Spectral quantization of transition state dynamics for the three‐dimensional H+H2 reaction

Optimal control of N-H photodissociation of pyridinyl

The N-H photodissociation dynamics of the pyridinyl radical upon continuous excitation to the optically bright, first excited ππ* electronic state by an ultra-violet (UV) laser pulse has been investigated within the mathematical framework of optimal control theory. The genetic algorithm (GA) is employed as the optimization protocol. We considered a three-state and three-mode model Hamiltonian, which includes the reaction coordinate, R (a1 symmetry); the coupling coordinates (namely, out-of-plane bending coordinate of the hydrogen atom of azine group), Θ (b1 symmetry); and the wagging mode, Q9 (a2 symmetry). The three electronic states are the ground, ππ*, and πσ* states. The πσ* state crosses both the ground state and the ππ* state, and it is a repulsive state on which N-H dissociation occurs upon photoexcitation. Different vibrational wave functions along the coupling coordinates, Θ and Q9, of the ground electronic state are used as the initial condition for solving the time-dependent Schrödinger equation. The optimal UV laser pulse is designed by applying the GA, which maximizes the dissociation yield. We obtained over 95% dissociation yield through the πσ* asymptote using the optimal pulse of a time duration of ∼30 000 a.u. (∼725.66 fs).

Optimal control of photodissociation of phenol using genetic algorithm

Photodissociation dynamics of the OH bond of phenol is studied with an optimally shaped laser pulse. The theoretical model consists of three electronic states (the ground electronic state, ππ* state, and πσ* state) in two nuclear coordinates (the OH stretching coordinate as a reaction coordinate, r, and the CCOH dihedral angle as a coupling coordinate, θ). The optimal UV laser pulse is designed using the genetic algorithm, which optimizes the total dissociative flux of the wave packet. The latter is calculated in the adiabatic asymptotes of the S0 and S1 electronic states of phenol. The initial state corresponds to the vibrational levels of the electronic ground state and is defined as | n r, n θ⟩, where n r and n θ represent the number of nodes along r and θ, respectively. The optimal UV field excites the system to the optically dark πσ* state predominantly over the optically bright ππ* state with the intensity borrowing effect for the |0, 0⟩ and |0, 1⟩ initial states. For the |0, 0⟩ initial condition, the photodissociation to the S1 asymptotic channel is favored slightly over the S0 asymptotic channel. Addition of one quantum of energy along the coupling coordinate increases the dissociation probability in the S1 channel. This is because the wave packet spreads along the coupling coordinate on the πσ* state and follows the adiabatic path. Hence, the S1 asymptotic channel gets more ([Formula: see text]11%) dissociative flux as compared to the S0 asymptotic channel for the |0, 1⟩ initial condition. The |1, 0⟩ and |1, 1⟩ states are initially excited to both the ππ* and πσ* states in the presence of the optimal UV pulse. For these initial conditions, the S1 channel gets more dissociative flux as compared to the S0 channel. This is because the high energy components of the wave packet readily reach the S1 channel. The central frequency of the optimal UV pulse for the |0, 0⟩ and |0, 1⟩ initial states has a higher value as compared to the |1, 0⟩ and |1, 1⟩ initial states. This is explained with the help of an excitation mechanism of a given initial state in relation to its energy.

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.

Dynamical resonances of the deuterated CH2+ complex in the electronic ground state: A quantum wavepacket study

We here investigate the effects of isotopic substituents on the vibrational energy levels of the CH₂⁺ complex, supported by the electronic ground (1 ²A') potential energy surface (PES) of the H + CH⁺ reaction. We calculate the transition state spectrum by Fourier transforming the time-autocorrelation function of the initial wavepacket (WP) chosen in the interaction region of the PES. Using the time-dependent WP approach, the dynamical resonances are identified as bound and quasibound in nature, and they are characterized in terms of the eigenfunctions and lifetimes. The present work on the isotopic variants [CHD⁺(CDH⁺) and CD₂⁺] is compared with our earlier work [P. Sundaram et al., Phys. Chem. Chem. Phys. 19, 20172 (2017)] on the parent CH₂⁺ species. The isotopic variants reveal a large number of peaks in the spectra and the eigenfunctions exhibit the systematic nodal progressions and periodic orbits, the same as in CH₂⁺. While the CD₂⁺ complex exactly mimics the resonance behaviors (local and hyperspherical modes) of the bound and quasibound CH₂⁺ complex, the CHD⁺(CDH⁺) complex reveals only the local mode behaviors at low energies and significantly less number of resonance structures at high energies. Lifetime analysis of the isotopic variants implies that the CD₂⁺ complex survives much longer than the CHD⁺(CDH⁺) complex and concludes the work by noting the following order in the decay profile of the deuterated CH₂⁺ resonances as CH₂⁺>CHD⁺(CDH⁺) >CD₂⁺.

