The P part consists of a partial wave (PW) sum of Regge poles (involving both positions and residues) together with a rapidly oscillating quadratic phase. The Q part of the decomposition is then constructed exactly by subtracting the rapidly oscillating phase and the PW Regge pole sum from the input PW S matrix. In practice, it is convenient to make a small modification, which we call the QmodPmod decomposition. All our calculations use only integer values of the total angular momentum quantum number, namely, J = 0, 1, 2,... We find that the QmodPmod decomposition is successful and physically meaningful, in that the properties of Qmod matrix are simpler than those of the input S matrix. We then carry out a QmodPmod analysis of the DCSs, which provides novel insights into interference structures present in the angular scattering. In particular, we find for all three reactions that Regge resonances contribute across the whole angular range of the DCSs, being particularly pronounced at small angles. The techniques of nearside-farside decomposition and local angular momentum analysis for resummed Legendre PW series are also employed to provide additional insights into the angular scattering.

High Order Split Operators for the Time-Dependent Wavepacket method of Triatomic Reactive Scattering in Hyperspherical Coordinates

Since the introduction of a series of methods for solving the time-dependent Schrödinger equation (TDSE) in the 80s of the last centry, such as the Fourier transform, the split operator (SO), the Chebyshev polynomial propagator, and complex absorbing potential, investigation of the molecular dynamics within quantum mechanics principle have become popular. In this paper, the application of the time-dependent wave packet (TDWP) method using high-order SO propagators in hyperspherical coordinates for solving triatomic reactive scattering was investigated. The fast sine transform was applied to calculate the derivatives of the wave function of the radial degree of freedom. These high-order SO propagators are examined in different forms, i.e., TVT (Kinetic–Potential–Kinetic) and VTV (Potential–Kinetic–Potential) forms with three typical triatomic reactions, H + H 2, O + O 2 and F + HD. A little difference has been observed among the performances of high-order SO propagators in the TVT and VTV representations in the hyperspherical coordinate. For obtaining total reaction probabilities with 1% error, some of the S class high-order SO propagators, which have symmetric forms, are more efficient than second order SO for reactions involving long lived intermediate states. High order SO propagators are very efficient for obtaining total reaction probabilities.

Orbiting resonances in the F + HD (v = 0, 1) reaction at very low collision energies. A quantum dynamical study

Time-independent, fully converged, quantum dynamical calculations have been performed for the F + HD (v = 0, j = 0) and F + HD (v = 1, j = 0) reactions on an accurate potential energy surface down to collision energies of 0.01 meV. The two isotopic exit channels, HF + D and DF + H, have been investigated. The calculations reproduce satisfactorily the Feshbach resonance structures for collision energies between 10 and 40 meV, previously reported in the literature for the HF + D channel. Contrary to the results of a former literature work, vibrational excitation of HD is found to enhance reactivity in all cases down to the lowest collision energy investigated. Shape-type orbiting resonances are found for collision energies lower than 2 meV. The resonances appear as peaks in the reaction cross sections that are associated to specific values of the total angular momentum, J. In contrast with the Feshbach resonances at higher energies, the orbiting resonance structure, which is caused by the van der Waals well of the entrance channel, is identical for the HF + D and DF + H exit channels. The orbiting resonance peaks for F + HD (v = 0) are very small, but those for F + HD (v = 1) could be observed, in principle, with a combination of Raman pumping and merged beams methods.

Quantum Dynamics and Kinetics of the F + H2 and F + D2 Reactions at Low and Ultra-Low Temperatures

Integral cross sections and rate constants for the prototypical chemical reactions of the fluorine atom with molecular hydrogen and deuterium have been calculated over a wide interval of collision energy and temperature ranging from the sub-thermal (50 K) down to the ultra-cold regimes (0.5 mK). Rigorous close coupling time-independent quantum reactive scattering calculations have been carried out on two potential energy surfaces, differing only at long-range in the reactants' channel. The results show that tunnel, resonance and virtual state effects enhance under-barrier reactivity giving rise to pronounced deviations from the Arrhenius law as temperature is lowered. Within the ultra-cold domain (below 1 mK), the reactivity is governed by virtual state effects and by tunneling through the reaction barrier; in the cold regime (1 mK–1 K), the shape resonances in the entrance channel of the potential energy surface make the quantum tunneling contribution larger so enhancing cross sections and rate constants by about one order of magnitude; at higher temperatures (above 10 K), the tunneling pathway enhanced by the constructive interference between two Feshbach resonances trapped in the reaction exit channel competes with the thermally activated mechanism, as the energy gets closer to the reaction barrier height. The results show that at low temperatures cross sections and rate constants are extremely sensitive to small changes in the long-range intermolecular interaction in the entrance channel of the potential energy surface, as well as to isotopic substitution.

