State-to-state reaction probabilities within the quantum transition state framework

Theoretical Development of the Interaction-Asymptotic Region Decomposition Method for Tetratomic Reactive Scattering

An accurate and efficient time-dependent wave packet method is proposed for solving the product state-resolved reaction probabilities of the tetratomic reactive system. In this method, the entire scattering process is divided into the interaction region and multiple asymptotic regions, sharing the same spirit as the interaction-asymptotic region decomposition (IARD) approach in a triatomic reactive scattering process. The hyperspherical coordinate is adopted in the interaction region, while the corresponding Jacobi coordinate is employed in each asymptotic region. Therefore, in this IARD method, the "coordinate problem", the difficulty of expressing the wave function in the entire region using a single coordinate system, can be effectively avoided, and only a very small number of the grid points (or the basis functions) are required. For the numerical illustration, the typical tetratomic reaction H2 + OH with zero total angular momentum is calculated, and compared with other quantum wave packet methods. Our proposed IARD method for the tetratomic reactive system is much more efficient and accurate.

Eigenstate calculation in the state-averaged (multi-layer) multi-configurational time-dependent Hartree approach

A new approach for the calculation of eigenstates with the state-averaged (multi-layer) multi-configurational time-dependent Hartree (MCTDH) approach is presented. The approach is inspired by the recent work of Larsson [J. Chem. Phys. 151, 204102 (2019)]. It employs local optimization of the basis sets at each node of the multi-layer MCTDH tree and successive downward and upward sweeps to obtain a globally converged result. At the top node, the Hamiltonian represented in the basis of the single-particle functions (SPFs) of the first layer is diagonalized. Here p wavefunctions corresponding to the p lowest eigenvalues are computed by a block Lanczos approach. At all other nodes, a non-linear operator consisting of the respective mean-field Hamiltonian matrix and a projector onto the space spanned by the respective SPFs is considered. Here, the eigenstate corresponding to the lowest eigenvalue is computed using a short iterative Lanczos scheme. Two different examples are studied to illustrate the new approach: the calculation of the vibrational states of methyl and acetonitrile. The calculations for methyl employ the single-layer MCTDH approach, a general potential energy surface, and the correlation discrete variable representation. A five-layer MCTDH representation and a sum of product-type Hamiltonian are used in the acetonitrile calculations. Very fast convergence and order of magnitude reductions in the numerical effort compared to the previously used block relaxation scheme are found. Furthermore, a detailed comparison with the results of Avila and Carrington [J. Chem. Phys. 134, 054126 (2011)] for acetonitrile highlights the potential problems of convergence tests for high-dimensional systems.

State-to-State Dynamics in Mode-Selective Polyatomic Reactions

Chemical reactions are intrinsically quantum mechanical transformations of reactants to products. Recent experimental and theoretical advances have enabled the exploration of reaction dynamics with a quantum state resolution for both reactants and products. To this end, reactions involving more than three atoms are of particular interest, because they exhibit rich dynamics concerning the role of different reactant modes in controlling reactivity and product energy disposal. A clear understanding of the state-to-state dynamics requires new paradigms. In this Perspective, we examine some new concepts that have emerged from recent state-to-state studies of polyatomic reactions and illustrate the key role played by the transition state.

Vibrational control of the reaction pathway in the H + CHD3 → H2 + CD3 reaction

An accurate full-dimensional quantum state-to-state simulation of the six-atom title reaction based on first-principles theory is reported. Counterintuitive effects are found: Increasing the energy in the reactant's CD₃ umbrella vibration reduces the energy in the corresponding product vibration. An in-depth analysis reveals the crucial role of the effective dynamical transition state: Its geometry is controlled by the vibrational states of the reactants and subsequently controls the quantum state distribution of the products. This finding enables generalizing the concept of transition state control of chemical reactions to the quantum state-specific level.

Toward a Comprehensive Understanding of Mode-Specific Dynamics of Polyatomic Reactions: A Full-Dimensional Quantum Dynamics Study of the H + NH3 Reaction

Mode specificity not only sheds light on reaction dynamics but also opens the door for chemical reaction control. This work reports a state-of-the-art full-dimensional quantum dynamics study on the prototypical hydrogen abstraction reaction of hydrogen with ammonia, which serves as a benchmark for advancing our fundamental understanding of polyatomic reaction dynamics. By taking advantage of the (3 + 1) Radau-Jacobi coordinates, the bond-specific probabilities are resolved with the reactant NH₃ initiated from either a non-degenerate or degenerate stretching vibrational state. The observed different atom-specific abstraction probabilities from individual states of the degenerate pair are rationalized in the local mode representation according to the different vibrational energy deposited in each N-H bond. It is verified that the three H atoms in NH₃ have the same abstraction probability as that from the degenerate pair and the linear combination of the degenerate pair gives the same reaction probability. In addition, the symmetric and asymmetric stretching modes of the reactant NH₃ have comparable efficacies on driving the reaction.