Effect of Initial Vibrational-State Excitation on Subfemtosecond Photodynamics of Water

We discuss the effect of initial vibrational-state excitation on the subfemtosecond photodynamics of water. Photoelectron spectra of Franck-Condon ionization to the (2)B1 state of the H2O(+) (D2O(+)) from the ground and several vibrationally excited states of the neutral are reported. Also calculated are ratios of the high-order harmonic generation (HHG) signals as a function of time for each initial vibrational state of the neutral molecule as predicted from the ratios of the square of the autocorrelation functions for D2O(+) and H2O(+). They reveal maxima as a function of time for each vibrational state of the neutral molecule. In turn, the HHG signals are found to be enhanced with vibrational excitation, with the calculated expectation values of the bond lengths and bond angle revealing quasiperiodic oscillations in time for all initial vibrational states of the neutral species. Although the bond lengths show only a marginal increase, the bond angle is found to be enhanced markedly by vibrational excitation, this being therefore responsible for the observed rise in the HHG signal.

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.

State-to-State Dynamics of Elementary Bimolecular Reactions

The study of state-to-state dynamics of elementary bimolecular reactions has provided remarkable insights into chemical reactivity at the most fundamental level. This review covers exciting developments in this important field in the past decade. I focus on recent studies of quantum-state-resolved molecular-beam reactive-scattering studies of elementary chemical reactions, from triatomic to polyatomic systems. Researchers have made great advances in the fundamental understanding of many elementary chemical reactions through state-to-state dynamics studies. The strong interaction between theory and experiment has significantly enhanced our understanding of the dynamics of these reactions. I hope this review provides a glimpse of this exciting research field to both experts and beginners.

The state-to-state-to-state model for direct chemical reactions: Application to D+H2→HD+H

A simple theoretical model is developed to predict the state-to-state dynamics of direct chemical reactions. Motivated by traditional ideas from transition state theory, expressions are derived for the reactive S matrix that may be computed using the local transition state dynamics. The key approximation involves the use of quantum bottleneck states to represent the near separable dynamics taking place near the transition state. Explicit expressions for the S matrix are obtained using a Franck-Condon treatment for the inelastic coupling between internal states of the collision complex. It is demonstrated that the energetic thresholds for various initial reagent states of the D+H(2) reaction can be understood in terms of our theory. Specifically, the helicity of the reagent states are found to correlate directly to the symmetry of the quantum bottleneck states, which thus possess very different thresholds. Furthermore, the rotational product state distributions for D+H(2) are found to be associated with interfering pathways through the quantum bottleneck states.

State to state to state dynamics of the D+H2 -->HD+H reaction: control of transition-state pathways via reagent orientation

The influence of reagent rotation on the dynamics of the D+H2 -->HD+H reaction is studied. The state-resolved differential cross section is measured using the Rydberg-atom scheme in a crossed beam experiment. It is found that the H2 rotation has a strong influence on the results. This effect was traced to the selection of the quantum bottleneck states through reagent orientation, thus suggesting a novel strategy to control the transition-state pathways in direct chemical reactions.

Photochemistry of pyrrole: Time-dependent quantum wave-packet description of the dynamics at the π1σ*-S0 conical intersections

The photoinduced hydrogen-elimination reaction in pyrrole via the conical intersections of the two (1)pi sigma(*) excited states with the electronic ground states [(1)B(1)(pi sigma(*))-S(0) and (1)A(2)(pi sigma(*))-S(0)] have been investigated by time-dependent quantum wave-packet calculations. Model potential-energy surfaces of reduced dimensionality have been constructed on the basis of accurate multireference ab initio electronic-structure calculations. For the (1)B(1)-S(0) conical intersection, the model includes the NH stretching coordinate as the tuning mode and the hydrogen out-of-plane bending coordinate as the coupling mode. For the (1)A(2)-S(0) conical intersection, the NH stretching coordinate and the screwing coordinate of the ring hydrogens are taken into account. The latter is the dominant coupling mode of this conical intersection. The electronic population-transfer processes at the conical intersections, the branching ratio between the dissociation channels, and their dependence on the initial preparation of the system have been investigated for pyrrole and deuterated pyrrole. It is shown that the excitation of the NH stretching mode strongly enhances the reaction rate, while the excitation of the coupling mode influences the branching ratio of different dissociation channels. The results suggest that laser control of the photodissociation of pyrrole via mode-specific vibrational excitation should be possible. The calculations provide insight into the microscopic details of ultrafast internal-conversion processes in pyrrole via hydrogen-detachment processes, which are aborted at the (1)pi sigma(*)-S(0) conical intersections. These mechanisms are of relevance for the photostability of the building blocks of life (e.g., the DNA bases).

