Time-dependent and time-independent wavepacket approaches to reactive scattering and photodissociation dynamics

Unraveling the effect of reagent vibrational excitation on the scattering mechanism of the benchmark H + H2 → H2 + H hydrogen exchange reaction in the coupled 12E' ground electronic manifold

The hydrogen exchange reaction, H + H2 → H2 + H, along with its isotopic variants, has been the cornerstone for the development of new and novel dynamical mechanisms of gas-phase bimolecular reactions since the 1930s. The dynamics of this reaction are theoretically investigated in this work to elucidate the effect of reagent vibrational excitation on differential cross sections (DCSs) in a nonadiabatic situation. The dynamical calculations are carried out using a time-dependent quantum mechanical method, both on the lower adiabatic potential energy surface and employing a two-state coupled diabatic theoretical model to explicitly include all the nonadiabatic couplings present in the 12E' ground electronic manifold of the H3 system. Towards this effort, the Boothroyd-Keogh-Martin-Peterson (BKMP2) surface of the lower adiabatic component is coupled with the double many-body expansion (DMBE) surface of the upper one. The smooth variation of energy along the D3h seam of the conical intersections is explicitly confirmed. The coupled two-state calculations are performed only for H2 (v = 3-4, j = 0), as the minimum of the conical intersections becomes energetically accessible for these vibrational levels in the considered energy range. Initial state-selected total and state-to-state DCSs are calculated to elucidate various mechanistic aspects of reagent vibrational excitation. The latter enhances the forward scattering and makes the backward scattering less prominent. Important roles of collision energy in the vibrational energy disposal of both forward- and backward-scattered products are examined. Analysis of the state-to-state DCSs of the vibrationally excited reagents reveals an important correlation among scattering angle, and the product rotational angular momentum and its helicity state. Such an analysis establishes a novel mechanism for the forward scattering of the reaction.

Electronic nonadiabatic effects in the state-to-state dynamics of the H + H2 → H2 + H exchange reaction with a vibrationally excited reagent

Out of the many major breakthroughs that the hydrogen-exchange reaction has led to, electronic nonadiabatic effects that are mainly due to the geometric phase has intrigued many. In this work we investigate such effects in the state-to-state dynamics of the H + H2 (v = 3, 4, j = 0) → H2 (v', j') + H reaction with a vibrationally excited reagent at energies corresponding to thermal conditions. The dynamical calculations are performed by a time-dependent quantum mechanical method both on the lower adiabatic potential energy surface (PES) and also using a two-states coupled diabatic theoretical model to explicitly include all the nonadiabatic couplings present in the 1E' ground electronic manifold of the H3 system. The nonadiabatic couplings are considered here up to the quadratic term; however, the effect of the latter on the reaction dynamics is found to be very small. Adiabatic population analysis showed a minimal participation of the upper adiabatic surface even for the vibrationally excited reagent. A strong nonadiabatic effect appears in the state-to-state reaction probabilities and differential cross sections (DCSs). This effect is manifested as "out-of-phase" oscillations in the DCSs between the results of the uncoupled and coupled surface situations. The oscillations persist as a function of both scattering angle and collision energy in both the backward and forward scattering regions. The origins of these oscillations are examined in detail. The oscillations that appear in the forward direction are found to be different from those due to glory scattering, where the latter showed a negligibly small nonadiabatic effect. The nonadiabatic effects are reduced to a large extent when summed over all product quantum states, in addition to the cancellation due to integration over the scattering angle and partial wave summation.

ABC+D: A time-independent coupled-channel quantum dynamics program for elastic and ro-vibrational inelastic scattering between atoms and triatomic molecules in full dimensionality

We discuss the details of a time-independent quantum mechanical method and its implementation for full-dimensional non-reactive scattering between a closed-shell triatomic molecule and a closed-shell atom. By solving the time-independent Schrödinger equation within the coupled-channel framework using a log-derivative method, the state-to-state scattering matrix (S-matrix) can be determined for inelastic scattering involving both the rotational and vibrational modes of the molecule. Various approximations are also implemented. The ABC+D code provides an important platform for understanding an array of physical phenomena involving collisions between atoms and molecules.

