Full-dimensional quantum dynamics calculations for H + CHD3 → H2 + CD3: The effect of multiple vibrational excitations

Higher-Order Split Operator Schemes for Solving Tetratomic Reactions Using the Time-Dependent Wave Packet Method

In this work, using the time-dependent quantum wave packet method, quite a few typical higher-order split operators (HOSOs) were for the first time applied to calculate the tetratomic reactive scattering processes in the hyperspherical coordinate. It was found that the HOSOs were hardly efficient for a tetratomic reaction calculation, unlike those for a triatomic reactive scattering calculation. We proposed an efficient HOSO with a force gradient (denoted as 2G1 in the main text) for efficiently and accurately calculating a tetratomic reaction using the quantum wave packet method. Several typical tetratomic reactions, such as H2 + OH, HF + OH, and H2 + OH+, are calculated for demonstrating the effectiveness of the proposed 2G1 in terms of (product state-resolved) reaction probability and inelastic probability, by comparing with the performance of the previously reported various HOSOs. We suggest that the 2G1 propagator could be applied to efficiently calculate a general tetratomic reaction.

QuTree: A tree tensor network package

We present QuTree, a C++ library for tree tensor network approaches. QuTree provides class structures for tensors, tensor trees, and related linear algebra functions that facilitate the fast development of tree tensor network approaches such as the multilayer multiconfigurational time-dependent Hartree approach or the density matrix renormalization group approach and its various extensions. We investigate the efficiency of relevant tensor and tensor network operations and show that the overhead for managing the network structure is negligible, even in cases with a million leaves and small tensors. QuTree focuses on providing simple, high-level routines while retaining easy access to the backend to facilitate novel developments. We demonstrate the capabilities of the package by computing the eigenstates of coupled harmonic oscillator Hamiltonians and performing random circuit simulations on a virtual quantum computer.

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.

Stretching-mode specificity in the Cl + CH3D(v1-I, v1-II, and v4 = 1; |jK〉) reactions: dependency on the initial |jK〉 selectivity

The title reactions were studied at a collisional energy of 5.4 kcal mol^-1 in a crossed-beam product-imaging experiment. The dynamics attributes of the dominant ground-state CH₂D(0₀) and the accompanied C-D bend-excited CH₂D(6₁) products were imaged in reactions with totally 16 ro-vibrationally selected states of the CH₃D(v_i, |jK〉) reagents. We found that all three vibrational excitations yielded marked |jK〉-dependent rate-enhancements in forming the (0₀, 0/1)_s product pairs. Furthermore, for a given rotational |jK〉-mode, a vibrational-mode propensity of v₄ > v₁-I > v₁-II in rate promotion and a clear manifestation of the Fermi-phase-induced interference effect of the latter two were observed. Compared to the reactivity of the rotationless state |jK〉 = |00〉, a minute rotational-excitation of all three stretch-excited CH₃D(v_i = 1) reagents could yield significantly higher reaction rates for the product pair (0₀, 0)_s, but not so for (0₀, 1)_s. The signals in forming the (6₁, 0)_s pair were clearly notable but smaller than that of the ground-state reaction product pair, (0₀, 0)_g. An opposite propensity of v₁-II ≈ v₁-I > v₄ with a milder dependency on the initial |jK〉-states was observed. The angular distributions of the (0₀, 0)_s pairs were nearly identical for all ro-vibrationally excited reagents, displaying the typical trait for a direct abstraction of the rebound mechanism. Similar distributions were found for the (6₁, 0)_s pairs; yet, both pairs deviated substantially from the peripheral feature of the ground-state reaction pair of (0₀, 0)_g. Those of the (0₀, 1)_s pairs in reactions with v₄-excitation featured a prominent forward-peaking distribution-suggestive of a time-delayed, resonance-mediated pathway, again with little dependency on the initial |jK〉-states. As for the reactions with the two Fermi-dyads, v₁-I and v₁-II, albeit showing globally similar distributions to that for v₄, a substantial variation with the initial rotational-mode excitation could be discerned in the forward-peaking features. To unravel the impact of the Fermi-phase on the |jK〉-dependent attributes, we adopted a comparative approach by contrasting the observations in reactions with the Fermi-dyad reagents (the superposition states) to those with the pure-state reagents. Remarkable distinctions are unveiled and elucidated with the unexplained results explicitly pointed out, which call for future theoretical investigations for deeper understanding.