Time-dependent quantum wave-packet description of the π1σ* photochemistry of phenol

The photoinduced hydrogen elimination reaction in phenol via the conical intersections of the dissociative 1pi sigma* state with the 1pi pi* state and the electronic ground state has been investigated by time-dependent quantum wave-packet calculations. A model including three intersecting electronic potential-energy surfaces (S0, 1pi sigma*, and 1pi pi*) and two nuclear degrees of freedom (OH stretching and OH torsion) has been constructed on the basis of accurate ab initio multireference electronic-structure data. The electronic population transfer processes at the conical intersections, the branching ratio between the two dissociation channels, and their dependence on the initial vibrational levels have been investigated by photoexciting phenol from different vibrational levels of its ground electronic state. The nonadiabatic transitions between the excited states and the ground state occur on a time scale of a few tens of femtoseconds if the 1pi pi*-1pi sigma* conical intersection is directly accessible, which requires the excitation of at least one quantum of the OH stretching mode in the 1pi pi* state. It is shown that the node structure, which is imposed on the nuclear wave packet by the initial preparation as well as by the transition through the first conical intersection (1pi pi*-1pi sigma*), has a profound effect on the nonadiabatic dynamics at the second conical intersection (1pi sigma*-S0). These findings suggest that laser control of the photodissociation of phenol via IR mode-specific excitation of vibrational levels in the electronic ground state should be possible.

Quantum study of the N+N2 exchange reaction: State-to-state reaction probabilities, initial state selected probabilities, Feshbach resonances, and product distributions

We report a detailed three-dimensional time-dependent quantum dynamics study of the state-to-state N+N(2) exchange scattering in the 2.1-3.2 eV range using a recently developed ab initio potential energy surface (PES). The reactive flux arrives at the dividing surface in the asymptotic product region in a series of six packets, instead of a single packet. Further study shows that these features arise from the "Lake Eyring" region of the PES, a region with a shallow well between two transition states. Trappings due to Feshbach resonances are found to be the major cause of the time delay. A detailed analysis of the Feshbach resonance features is carried out using an L(2) calculation of the metastable states in the "Lake Eyring" region. Strong resonance features are found in the state-to-state and initial state selected reaction probabilities. The metastable states with bending motions and/or bending coupled with stretching motions are found to be the predominant source of the resonance structure. Initial state selected reaction probabilities further indicate that the lifetimes of the metastable states with bending motions in the "Lake Eyring" region are longer than those of states with stretching motions and thus dominate the reactive resonances. Resonance structures are also visible in some of the integral cross sections and should provide a means for future experimental observation of the resonance behavior. A study of the final rotational distributions shows that, for the energy range studied here, the final products are distributed toward high-rotational states. Final vibrational distributions at the temperatures 2000 and 10,000 K are also reported.

Resonances in three-dimensional H+HLi scattering: A time-dependent wave packet dynamical study

This paper examines the resonances in H + HLi scattering. The signature of these resonances is obtained from the oscillations in its reaction probability versus energy curves. They are identified here from a set of pseudospectra calculated for different initial locations of a stationary Gaussian wave packet on the ab initio potential energy surface (PES) reported by Dunne, Murrel, and Jemmer. The nuclear motion on this PES is monitored with the aid of a time-dependent wave packet method and the pseudospectrum are calculated by Fourier transforming the time autocorrelation function of the initial wave packet. The resonances are further examined and assigned by computing their eigenfunctions through spectral quantization algorithm. Both the linewidth as well as decay lifetimes of the resonances are reported.

Time-dependent quantum wave-packet description of the1πσ* photochemistry of pyrrole

The photoinduced hydrogen elimination reaction in pyrrole via the conical intersection of the 1B1 (1pi sigma*) excited state with the electronic ground state has been investigated by time-dependent quantum wave-packet dynamics. A two-dimensional model potential-energy surface has been constructed as a function of the NH stretching and the hydrogen out-of-plane bending mode, employing multi-reference ab initio electronic-structure methods. The branching ratio of the reactive flux at the conical intersection has been investigated in dependence on the initial vibrational state of the molecule. The results suggest that laser control of the photodissociation of pyrrole via mode-specific vibrational excitation should be possible.