A neural network potential energy surface for the F + CH4reaction including multiple channels based on coupled cluster theory

We report here a new global and full dimensional potential energy surface (PES) for the F + CH₄reaction.

Accurate potential energy surfaces for hydrogen abstraction reactions: A benchmark study on the XYG3 doubly hybrid density functional

The potential energy surface (PES) for the H + CH₄ system has been constructed with the recently developed XYG3 doubly hybrid functional, while those with the standard B3LYP hybrid functional, and the Møller-Plesset perturbation theory up to the second order (MP2) are also presented for comparison. Quantum dynamics studies demonstrated that satisfactory results on the reaction probabilities and the rate coefficients can be obtained on top of the XYG3-PES, as compared to the results based on the highly accurate, yet expensive, CCSD(T)-PES (Li et al., J. Chem. Phys. 2015, 142, 204302). Further investigation suggested that the XYG3 functional is useful in providing accurate rate coefficients for some larger systems involving H atom abstractions. © 2017 Wiley Periodicals, Inc.

State-to-State F + H2 Reaction at Etrans = 0.04088 eV: QP Decomposition, Parametrized S Matrix Incorporating Regge Poles, and Uniform Asymptotic Complex Angular Momentum Analysis of the Angular Scattering

We report two new contributions for understanding the quantum dynamics of the benchmark state-to-state reaction, F + H2(vi, ji, mi) → FH(vf, jf, mf) + H, where (vi, ji, mi) and (vf, jf, mf) are the initial and final vibrational, rotational, and helicity quantum numbers, respectively. We analyze product differential cross sections (DCSs) for the transitions, 000 → 300, 000 → 310, and 000 → 320, at a translational energy of 0.04088 eV using the potential energy surface of Fu-Xu-Zhang. The two new contributions are as follows: (1) We exploit the recently introduced QP decomposition of J. N. L. Connor [ J. Chem. Phys . 2013 , 138 , 124310 ] to transform numerical partial-wave scattering (S) matrix elements for the three transitions into parametrized (analytic) formulas, in which all terms in the three parametrized S matrices have a direct physical interpretation. In particular, they contain the positions and residues of Regge poles in the first quadrant of the complex angular momentum (CAM) plane. We obtain very close agreement between the values of the parametrized and numerical S matrix elements. (2) We then apply a uniform asymptotic Watson/CAM theory, which allows a Regge pole to be close to a saddle point. It uses the parametrized S matrices and is applied to the partial wave series (PWS) representation for the scattering amplitude to understand structure in a DCS in terms of three contributing subamplitudes. We prove using this powerful CAM theory that resonance Regge poles contribute to the small-angle scattering in the DCSs for all three transitions, with the oscillations at larger angles arising from nearside-farside interference. We obtain very good agreement between the uniform asymptotic Watson/CAM DCSs and the corresponding PWS DCSs, except for angles close to the forward and backward directions, where (as expected) the Watson/CAM formulas become nonuniform.

Recent Advances in Quantum Dynamics of Bimolecular Reactions

In this review, we survey the latest advances in theoretical understanding of bimolecular reaction dynamics in the past decade. The remarkable recent progress in this field has been driven by more accurate and efficient ab initio electronic structure theory, effective potential-energy surface fitting techniques, and novel quantum scattering algorithms. Quantum mechanical characterization of bimolecular reactions continues to uncover interesting dynamical phenomena in atom-diatom reactions and beyond, reaching an unprecedented level of sophistication. In tandem with experimental explorations, these theoretical developments have greatly advanced our understanding of key issues in reaction dynamics, such as microscopic reaction mechanisms, mode specificity, product energy disposal, influence of reactive resonances, and nonadiabatic effects.

A new potential energy surface for the ground electronic state of the LiH2 system, and dynamics studies on the H((2)S) + LiH(X(1)Σ(+)) → Li((2)S) + H2(X(1)Σg(+)) reaction

A new global potential energy surface (PES) is obtained for the ground electronic state of the LiH2 system based on high-level energies. The energy points are calculated at the multireference configuration interaction level with aug-cc-pVXZ (X = Q, 5) basis sets, and these energies are extrapolated to the complete basis set limit. The neural network method and hierarchical construction scheme are applied in the fitting process and the root mean square error of the fitting result is very small (0.004 eV). The dissociation energies and equilibrium distances for LiH(X(1)Σ(+)) and H2(X(1)Σg(+)) obtained from the new PES are in good agreement with the experimental data. On the new PES, time-dependent wave packet studies for the H((2)S) + LiH(X(1)Σ(+)) → Li((2)S) + H2(X(1)Σg(+)) reaction have been carried out. In this reaction, no threshold is found due to the absence of an energy barrier on the minimum energy path. The calculated integral cross sections are high at low collision energy and will decrease with the increase of the collision energy. The product molecule H2 tends to be forward scattering due to direct reactive collisions, which becomes more evident at higher collision energies.

