Coriolis-Coupled Quantum Dynamics for O(1D) + H2 → OH + H

An effective approximation of Coriolis coupling in reactive scattering: application to the time-dependent wave packet calculations

Coriolis coupling plays a crucial role in reactive scattering, but dynamics calculations including the complete Coriolis coupling significantly increase the difficulty of numerical evolution due to the corresponding expensive matrix processing. The coupled state approximation that completely ignores the off-diagonal Coriolis coupling saves computational cost significantly but its error is usually unacceptable. In this paper, an improved coupled state approximation inspired by recently published results [D. Yang, X. Hu, D. H. Zhang and D. Xie, J. Chem. Phys., 2018, 148, 084101.] of the inelastic scattering problem is extended to deal with the reactive scattering. The calculations using the time-dependent wave packet method reveal that the new method can accurately reproduce the rigorous results of the H + HD (j0 < 3) → D + H2 reaction and immensely improve the computational efficiency. Additionally, we extend the new method to the non-adiabatic Li(2p) + H2 (v0 = 0, j0 = 0, 1) → H + LiH reaction, showcasing its advantages of low computational cost and high accuracy.

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.

Accurate global potential energy surface for SiH2 +(X2A1) and quantum dynamics of related reaction H(2S) + SiH+(X1Σ+)

With the many-body expansion method, an accurate global potential energy surface (PES) is constructed for SiH₂ ⁺(X²A₁) by mapping 4762 ab initio energy points calculated on the multireference configuration interaction level including Davidson corrections with aug-cc-pV6Z Dunning's basis set. The dissociation energies and equilibrium geometries of SiH⁺(X¹Σ⁺) and H₂(X¹Σ_g ⁺) agree well with the experimental results. The topographical characteristics of all stationary points for the SiH₂ ⁺(X²A₁) PES are discussed in detail and compared with other theoretical and experimental results. In order to verify the validity and usability of the present PES, the dynamics calculations based on the Chebyshev quantum wave packet method are performed for the H(S2)+SiH⁺(X¹Σ⁺)→Si⁺(P2)+H₂(X¹Σ_g ⁺) reaction. The probabilities, the total integral cross sections, and the rate constants are computed, and the analogies with the corresponding ones of reaction H(S2) + CH⁺(X¹Σ⁺)→C⁺(P2) + H₂(X¹Σ_g ⁺) are also made. The reasonable dynamical behavior throughout the entire configuration space indicates that the PES is suitable for relevant dynamics investigations and serves as a building block for constructing the PES of larger molecular systems containing Si⁺/H.

A combined theoretical and experimental investigation of the kinetics and dynamics of the O(1D) + D2 reaction at low temperature

The O(¹D) + H₂ reaction is a prototype for simple atom-diatom insertion type mechanisms considered to involve deep potential wells. While exact quantum mechanical methods can be applied to describe the dynamics, such calculations are challenging given the numerous bound quantum states involved. Consequently, efforts have been made to develop alternative theoretical strategies to portray accurately the reactive process. Here we report an experimental and theoretical investigation of the O(¹D) + D₂ reaction over the 50-296 K range. The calculations employ three conceptually different approaches - mean potential phase space theory, the statistical quantum mechanical method and ring polymer molecular dynamics. The calculated rate constants are in excellent agreement over the entire temperature range, exhibiting only weak temperature dependence. The agreement between experiment and theory is also very good, with discrepancies smaller than 26%. Taken together, the present and previous theoretical results validate the hypothesis that long-lived complex formation dominates the reaction dynamics at low temperature.

CHEMICAL REACTION DYNAMICS WITH REAL WAVE PACKETS

An approach to carrying out accurate quantum dynamics simulations of chemical reactions, termed the real wave packet (RWP) method, is outlined. The method focuses on propagation of just the real part of a complex-valued wave packet, halving computational memory and effort requirements in comparison with comparable high accuracy quantum propagation methods. Applications to 3-atom and 4-atom chemical reactions are reviewed. Potential future directions are indicated.