Interference of quantized transition-state pathways in the H + D2 -> D + HD chemical reaction

The collision-energy dependence of the state-resolved differential cross section at a specific backward-scattering angle for the reaction H + D2 --> D + HD is measured with the D-atom Rydberg "tagging" time-of-flight technique. The reaction was modeled theoretically with converged quantum scattering calculations that provided physical interpretation of the observations. Oscillations in the differential cross sections in the backward-scattering direction are clearly observed and are attributed to the transition-state structures that originate from the interferences of different quantized transition-state pathways.

Quantum scattering calculations on chemical reactions

This review discusses recent quantum scattering calculations on bimolecular chemical reactions in the gas phase. This theory provides detailed and accurate predictions on the dynamics and kinetics of reactions containing three atoms. In addition, the method can now be applied to reactions involving polyatomic molecules. Results obtained with both time-independent and time-dependent quantum dynamical methods are described. The review emphasises the recent development in time-dependent wave packet theories and the applications of reduced dimensionality approaches for treating polyatomic reactions. Calculations on over 40 different reactions are described.

Forward scattering due to slow-down of the intermediate in the H + HD --> D + H(2) reaction

Quantum dynamical processes near the energy barrier that separates reactants from products influence the detailed mechanism by which elementary chemical reactions occur. In fact, these processes can change the product scattering behaviour from that expected from simple collision considerations, as seen in the two classical reactions F + H(2) --> HF + H and H + H(2) --> H(2) + H and their isotopic variants. In the case of the F + HD reaction, the role of a quantized trapped Feshbach resonance state had been directly determined, confirming previous conclusions that Feshbach resonances cause state-specific forward scattering of product molecules. Forward scattering has also been observed in the H + D(2) --> HD + D reaction and attributed to a time-delayed mechanism. But despite extensive experimental and theoretical investigations, the details of the mechanism remain unclear. Here we present crossed-beam scattering experiments and quantum calculations on the H + HD --> H(2) + D reaction. We find that the motion of the system along the reaction coordinate slows down as it approaches the top of the reaction barrier, thereby allowing vibrations perpendicular to the reaction coordinate and forward scattering. The reaction thus proceeds, as previously suggested, through a well-defined 'quantized bottleneck state' different from the trapped Feshbach resonance states observed before.

Scattering resonances in the simplest chemical reaction

Recent studies of state-resolved angular distributions show the participation of reactive scattering resonances in the simplest chemical reaction. This review is intended for those who wish to learn about the state-of-the-art in the study of the H + H2 reaction family that has made this breakthrough possible. This review is also intended for those who wish to gain insight into the nature of reactive scattering resonances. Following a tour across several fields of physics and chemistry where the concept of resonance has been crucial for the understanding of new phenomena, we offer an operational definition and taxonomy of reactive scattering resonances. We introduce simple intuitive models to illustrate each resonance type. We focus next on the last decade of H + H2 reaction dynamics. Emphasis is placed on the various experimental approaches that have been applied to the search for resonance behavior in the H + H2 reaction family. We conclude by sketching the road ahead in the study of H + H2 reactive scattering resonances.

Observation and interpretation of a time-delayed mechanism in the hydrogen exchange reaction

Extensive theoretical and experimental studies have shown the hydrogen exchange reaction H+H2 --> H2+H to occur predominantly through a 'direct recoil' mechanism: the H--H bonds break and form concertedly while the system passes straight over a collinear transition state, with recoil from the collision causing the H2 product molecules to scatter backward. Theoretical predictions agree well with experimental observations of this scattering process. Indirect exchange mechanisms involving H3 intermediates have been suggested to occur as well, but these are difficult to test because bimolecular reactions cannot be studied by the femtosecond spectroscopies used to monitor unimolecular reactions. Moreover, full quantum simulations of the time evolution of bimolecular reactions have not been performed. For the isotopic variant of the hydrogen exchange reaction, H+D2 --> HD+D, forward scattering features observed in the product angular distribution have been attributed to possible scattering resonances associated with a quasibound collision complex. Here we extend these measurements to a wide range of collision energies and interpret the results using a full time-dependent quantum simulation of the reaction, thus showing that two different reaction mechanisms modulate the measured product angular distribution features. One of the mechanisms is direct and leads to backward scattering, the other is indirect and leads to forward scattering after a delay of about 25 femtoseconds.