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.

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.

State-to-State Dynamics in Mode-Specific Reactions of Cl + CH3D(v1-I, v1-II, and v4 = 1; |10⟩): Loss of Memory or Not

Several decades of the study of reaction dynamics culminate in the concept of mode specificity and bond selectivity in polyatomic systems. Until very recently, the main concern of those studies has been total reactivity and little attention has been paid to the mode-specific effects on the more detailed product-state and angular distributions. Conventional wisdom would anticipate that the fine detail should reveal a more pronounced mode dependency. However, a few recent studies showed that the product distributions could appear to be surprisingly insensitive to the modes of internal excitation of reagents. This counterintuitive finding led to a concept of loss of memory. Here, we present detailed experimental results in the reactions of the Cl atom with three distinct stretching-excited CH₃D(v_CH3 = 1) reagents. In conjunction with the previous reports on various aspects of this reaction, such a comprehensive set of data enables us to perform an in-depth examination of the validity of this new concept.

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.

Multilayer Multiconfiguration Time-Dependent Hartree Study on the Mode-/Bond-Specific Quantum Dynamics of Water Dissociation on Cu(111)

In this work, full-dimensional (9D) quantum dynamics calculations on mode-/bond-specific surface scattering of a water molecule on a copper (111) rigid surface are performed through the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method. To easily perform the ML-MCTDH calculations on such a triatomic molecule-surface system, we first choose specific Jacobi coordinates as a set of coordinates of water. Next, to efficiently perform the 9D ML-MCTDH wavepacket propagation, the potential energy surface is transferred to a canonical polyadic decomposition form with the aid of a Monte Carlo-based method. Excitation-specific dissociation probabilities of H₂O on Cu(111) are computed, and mode-/bond-specific dynamics are demonstrated by comparison with a probability curve computed for a water molecule in the ground state. The dependence of the dissociation probability of the initial state of H₂O is studied, and it is found that the excitation-specific dissociation probabilities can be divided into three groups. We find that the vibrationally excited states enhance the dissociation reactivity of H₂O, while the rotationally excited states hardly influence it.

Imaging the Mode-Specificity in Cl + CH3D(v1-I, v1-II, v4 = 1; |jK⟩ = |10⟩) → CH2D(41) + HCl(v)

We report a crossed-beam imaging experiment on the title reactions at two collisional energies (E_c) of 5.3 and 10 kcal mol^-1. Both the integral cross sections relative to the ground-state reactivity and the differential cross sections were measured and compared. We found that one-quantum excitations of the CH₃-stretching vibrations of the CH₃D reagent exerted profound mode-specificity in forming the umbrella-mode-excited CH₂D(4₁) products with the vibrational efficacy of v₄ > v₁-I > v₁-II at both E_c values. The concomitantly formed HCl(v) coproducts were vibrationally cold. Interestingly, the branching ratios of (v = 1)/(v = 0) appeared invariant to the initial stretch-modes of excitation at E_c = 5.3 kcal mol^-1, yet exhibited a pronounced mode-specific dependency in the order of v₁-II > v₁-I > v₄ at E_c = 10.3 kcal mol^-1. This large and E_c-dependent disparity between the two Fermi-coupled reagents, v₁-I and v₁-II, is particularly significant and could be another facet─in addition to that in the recently reported vibrational enhancement factors─of the Fermi-phase-induced interference effect manifested in the product vibrational branching ratio. The pair-correlated angular distributions (v_CH2D, v_HCl)_s = (4₁, 0)_s in the three stretch-excited reactions were globally alike and resembled that of the ground-state reaction pair (0₀, 0)_g, suggestive of a direct abstraction mechanism of the peripheral type. This is in sharp contrast to all other vibrationally excited pairs of (1₁, 0)_s, (3₁, 0)_s, and (6₁, 0)_s previously reported in the CH₂D + HCl isotopic channel, for which both the direct abstraction and a time-delayed resonance pathway partake.

Fermi-phase-induced interference in the reaction between Cl and vibrationally excited CH3D

Mode selectivity is a well-established concept in chemical dynamics. A polyatomic molecule possesses multiple vibrational modes and the mechanical couplings between them can result in complicated anharmonic motions that defy a simple oscillatory description. A prototypical example of this is Fermi-coupled vibration, in which an energy-split eigenstate executes coherent nuclear motion that is comprised of the constituent normal modes with distinctive phases. Will this vibrational phase affect chemical reactivity? How can this phase effect be disentangled from more classical amplitude effects? Here, to address these questions, we study the reaction of Cl with a pair of Fermi states of CH₃D(v₁-I and v₁-II). We find that the reactivity ratio of (v₁-I)/(v₁-II) in forming the CH₂D(v = 0) + HCl(v) products deviates significantly from that permitted by the conventional reactivity-borrowing framework. Based on a proposed metric, this discrepancy can only be explained when the scattering interferences mediated by the CH₃D vibrational phases are explicitly considered, which expands the concept of vibrational control of chemical reactivity into the quantum regime.