Quantum interference in the mechanism of H + LiH+ → H2 + Li+ reaction dynamics

In this work, the detailed reaction mechanism of the astrochemically relevant exoergic and barrierless H + LiH⁺ → H₂ + Li⁺ reaction is investigated by both time-dependent wave packet and quasi-classical trajectory (QCT) methods on the ab initio electronic ground state potential energy surface reported by Martinazzo et al. [Martinazzo et al., J. Chem. Phys., 2003, 119, 11241]. The interference terms due to the coherence between the partial waves are quantified. When plotted along the scattering angle they reveal interference of constructive or destructive nature. Significant interference was found in the differential cross-section (DCS) which is a symbolic of the non-statistical nature of the reaction. This is further complemented by calculating the lifetime of the collision complex by the QCT method. It is found that the reaction follows a direct stripping mechanism at higher collision energies and yields forward scattered products from collisions involving high total angular momentum. At low collision energies, the reaction follows a mixed direct/indirect mechanism but with a dominant indirect contribution. The product state-resolved DCSs reveal that two opposite mechanisms co-exist, both at low and high collision energies. The microscopic scattering mechanism of the reaction is found to be unaffected by the ro-vibrational excitation of the reagent diatom.

High-fidelity first principles nonadiabaticity: diabatization, analytic representation of global diabatic potential energy matrices, and quantum dynamics

Nonadiabatic dynamics, which goes beyond the Born-Oppenheimer approximation, has increasingly been shown to play an important role in chemical processes, particularly those involving electronically excited states. Understanding multistate dynamics requires rigorous quantum characterization of both electronic and nuclear motion. However, such first principles treatments of multi-dimensional systems have so far been rather limited due to the lack of accurate coupled potential energy surfaces and difficulties associated with quantum dynamics. In this Perspective, we review recent advances in developing high-fidelity analytical diabatic potential energy matrices for quantum dynamical investigations of polyatomic uni- and bi-molecular nonadiabatic processes, by machine learning of high-level ab initio data. Special attention is paid to methods of diabatization, high fidelity construction of multi-state coupled potential energy surfaces and property surfaces, as well as quantum mechanical characterization of nonadiabatic nuclear dynamics. To illustrate the tremendous progress made by these new developments, several examples are discussed, in which direct comparison with quantum state resolved measurements led to either confirmation of the observation or sometimes reinterpretation of the experimental data. The insights gained in these prototypical systems greatly advance our understanding of nonadiabatic dynamics in chemical systems.

Dissociative photodetachment of H3O2-: a full-dimensional quantum dynamics study

The transition state is a central concept of chemistry. Photoelectron-photofragment coincidence (PPC) spectroscopy has been proven as an attractive method to study the transition state dynamics. Within a state-of-the-art full-dimensional quantum mechanical model, the dissociative photodetachment dynamics of H₃O₂^- is investigated on accurate anion and neutral potential energy surfaces. The calculated PPC spectrum of H₃O₂^- agrees well with the experimental measurement. The dissociative product OH is exclusively populated on the ground vibrational state, implying the character of the spectator bond. In contrast, the product H₂O is predominantly populated in the ground and fundamental states of the symmetric and antisymmetric stretching modes, which is caused by the strong coupling between the antisymmetric motion of the transferred H atom in the transient intermediate [H₃O₂]* and both stretching modes of the product H₂O.

Theoretical Study of the Energy Disposal Mechanism and the State-Resolved Quantum Dynamics of the H + LiH+ → H2 + Li+ Reaction

Despite several studies in the literature, the detailed quantum state-to-state level mechanism of the astrophysically important exoergic barrierless H + LiH⁺ → H₂ + Li⁺ reaction is yet to be understood. In this work, we have investigated the energy disposal mechanism of the reaction in terms of integral reaction cross section, product internal state distributions, differential cross section, and rate constant. Fully converged and Coriolis coupled quantum mechanical calculations based on a time-dependent wave packet method have been performed at the state-to-state level on the ab initio electronic ground state potential energy surface (PES) constructed by Martinazzo et al. (J. Chem. Phys. 2003, 119, 11241-11248). The agreement between the present quantum mechanical and previous quasi-classical results is found even at very low relative translational energies of reagents. A non-statistical inverse Boltzmann vibrational distribution for the product is found. This is attributed to the "attractive" nature of the underlying PES, which facilitates the excess energy release mostly as product vibration (60-80%). The energy disposal in products is found to be unaffected by the rovibrational excitation of the reagent diatom due to the weak coupling between the vibrational modes of the reagent and the product. The mild effect of collision energy on the product energy disposal is ascribed to the effective coupling between the translational modes of the reagent and the product. It is found that the collisions lead to the formation of the product H₂ in its rovibrationally excited levels.