Representation of Diabatic Potential Energy Matrices for Multiconfiguration Time-Dependent Hartree Treatments of High-Dimensional Nonadiabatic Photodissociation Dynamics

Conventional quantum mechanical characterization of photodissociation dynamics is restricted by steep scaling laws with respect to the dimensionality of the system. In this work, we examine the applicability of the multi-configurational time-dependent Hartree (MCTDH) method in treating nonadiabatic photodissociation dynamics in two prototypical systems, taking advantage of its favorable scaling laws. To conform to the sum-of-product form, elements of the ab initio diabatic potential energy matrix (DPEM) are re-expressed using the recently proposed Monte Carlo canonical polyadic decomposition method, with enforcement of proper symmetry. The MCTDH absorption spectra and product branching ratios are shown to compare well with those calculated using conventional grid-based methods, demonstrating its promise for treating high-dimensional nonadiabatic photodissociation problems.

A non-hierarchical correlation discrete variable representation

The correlation discrete variable representation (CDVR) facilitates (multi-layer) multi-configurational time-dependent Hartree (MCTDH) calculations with general potentials. It employs a layered grid representation to efficiently evaluate all potential matrix elements appearing in the MCTDH equations of motion. The original CDVR approach and its multi-layer extension show a hierarchical structure: the size of the grids employed at the different layers increases when moving from an upper layer to a lower one. In this work, a non-hierarchical CDVR approach, which uses identically structured quadratures at all layers of the MCTDH wavefunction representation, is introduced. The non-hierarchical CDVR approach crucially reduces the number of grid points required, compared to the hierarchical CDVR, shows superior scaling properties, and yields identical results for all three representations showing the same topology. Numerical tests studying the photodissociation of NOCl and the vibrational states of CH₃ demonstrate the accuracy of the non-hierarchical CDVR approach.

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.

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.

Symmetries in the multi-configurational time-dependent Hartree wavefunction representation and propagation

In multi-configurational time-dependent Hartree (MCTDH) approaches, different multi-layered wavefunction representations can be used to represent the same physical wavefunction. Transformations between different equivalent representations of a physical wavefunction that alter the tree structure used in the multi-layer MCTDH wavefunction representation interchange the role of single-particle functions (SPFs) and single-hole functions (SHFs) in the MCTDH formalism. While the physical wavefunction is invariant under these transformations, this invariance does not hold for the standard multi-layer MCTDH equations of motion. Introducing transformed SPFs, which obey normalization conditions typically associated with SHFs, revised equations of motion are derived. These equations do not show the singularities resulting from the inverse single-particle density matrix and are invariant under tree transformations. Based on the revised equations of motion, a new integration scheme is introduced. The scheme combines the advantages of the constant mean-field approach of Beck and Meyer [Z. Phys. D 42, 113 (1997)] and the singularity-free integrator suggested by Lubich [Appl. Math. Res. Express 2015, 311]. Numerical calculations studying the spin boson model in high dimensionality confirm the favorable properties of the new integration scheme.

Direct product-type grid representations for angular coordinates in extended space and their application in the MCTDH approach

Multi-configurational time-dependent Hartree (MCTDH) calculations using time-dependent grid representations can be used to accurately simulate high-dimensional quantum dynamics on general ab initio potential energy surfaces. Employing the correlation discrete variable representation, sets of direct product type grids are employed in the calculation of the required potential energy matrix elements. This direct product structure can be a problem if the coordinate system includes polar and azimuthal angles that result in singularities in the kinetic energy operator. In the present work, a new direct product-type discrete variable representation (DVR) for arbitrary sets of polar and azimuthal angles is introduced. It employs an extended coordinate space where the range of the polar angles is taken to be [-π, π]. The resulting extended space DVR resolves problems caused by the singularities in the kinetic energy operator without generating a very large spectral width. MCTDH calculations studying the F·CH₄ complex are used to investigate important properties of the new scheme. The scheme is found to allow for more efficient integration of the equations of motion compared to the previously employed cot-DVR approach [G. Schiffel and U. Manthe, Chem. Phys. 374, 118 (2010)] and decreases the required central processing unit times by about an order of magnitude.