The symmetric C-D stretching spectator mode in the H + CHD3 → H2 + CD3 reaction and its effect on dynamical modeling

The symmetric C-D stretching mode is a spectator mode in the H + CHD3 → H2 + CD3 reaction. Effects of multiple vibrational excitations of the CHD3 reactant are studied with the quantum transition-state (QTS) framework and an eight-dimensional (8D) model Hamiltonian developed by Palma and Clary. By including many thermal flux eigenstates, results have been obtained up to high energies, allowing the study of the symmetric C-D stretching spectator mode. A new concept of a state-specific thermal flux operator is proposed to analyze the C-D stretching spectator mode in detail, providing a new and insightful venue for studying transition-state control of chemical reactions. Furthermore, as a spectator mode, whether the C-D stretching motion can be excluded in a seven-dimensional (7D) model has not been fully interrogated, although the 7D model is a reasonable approximation and has provided accurate theoretical predictions. By comparing with available results of full-dimensional calculations, both the 7D and 8D models predict reasonably accurate results. However, the 7D model underestimates the mixing of two vibrational states that are in Fermi resonance. Despite its spectator nature, the C-D stretch is important in the dynamical modeling of chemical reaction systems affected by state mixing.

Time-resolving the UV-initiated photodissociation dynamics of OCS

We present a time-resolved study of the photodissociation dynamics of OCS after UV-photoexcitation at λ = 237 nm. OCS molecules (X1Σ+) were primarily excited to the 11A'' and the 21A' Renner-Teller components of the 1Σ- and 1Δ states. Dissociation into CO and S fragments was observed through time-delayed strong-field ionisation and imaging of the kinetic energy of the resulting CO+ and S+ fragments by intense 790 nm laser pulses. Surprisingly, fast oscillations with a period of ∼100 fs were observed in the S+ channel of the UV dissociation. Based on wavepacket-dynamics simulations coupled with a simple electrostatic-interaction model, these oscillations do not correspond to the known highly-excited rotational motion of the leaving CO(X1Σ+, J ≫ 0) fragments, which has a timescale of ∼140 fs. Instead, we suggest to assign the observed oscillations to the excitation of vibrational wavepackets in the 23A'' or 21A'' states of the molecule that predissociate to form S(3PJ) photoproducts.

Advances and New Challenges to Bimolecular Reaction Dynamics Theory

Dynamics of bimolecular reactions in the gas phase are of foundational importance in combustion, atmospheric chemistry, interstellar chemistry, and plasma chemistry. These collision-induced chemical transformations are a sensitive probe of the underlying potential energy surface(s). Despite tremendous progress in past decades, our understanding is still not complete. In this Perspective, we survey the recent advances in theoretical characterization of bimolecular reaction dynamics, stimulated by new experimental observations, and identify key new challenges.

Calculations of quantum tunnelling rates for muonium reactions with methane, ethane and propane

Thermal rate constants for Mu + CH₄, Mu + C₂H₆ and Mu + C₃H₈ and their equivalent reactions with H were evaluated with ab initio instanton rate theory. The potential-energy surfaces are fitted using Gaussian process regression to high-level electronic-structure calculations evaluated around the tunnelling pathway. This method was able to successfully reproduce various experimental measurements for the rate constant of these reactions. However, it was not able to reproduce the faster-than-expected rate of Mu + C₃H₈ at 300 K reported by Fleming et al. [Phys. Chem. Chem. Phys., 2015, 17, 19901 and Phys. Chem. Chem. Phys., 2020, 22, 6326]. Analysis of our results indicates that the kinetic isotope effect at this temperature is not significantly influenced by quantum tunnelling. We consider many possible factors for the discrepancy between theory and experiment but conclude that in each case, the instanton approximation is unlikely to be the cause of the error. This is in part based on the good agreement we find between the instanton predictions and new multiconfigurational time-dependent Hartree (MCTDH) calculations for Mu + CH₄ using the same potential-energy surface. Further experiments will therefore be needed to resolve this issue.

Kinetic isotope effects in the water forming reaction H2/D2 + OH from rigorous close-coupling quantum dynamics simulations

Rigorous quantum dynamics simulations of thermal rate constants and kinetic isotope effects for the water-forming H₂/D₂ + OH reaction are presented, which show increased tunneling below 300 K and can serve as benchmarks for approximate methods.