Time-dependent quantum mechanical wave packet dynamics

Starting from a model study of the collinear (H, H₂) exchange reaction in 1959, the time-dependent quantum mechanical wave packet (TDQMWP) method has come a long way in dealing with systems as large as Cl + CH₄. The fast Fourier transform method for evaluating the second order spatial derivative of the wave function and split-operator method or Chebyshev polynomial expansion for determining the time evolution of the wave function for the system have made the approach highly accurate from a practical point of view. The TDQMWP methodology has been able to predict state-to-state differential and integral reaction cross sections accurately, in agreement with available experimental results for three dimensional (H, H₂) collisions, and identify reactive scattering resonances too. It has become a practical computational tool in predicting the observables for many A + BC exchange reactions in three dimensions and a number of larger systems. It is equally amenable to determining the bound and quasi-bound states for a variety of molecular systems. Just as it is able to deal with dissociative processes (without involving basis set expansion), it is able to deal with multi-mode nonadiabatic dynamics in multiple electronic states with equal ease. We present an overview of the method and its strength and limitations, citing examples largely from our own research groups.

Modified Gaussian Wave Packet Method for Calculating Initial State Wave Functions in Photodissociation

A modified Gaussian wave packet relaxation method is proposed to calculate the ground state wave function using an expansion of frozen Gaussian wave packets. This new procedure consists of two steps. In the first step, a multidimensional Gaussian product placed at the ground state equilibrium geometry is propagated in imaginary time. The relaxation optimizes the widths of the one-dimensional Gaussians. In the second step, additional Gaussian wave packets with the same widths are placed near the equilibrium geometry, and the corresponding expansion coefficients are optimized using the same relaxation method. This new algorithm is tested in photodissociation of NOCl and NH₃, and the results show good agreement with the exact results in the energy, wave function, and absorption spectrum. In particular, the highly structured absorption spectrum of NH₃ is reproduced, underscoring the accuracy of both the initial wave packet and the excited state propagation.

Active vs. spectator modes in nonadiabatic photodissociation dynamics of the hydroxymethyl radical via the 22A(3s) Rydberg state

The choice of the active degrees of freedom (DOFs) is a pivotal issue in a reduced-dimensional model of quantum dynamics when a full-dimensional one is not feasible. Here, several five-dimensional (5D) models are used to investigate the nonadiabatic photodissociation dynamics of the hydroxymethyl (CH₂OH) radical, which possesses nine internal DOFs, in its lowest absorption band. A normal-mode based scheme is used to identify the active and spectator modes, and its predictions are confirmed by 5D quantum dynamical calculations. Our results underscore the important role of the CO stretching mode in the photodissociation dynamics of CH₂OH, originating from the photo-induced promotion of an electron from the half-occupied π*_CO antibonding orbital to a carbon Rydberg orbital.

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.

Laser-induced dissociation dynamics of triatomic molecule in electronic excited states: A full-dimensional quantum mechanics study

We present a detailed theoretical approach to investigate the laser-induced dissociation dynamics of a triatomic molecule on its electronic excited state in full dimensional case. In this method, the time evolution of the time-dependent system is propagated via combined the split operator method and the expansion of Chebyshev polynomials (or short-time Chebyshev propagation) and the system wave functions are expanded in terms of molecular rotational bases. As an example of the application of this formalism, the dissociation dynamics of H3(+)→H2(+)+H induced by ultrashort UV laser pulses are investigated on new Born-Oppenheimer potential energy surfaces. Our numerical results show that the signals of dissociation products will be easier to observe as the increasing of field strength. Driving by a 266 nm laser beam, the calculated central value of kinetic-energy-release is 2.04 eV which shows excellent agreement with the experimental estimation of 2.1 eV. When the H3(+) ion is rotationally excited, the spatial distribution of product fragments will become well converged.