Full-dimensional quantum dynamics study of isotope effects for the H2 + NH2/ND2/NHD and H2/D2/HD + NH2 reactions

A full-dimensional quantum dynamical study for the bimolecular reactions of hydrogen molecules with amino radicals for different isotopologues is reported. The nonreactive amino radical is described by two Radau vectors that are very close to the valence bond coordinates. Potential-optimized discrete variable representation basis is used for the vibrational coordinates of the amino radical. Starting from the reaction H₂ + NH₂, we study the isotope effects for the two reagents separately, i.e., H₂ + NH₂/ND₂/NHD and H₂/D₂/HD + NH₂. The effects of different vibrational mode excitations of the reagents on the reactivities are studied. Physical explanations about the isotope effects are also provided thoroughly including the influence of vibrational energy differences between the different isotopologues and the impact of the tunneling effect.

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.

A Quasi-Classical Evaluation of the J-Shifting Approximation for the Reactive Cross Sections of F + CHD3 and F + CH4

We evaluated the accuracy of the J-shifting approximation to estimate reactant state-selected cross sections for the F+CH₄ → HF+CH₃ and F+CHD₃ → HF+CD₃/DF+CHD₂ reactions. In particular, we analyzed how the rotational state of methane influences the quality of the approximation. The systems were considered in full dimensionality. Since full-quantum scattering calculations are still unfeasible for these reactions, we employed quasi-classical trajectories (QCT) to calculate the cross sections. The characteristics of the Born-Oppenheimer potential energy surface of these reactions pose a great challenge to the assumptions of the J-shifting approach. In spite of this, we found that it performs well for both reactions if the methane molecule is in the rotational ground state. However, when methane is rotationally excited, the approach affords good results for the F+CH₄ system but clearly fails for F+CHD₃. The reasons for this failure will be discussed, and a simple procedure to recover good estimators for the cross sections from J = 0 calculations will be introduced.

Nonthermal rate constants for CH4 * + X → CH3 + HX, X = H, O, OH, and O2

Quasiclassical trajectories are used to compute nonthermal rate constants, k^*, for abstraction reactions involving highly-excited methane CH₄ ^* and the radicals H, O, OH, and O₂. Several temperatures and internal energies of methane, E_vib, are considered, and significant nonthermal rate enhancements for large E_vib are found. Specifically, when CH₄ ^* is internally excited close to its dissociation threshold (E_vib ≈ D₀ = 104 kcal/mol), its reactivity with H, O, and OH is shown to be collision-rate-limited and to approach that of comparably-sized radicals, such as CH₃, with k^* > 10^-10 cm³ molecule^-1 s^-1. Rate constants this large are more typically associated with barrierless reactions, and at 1000 K, this represents a nonthermal rate enhancement, k^*/k, of more than two orders of magnitude relative to thermal rate constants k. We show that large nonthermal rate constants persist even after significant internal cooling, with k^*/k > 10 down to E_vib ≈ D₀/4. The competition between collisional cooling and nonthermal reactivity is studied using a simple model, and nonthermal reactions are shown to account for up to 35%-50% of the fate of the products of H + CH₃ = CH₄ ^* under conditions of practical relevance to combustion. Finally, the accuracy of an effective temperature model for estimating k^* from k is quantified.

Parallel Implementation of Semiclassical Transition State Theory

This paper presents the parsctst code, an efficient parallel implementation of the semiclassical transition state theory (SCTST) for reaction rate constant calculations. Parsctst is developed starting from a previously presented approach for the computation of the vibrational density of states of fully coupled anharmonic molecules ( Nguyen et al. Chem. Phys. Lett. 2010 , 499 , 915 ). The parallel implementation makes it practical to tackle reactions involving more than 100 fully coupled anharmonic vibrational degrees of freedom and also includes multidimensional tunneling effects. After describing the pseudocode and demonstrating its computational efficiency, we apply the new code for estimating the rate constant of the proton transfer isomerization reaction of the 2,4,6-tri- tert-butylphenyl to 3,5-di- tert-butylneophyl. Comparison with both theoretical and experimental results is presented. Parsctst code is user-friendly and provides a significant computational time saving compared to serial calculations. We believe that parsctst can boost the application of SCTST as an alternative to the basic transition state theory for accurate kinetics modeling not only in combustion or atmospheric chemistry, but also in organic synthesis, where bigger reactive systems are encountered.

A critical comparison of neural network potentials for molecular reaction dynamics with exact permutation symmetry

Several symmetry strategies have been compared in fitting full dimensional accurate potentials for reactive systems based on a neural network approach.

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.