A COMPARATIVE STUDY OF ITERATIVE CHEBYSHEV AND LANCZOS IMPLEMENTATIONS OF THE BOUNDARY INHOMOGENEITY METHOD FOR QUANTUM SCATTERING

We have recently developed a scaleable Artificial Boundary Inhomogeneity (ABI) method [Chem. Phys. Lett.366, 390–397 (2002)] based on the utilization of the Lanczos algorithm, and in this work explore an alternative iterative implementation based on the Chebyshev algorithm. Detailed comparisons between the two iterative methods have been made in terms of efficiency as well as convergence behavior. The Lanczos subspace ABI method was also further improved by the use of a simpler three-term backward recursion algorithm to solve the subspace linear system. The two different iterative methods are tested on the model collinear H+H 2 reactive state-to-state scattering.

Coriolis coupling and nonadiabaticity in chemical reaction dynamics

The nonadiabatic quantum dynamics and Coriolis coupling effect in chemical reaction have been reviewed, with emphasis on recent progress in using the time-dependent wave packet approach to study the Coriolis coupling and nonadiabatic effects, which was done by K. L. Han and his group. Several typical chemical reactions, for example, H+D(2), F+H(2)/D(2)/HD, D(+)+H(2), O+H(2), and He+H(2)(+), have been discussed. One can find that there is a significant role of Coriolis coupling in reaction dynamics for the ion-molecule collisions of D(+)+H(2), Ne+H(2)(+), and He+H(2)(+) in both adiabatic and nonadiabatic context.

Nonadiabatic quantum dynamics calculations for the N + NH --> N(2) + H reaction

Nonadiabatic quantum dynamics calculations on the two coupled potential energy surfaces (PESs) (1(2)A' and 2(2)A') and also adiabatic quantum calculations on the lowest adiabatic PES are reported for the title reaction. Reaction probabilities for total angular momenta, J, varying from 0 to 160, are calculated to obtain the integral cross section (ICS) for collision energies ranging from 0.05 to 1.0 eV. Calculations using both the close coupling and the Centrifugal Sudden (CS) approximation are carried out to evaluate the role of Coriolis coupling effects for this reaction. The results of the nonadiabatic calculations show that the nonadiabatic effects in the title reaction for the initial state of NH (v = 0, j = 0) could be neglected, at least in the collision energy range considered in this study.

Study of the H+O2 reaction by means of quantum mechanical and statistical approaches: the dynamics on two different potential energy surfaces

The possible existence of a complex-forming pathway for the H+O(2) reaction has been investigated by means of both quantum mechanical and statistical techniques. Reaction probabilities, integral cross sections, and differential cross sections have been obtained with a statistical quantum method and the mean potential phase space theory. The statistical predictions are compared to exact results calculated by means of time dependent wave packet methods and a previously reported time independent exact quantum mechanical approach using the double many-body expansion (DMBE IV) potential energy surface (PES) [Pastrana et al., J. Phys. Chem. 94, 8073 (1990)] and the recently developed surface (denoted XXZLG) by Xu et al. [J. Chem. Phys. 122, 244305 (2005)]. The statistical approaches are found to reproduce only some of the exact total reaction probabilities for low total angular momenta obtained with the DMBE IV PES and some of the cross sections calculated at energy values close to the reaction threshold for the XXZLG surface. Serious discrepancies with the exact integral cross sections at higher energy put into question the possible statistical nature of the title reaction. However, at a collision energy of 1.6 eV, statistical rotationally resolved cross sections managed to reproduce the experimental cross sections for the H+O(2)(v=0,j=1)-->OH(v(')=1,j('))+O process reasonably well.

Effect of Coriolis coupling in chemical reaction dynamics

It is essential to evaluate the role of Coriolis coupling effect in molecular reaction dynamics. Here we consider Coriolis coupling effect in quantum reactive scattering calculations in the context of both adiabaticity and nonadiabaticity, with particular emphasis on examining the role of Coriolis coupling effect in reaction dynamics of triatomic molecular systems. We present the results of our own calculations by the time-dependent quantum wave packet approach for H + D2 and F(2P3/2,2P1/2) + H2 as well as for the ion-molecule collisions of He + H2 +, D(-) + H2, H(-) + D2, and D+ + H2, after reviewing in detail other related research efforts on this issue.