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.

Semiclassical Wigner theory of photodissociation in three dimensions: Shedding light on its basis

The semiclassical Wigner theory (SCWT) of photodissociation dynamics, initially proposed by Brown and Heller [J. Chem. Phys. 75, 186 (1981)] in order to describe state distributions in the products of direct collinear photodissociations, was recently extended to realistic three-dimensional triatomic processes of the same type [Arbelo-González et al., Phys. Chem. Chem. Phys. 15, 9994 (2013)]. The resulting approach, which takes into account rotational motions in addition to vibrational and translational ones, was applied to a triatomic-like model of methyl iodide photodissociation and its predictions were found to be in nearly quantitative agreement with rigorous quantum results, but at a much lower computational cost, making thereby SCWT a potential tool for the study of polyatomic reaction dynamics. Here, we analyse the main reasons for this agreement by means of an elementary model of fragmentation explicitly dealing with the rotational motion only. We show that our formulation of SCWT makes it a semiclassical approximation to an approximate planar quantum treatment of the dynamics, both of sufficient quality for the whole treatment to be satisfying.

Product fine-structure resolved photodissociation dynamics: the A band of H2O

The photodissociation dynamics of H2O in its first absorption band is investigated on an accurate potential energy surface based on a large number of high-level ab initio points. Several ro-vibrational states of the parent molecule are considered. Different from most previous theoretical studies, the spin-orbit and Λ-doublet populations of the open-shell OH fragment are reported from full-dimensional wave packet calculations. The populations of the two spin-orbit manifolds are in most cases close to the statistical limit, but the Λ-doublet is dominated by the A(") component, thanks largely to the fast in-plane dissociation of H2O(Ã(1)A('')). Comparisons with experimental data and a Franck-Condon model are generally very good, although some discrepancies exist.

New insights into the semiclassical Wigner treatment of photodissociation dynamics

The semiclassical Wigner treatment of Brown and Heller [J. Chem. Phys. 1981, 75, 186] is applied to direct triatomic (or triatomic-like polyatomic) photodissociations with the aim of accurately predicting final state distributions at relatively low computational cost, and having available a powerful interpretative tool. For the first time, the treatment takes rotational motions into account. The proposed formulation closely parallels the quantum description as far as possible. An approximate version is proposed, which is still accurate while numerically much more efficient. In addition to being weighted by usual vibrational Wigner distributions, final phase space states appear to be weighted by new rotational Wigner distributions. These densities have remarkable structures clearly showing that classical trajectories most contributing to rotational state j are those reaching the products with a rotational angular momentum close to [j(j + 1)](1/2) (in ℏ units). The previous methods involve running trajectories from the reagent molecule onto the products. The alternative backward approach [L. Bonnet, J. Chem. Phys., 2010, 133, 174108], in which trajectories are run in the reverse direction, is shown to strongly improve the numerical efficiency of the most rigorous method in addition to being state-selective, and thus, ideally suited to the description of state-correlated distributions measured in velocity imaging experiments. The results obtained by means of the previous methods are compared with rigorous quantum results in the case of Guo's triatomic-like model of methyl iodide photodissociation [J. Chem. Phys., 1992, 96, 6629] and close agreement is found. In comparison, the standard method of Goursaud et al. [J. Chem. Phys., 1976, 65, 5453] is only semi-quantitative.

Theoretical methods for ultrafast spectroscopy

Time-resolved spectroscopy in the femtosecond and attosecond time domain is a tool to unravel the dynamics of nuclear and electronic motion in molecular systems. Theoretical insight into the underlying physical processes is ideally gained by solving the time-dependent Schrödinger equation. In this work, methods currently used to solve this equation are reviewed in a compact presentation. These methods involve numerical representations of wavefunctions and operators, the calculation of time evolution operators, the setting up of the Hamiltonian operators and the types of coordinates to be used hereto. The advantages and disadvantages of some methods are discussed.