Natural reaction channels in H + CHD3 → H2 + CD3

Natural reaction channels control the mode-specific chemistry of methane and its isotopomeres.

Recent advances in quantum scattering calculations on polyatomic bimolecular reactions

This review surveys quantum scattering calculations on chemical reactions of polyatomic molecules in the gas phase published in the last ten years.

Control of chemical reactivity by transition-state and beyond

It has been long established that the transition state for an activated reaction controls the overall reactivity, serving as the bottleneck for reaction flux. However, the role of the transition state in regulating quantum state resolved reactivity has only been addressed more recently, thanks to advances in both experimental and theoretical techniques. In this perspective, we discuss some recent advances in understanding mode-specific reaction dynamics in bimolecular reactions, mainly focusing on the X + H2O/CH4 (X = H, F, Cl, and O(3P)) systems, extensively studied in our groups. These advances shed valuable light on the importance of the transition state in mode-specific and steric dynamics of these prototypical reactions. It is shown that many mode-specific phenomena can be understood in terms of a transition-state based model, which assumes in the sudden limit that the ability of a reactant mode for promoting the reaction stems from its coupling with the reaction coordinate at the transition state. Yet, in some cases the long-range anisotropic interactions in the entrance (or exit) valley, which govern how the trajectories reach (or leave) the transition state, also come into play, thus modifying the reactive outcomes.

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.

Modulations of Transition-State Control of State-to-State Dynamics in the F + H2O → HF + OH Reaction

The full-dimensional quantum dynamics of the F + H2O → HF + OH reaction is investigated at the state-to-state level for the first time using a transition-state wave packet method on an accurate global potential energy surface. It is found that the H2O rotation enhances the reactivity and the product-state distribution is dominated by HF vibrational excitation while the OH moiety serves effectively as a spectator. These observations underscore the transition-state control of the reaction dynamics, as both the H2O rotational and HF vibrational modes are strongly coupled to the reaction coordinate at the transition state. It is also shown that the transition-state dominance of the reaction dynamics is modulated by other features on the potential energy surface, such as the prereaction well.

Loss of Memory in H + CH4 → H2 + CH3 State-to-State Reactive Scattering

State-to-state reaction probabilities for the H + CH4→ H2 + CH3 reaction are calculated by accurate full-dimensional quantum dynamics calculations employing the multilayer multiconfigurational time-dependent Hartree approach and the quantum transition-state concept. Reactions starting from different vibrational and rotational states of the methane reactant are investigated for vanishing total angular momentum. The vibrational state distributions of the products are found to be essentially independent of the initial rovibrational state of the reactants. The reaction products only show vibrational excitation in the methyl umbrella mode. No excitation in H2 vibration or another CH3 vibration is observed. Analyzing the results, the observed loss of vibrational memory can be explained by a transition-state-based view of the reaction process.

The sudden vector projection model for reactivity: mode specificity and bond selectivity made simple

CONSPECTUS: Mode specificity is defined by the differences in reactivity due to excitations in various reactant modes, while bond selectivity refers to selective bond breaking in a reaction. These phenomena not only shed light on reaction dynamics but also open the door for laser control of reactions. The existence of mode specificity and bond selectivity in a reaction indicates that not all forms of energy are equivalent in promoting the reactivity, thus defying a statistical treatment. They also allow the enhancement of reactivity and control product branching ratio. As a result, they are of central importance in chemistry. This Account discusses recent advances in our understanding of these nonstatistical phenomena. In particular, the newly proposed sudden vector projection (SVP) model and its applications are reviewed. The SVP model is based on the premise that the collision in many direct reactions is much faster than intramolecular vibrational energy redistribution in the reactants. In such a sudden limit, the coupling of a reactant mode with the reaction coordinate at the transition state, which dictates its ability to promote the reaction, is approximately quantified by the projection of the former onto the latter. The SVP model can be considered as a generalization of the venerable Polanyi's rules, which are based on the location of the barrier. The SVP model is instead based on properties of the saddle point and as a result capable of treating the translational, rotational, and multiple vibrational modes in reactions involving polyatomic reactants. In case of surface reactions, the involvement of surface atoms can also be examined. Taking advantage of microscopic reversibility, the SVP model has also been used to predict product energy disposal in reactions. This simple yet powerful rule of thumb has been successfully demonstrated in many reactions including uni- and bimolecular reactions in the gas phase and gas-surface reactions. The success of the SVP model underscores the importance of the transition state in controlling mode-specific and bond-selective chemistry.