Coriolis coupling effects in the calculation of state-to-state integral and differential cross sections for the H+D2 reaction

The quantum wavepacket parallel computational code DIFFREALWAVE is used to calculate state-to-state integral and differential cross sections for the title reaction on the BKMP2 surface in the total energy range of 0.4-1.2 eV with D2 initially in its ground vibrational-rotational state. The role of Coriolis couplings in the state-to-state quantum calculations is examined in detail. Comparison of the results from calculations including the full Coriolis coupling and those using the centrifugal sudden approximation demonstrates that both the energy dependence and the angular dependence of the calculated cross sections are extremely sensitive to the Coriolis coupling, thus emphasizing the importance of including it correctly in an accurate state-to-state calculation.

HO2 Ro-Vibrational Bound-State Calculations for Large Angular Momentum: J = 30, 40, and 50

The Lanczos homogeneous filter diagonalization method and the real Chebyshev filter diagonalization scheme incorporating doubling of the autocorrelation functions have been employed to compute the HO2 ro-vibrational states for high total angular momenta, J = 30, 40, and 50. For such computationally challenging calculations, we have adopted a parallel computing strategy to perform the matrix-vector multiplications. Low-lying bound states and high-lying bound states close to the dissociation threshold are reported. For low-lying bound states, a spectroscopic assignment has been attempted and the widely used approximate J-shifting method has been tested for this deep-well system. For high-lying bound states, the attempted spectroscopic assignments as well as the J-shifting approximation fail because of very strong Coriolis mixing, indicating that the Coriolis couplings are important for this system.

Unimolecular rovibrational bound and resonance states for large angular momentum: J=20 calculations for HO2

We explore the calculation of unimolecular bound states and resonances for deep-well species at large angular momentum using a Chebychev filter diagonalization scheme incorporating doubling of the autocorrelation function as presented recently by Neumaier and Mandelshtam [Phys. Rev. Lett. 86, 5031 (2001)]. The method has been employed to compute the challenging J=20 bound and resonance states for the HO2 system. The methodology has firstly been tested for J=2 in comparison with previous calculations, and then extended to J=20 using a parallel computing strategy. The quantum J-specific unimolecular dissociation rates for HO2-->H+O2 in the energy range from 2.114 to 2.596 eV have been reported for the first time, and comparisons with the results of Troe and co-workers [J. Chem. Phys. 113, 11019 (2000) Phys. Chem. Chem. Phys. 2, 631 (2000)] from statistical adiabatic channel method/classical trajectory calculations have been made. For most of the energies, the reported statistical adiabatic channel method/classical trajectory rate constants agree well with the average of the fluctuating quantum-mechanical rates. Near the dissociation threshold, quantum rates fluctuate more severely, but their average is still in agreement with the statistical adiabatic channel method/classical trajectory results.

A wave packet based statistical approach to complex-forming reactions

A wave packet based statistical model is suggested for complex-forming reactions. This model assumes statistical formation and decay of the long-lived reaction complex and computes reaction cross sections and their energy dependence from capture probabilities. This model is very efficient and reasonably accurate for reactions dominated by long-lived resonances, as confirmed by its application to the C((1)D)+H(2) reaction.

Quantum wave-packet dynamics of H+HLi scattering: Reaction cross section and thermal rate constant

The channel specific and initial state-selected reaction cross section and temperature-dependent rate constant for the title system is calculated with the aid of a time-dependent wave-packet approach and using the ab initio potential energy surface of Dunne et al. [Chem. Phys. Lett. 336, 1 (2001)]. All partial-wave contributions up to the total angular momentum J=74 are explicitly calculated within the coupled states (CS) approximation. Companion calculations are also carried out employing the standard as well as the uniform J-shifting (JS) approximation. The overall variation of reaction cross sections corresponds well to the behavior of a barrierless reaction. The hydrogen exchange channel yielding HLi+H products is seen to be more favored over the HLi depletion channel yielding Li+H(2) products at low and moderate collision energies. Sharp resonance features are observed in the cross-section results for the HLi depletion channel at low energies. Resonance features in the reaction cross sections average out with various partial-wave contributions, when compared to the same observed in the individual reaction probability curve. Except near the onset of the reaction, the vibrational and rotational excitation of the reagent HLi, in general, does not dramatically influence the reactivity of either channel. The thermal rate constants calculated up to 4000 K show nearly Arrhenius type behavior. The rate constant decreases with vibrational excitation of the reagent HLi, indicating that the cold HLi molecules are efficiently depleted in the reactive encounter with H at relatively low temperatures. The results obtained from the JS approximation are found to agree well qualitatively with the CS results.

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.