Complex angular momentum theory of state-to-state integral cross sections: resonance effects in the F + HD → HF(v′ = 3) + D reaction

State-to-state reactive integral cross sections (ICSs) are often affected by quantum mechanical resonances, especially in the neighborhood of a reactive threshold.

Isotope-Dependent Rotational States Distributions Enhanced by Dynamic Resonance States: A Comparison Study of the F + HD → HF(vHF = 2) + D and F + H2 → HF(vHF = 2) + H Reaction

An interesting trimodal structure in the HF (v' = 2) rotational distribution produced by the F + HD (v = 0, j = 0) reaction, but monomodal structure in the HF (v' = 2) rotational distribution produced by the F + H2 (v = 0, j = 0) reaction, were observed using a high-resolution crossed molecular beam apparatus. The rotational states of product HF (v' = 2) are much hotter in the F + HD reaction. It is uncovered that the observations are due to the dominant role of the dynamical resonance states in these two isotopic reactions. The angular potential well in the region of the resonance state of the F + HD reaction is much deeper and supports wave function with high angular kinetic energy, which in turn comes from different H tunneling processes in the F + HD and F + H2 reaction.

Theoretical reaction kinetics astride the transition between moderate and deep tunneling regimes: the F + HD case

For the reaction between F and HD, giving HF + D and DF + H, the rate constants, obtained from rigorous quantum scattering calculations at temperatures ranging from 350 K down to 100 K, show deviations from the Arrhenius behavior that have been interpreted in terms of tunneling of either H or D atoms through a potential energy barrier. The interval of temperature investigated extends from above to below a crossover value Tc, a transition temperature separating the moderate and deep quantum tunneling regimes. Below Tc, the rate of the H or D exchange reaction is controlled by the prevalence of tunneling over the thermal activation mechanism. In this temperature range, Bell's early treatment of quantum tunneling, based on a semiclassical approximation for the barrier permeability, provides a reliable tool to quantitatively account for the contribution of the tunneling effect. This treatment is here applied for extracting from rate constants properties of the effective tunneling path, such as the activation barrier height and width. We show that this is a way of parametrizing the dependence of the apparent activation energy on temperature useful for both calculated and experimental rate constants in an ample interval of temperature, from above to below Tc, relevant for modelization of astrophysical and in general very low-temperature environments.

State-to-state quantum dynamics of the N(4S) + CH(X2Π) → CN(X2Σ+,A2Π) + H(2S) reactions

The reactions between N((4)S) and CH(X(2)Π) lead to H((2)S) plus CN in its two lowest electronic states (X(2)Σ(+) and A(2)Π), which are responsible for the interstellar CN formation. Accurate quantum dynamics of these reactions are investigated on new global potential energy surfaces of the two lowest-lying triplet states of HCN (1(3)A' and 1(3)A") fitted to more than 37,000 points at the internally contracted multi-reference configuration interaction level with the Davidson correction. The pathways for these highly exothermic and barrierless reactions feature both the HCN and HNC wells. Long-lived resonances supported by these wells manifest in reaction probabilities as numerous oscillations, particularly for low J partial waves. The 1(3)A" state is found to be more reactive than the 1(3)A' state, due apparently to its more attractive nature in the entrance channel. The CN products in both electronic states are highly excited in both vibrational and rotational degrees of freedom. The near forward-backward symmetric differential cross sections are consistent with a complex-forming mechanism.

Global potential energy surface, vibrational spectrum, and reaction dynamics of the first excited (Ã (2)A(')) state of HO(2)

The authors report extensive high-level ab initio studies of the first excited (Ã (2)A(')) state of HO(2). A global potential energy surface (PES) was developed by spline-fitting 17 000 ab initio points at the internal contracted multireference configuration interaction (icMRCI) level with the AVQZ basis set. To ascertain the spectroscopic accuracy of the PES, the near-equilibrium region of the molecule was also investigated using three interpolating moving least-squares-based PESs employing dynamically weighted icMRCI methods in the complete basis set limit. Vibrational energy levels on all four surfaces agree well with each other and a new assignment of some vibrational features is proposed. In addition, the dynamics of both the forward and reverse directions of the H+O(2)(ã (1)Δ(g))↔OH+O reaction (J=0) were studied using an exact wave packet method. The reactions are found to be dominated by sharp resonances.