Pair-Correlated Imaging of Cl + CH3D(v4, v1-I, v1-II = 1, |jK⟩) → CH2D(vi) + HCl(v)

The title reactions were studied at a collisional energy of 10.0 kcal mol^-1 in a crossed-beam, product-imaging experiment. In terms of integral cross sections, all three CH₃-stretching excited CH₃D(v_CH3 = 1) reagents promote the reactivity in forming the predominant product pair of (v_CH2D, v_HCl)_s = (0₀, 0/1)_s with a prominent mode-propensity of v₄ > v₁-I > v₁-II, where v₄ denotes the degenerate mode of CH₃ asymmetric stretch and v₁-I and v₁-II are a pair of Fermi-coupled, symmetric-stretch states. The vibrationally excited CH₂D product pairs of (6₁, 0)_s, (1₁, 0)_s, and (3₁, 0)_s appear to be minor channels and display a reverse propensity of v₄ < v₁-I ≈ v₁-II for (6₁, 0)_s, while v₄ > v₁-I for (1₁, 0)_s. Based on the observed angular distributions, we conjecture that, irrespective of the initial mode of excitation, the (0₀, 0)_s product pair proceeds by a direct abstraction of the peripheral type, whereas the (0₀,1)_s pair is mediated via a resonance pathway. Intriguingly, the angular distributions of the excited product pairs-(6₁, 0)_s, (1₁, 0)_s, and (3₁, 0)_s-are remarkably similar and comprise the traits of both the peripheral mechanism and resonance pathway. Possible interpretation and implication are suggested. In addition, due to the spectral overlap of the REMPI bands and heavily congested image features, a robust data analysis method is developed, which enables us to extract the dynamics attributes of a weak feature buried in the proximate, more intense ones with high fidelity.

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.

Mode- and Bond-Selected Reaction of H with Local Mode Molecule HDS

Understanding mode- and bond-selected dynamics of elementary chemical reactions is of central importance in molecular reaction dynamics. The initial state-selected time-dependent wave packet method is employed to study the mode and bond selectivity, isotopic branching ratio, and temperature dependence of rate constants of the two-channel reaction of H with local mode molecule HDS. For the abstraction channel, fundamental excitation of the HS (DS) bond of the reactant HDS significantly enhances the H-abstraction (D-abstraction) reaction, whose efficacy is higher than the same amount of translational energy except at low energies just above the energy threshold. This is in sharp contrast to the prediction of Polanyi rules: translational energy is more efficient than vibrational energy in enhancing a reaction with an early barrier. The recent sudden vector projection model is then applied to rationalize the observed mode specificity, which, however, shows that the translational mode vector has a larger coupling with the reaction coordinate than the stretching vector of the active bond, implying a reversed relative efficacy on promoting the reaction as well. In contrast, the mode and bond specificity for the exchange channel is not as strong as for the abstraction channel due to the regulation of the shallow well along the reaction path.

Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective

The onset of facile intramolecular vibrational energy flow can be related to features in the connected network of anharmonic resonances in the classical phase space.

Kinetics and dynamics study of the OH + C2H6 → H2O + C2H5 reaction based on an analytical global potential energy surface

To describe the gas-phase hydrogen abstraction reaction between the hydroxyl radical and the ethane molecule, an analytical full-dimensional potential energy surface was developed within the Born-Oppenheimer approximation. This reactive process is a ten-body system with 24 degrees of freedom, which represents a theoretical challenge. The new surface, named PES-2020, presents low barrier, 3.76 kcal mol-1, high exothermicity, -16.20 kcal mol-1, and intermediate complexes in the entrance and exit channels. To test the quality and accuracy of the analytical surface several stringent tests were performed and, in general, PES-2020 reasonably simulates the theoretical information used as input, it is a continuous and smooth potential, without spurious minima, it presents great versatility and a reasonable description of this ten-body reaction. Based on this surface, an exhaustive kinetics and dynamics study was performed with a double objective: to analyze the capacity of the new surface to simulate the experimental evidence, and to help understand the mechanism of reaction and the role of the ethyl group in the reaction. In the kinetics study, three approaches were used: variational transition-state theory with multidimensional tunnelling (VTST/MT), ring polymer molecular dynamics (RPMD) and quasi-classical trajectory (QCT) results, in the temperature range 200-2000 K. There is general agreement between the three approaches and they reasonably simulate the experimental behaviour, which gives confidence to the fitness of the new surface to describe the system. In the dynamics study, QCT calculations were performed at 298 K for a direct comparison with the only experimental result reported. We found that ethyl fragment presents a noticeable internal energy (∼20%) and so cannot be considered as a spectator. The water product vibrational energy is reasonably reproduced, though when a level-by-level distribution is analyzed the agreement is only qualitative.