State-to-state quantum dynamics of the O(P3)+OH(Π2)→H(S2)+O2(Σ3g−) reaction

Gaussian Process Regression for State-to-State Integral Cross Sections: The Case of the O + O2 Collision Dissociation Reactions

Research on hypersonic vehicles has become increasingly important worldwide in recent years. However, accurately simulating the dynamics of the nonequilibrium high-temperature reactions that are in the hypersonic flow around the vehicles presents a significant challenge as a large number of states and transitions are accessible even for the smallest atom-diatom reaction systems. It is quite difficult, sometimes even impossible, to exhaustively investigate all relevant combinations or determine high-dimensional analytical representations for the state-to-state reaction probabilities. In this study, we used Gaussian process regression (GPR) to fit a model based on only 807 QCT data for training. The confidence interval of the GPR prediction and the Kullback-Leibler (KL) divergence were used to help minimize the sampling amount of data for fitting the converged GPR model. The model aims to predict the state-to-state integral cross section (ICS) of the O + O2 → 3O dissociation reaction under random initial conditions (Et, v, j). In total, it took almost a month to obtain this converged GPR model, but it took only a few seconds to predict the ICS value for any initial condition. For 330 initial conditions not included in the training set, the mean-square error (MSE) between the QCT-calculated ICSs and the GPR-predicted ones is only 0.08 Å2 and the R2 is 0.9986, indicating that the GPR model can replace the direct expensive QCT calculation with high accuracy. Finally, we calculated the equilibrium dissociation rate coefficients based on the StS ICS values predicted by the GPR model, and the results were in good agreement with available experimental and theoretical results. Thus, this study provides an effective and accurate approach to the extensive direct state-to-state reaction dynamic calculations.

Accurate Full-Dimensional Global Diabatic Potential Energy Matrix for the Two Lowest-Lying Electronic States of the H + O2 ↔ HO + O Reaction

A new and more accurate diabatic potential energy matrix (DPEM) is developed for the two lowest-lying electronic states of HO₂, covering both the strong interaction region and reaction asymptotes. The ab initio calculations were performed at the Davidson corrected multireference configuration interaction level with the augmented correlation-consistent polarized valence quintuple-zeta basis set (MRCI+Q/AV5Z). The accuracy of the electronic structure calculations is validated by excellent agreement with the experimental HO₂ equilibrium geometry, fundamental vibrational frequencies, and H + O₂ ↔ OH + O reaction energy. Through the combination of an electronic angular momentum-method and a configuration interaction vector-based method, the mixing angle between the first two ²A″ states of HO₂ was successfully determined. Elements of the 2×2 DPEM were fit to neural networks with a proper account of the complete nuclear permutation inversion symmetry of HO₂. The DPEM correctly predicted the properties of conical intersection seams at linear and T-shape geometries, thus providing a reliable platform for studying both the spectroscopy of HO₂ and the nonadiabatic dynamics for the H + O₂ ↔ OH + O reaction.

Dynamical calculations of O(3P) + OH(2Π) reaction on the CHIPR potential energy surface using the fully coupled time-dependent wave-packet approach in hyperspherical coordinates

We have carried out quantum dynamics calculations for the O + OH → H + O₂ reaction on the CHIPR [A. J. C. Varandas, J. Chem. Phys., 2013, 138, 134117] potential energy surface (PES) for ground state HO₂ using the fully coupled 3D time-dependent wavepacket formalism [S. Adhikari and A. J. C. Varandas, Comput. Phys. Commun., 2013, 184, 270] in hyperspherical coordinates. Reaction probabilities for J > 0 are calculated for different initial rotational states of the OH radical (v = 0; j = 0, 1). State-to-state as well as total integral cross sections and rate-coefficients are evaluated and compared with previous theoretical calculations and available experimental studies. Using the rate constant for the forward (hereinafter considered to be H + O₂ → O + OH) and backward (O + OH → H + O₂) reactions of this reactive system, the equilibrium constant of the reversible process [H + O₂ ⇌ O + OH] is calculated as a function of temperature and compared with previous experimental measurements.

Dynamics study on the non-adiabatic Na(3p) + HD → NaH/NaD + D/H reaction: insertion-abstraction mechanism

Time-dependent wave packet calculations are carried out for two reaction channels of the non-adiabatic Na(3p) + HD → NaH/NaD + D/H reaction. The potential well on the excited state potential energy surface makes the reaction preferable to proceed through the insertion reaction path. The dominance of the NaD + H reaction channel and product rotational state distributions are found to be in agreement with the characteristics of typical adiabatic insertion reactions. However, significant forward scattering peaks in the differential cross sections (DCS) are found to be inconsistent with the forward-backward symmetric scattering characteristic of typical adiabatic insertion reactions, which indicate that the Na(3p) + HD reaction is dominated by a direct reaction mechanism. The comparison between adiabatic and non-adiabatic calculated DCSs reveals that the non-adiabatic couplings in the reaction could reduce the lifetime of the intermediate complex. Finally, the insertion-abstraction mechanism is put forward for the non-adiabatic Na(3p) + HD reaction.

Molecular Dynamics of Combustion Reactions in Supercritical Carbon Dioxide. 6. Computational Kinetics of Reactions between Hydrogen Atom and Oxygen Molecule H + O2 ⇌ HO + O and H + O2 ⇌ HO2

Reactions of the hydrogen atom and the oxygen molecule are among the most important ones in the hydrogen and hydrocarbon oxidation mechanisms, including combustion in a supercritical CO₂ (sCO₂) environment, known as oxy-combustion or the Allam cycle. Development of these energy technologies requires understanding of chemical kinetics of H + O₂ ⇌ HO + O and H + O₂ ⇌ HO₂ in high pressures and concentrations of CO₂. Here, we combine quantum treatment of the reaction system by the transition state theory with classical molecular dynamics simulation and the multistate empirical valence bonding method to treat environmental effects. Potential of mean force in the sCO₂ solvent at various temperatures 1000-2000 K and pressures 100-400 atm was obtained. The reaction rate for H + O₂ ⇌ HO + O was found to be pressure-independent and described by the extended Arrhenius equation 4.23 × 10^-7 T^-0.73 exp(-21 855.2 cal/mol/RT) cm³/molecule/s, while the reaction rate H + O₂ ⇌ HO₂ is pressure-dependent and can be expressed as 5.22 × 10^-2 T^-2.86 exp(-7247.4 cal/mol/RT) cm³/molecule/s at 300 atm.

Quantum dynamics study on the CHIPR potential energy surface for the hydroperoxyl radical: the reactions O + OH⇋O2 + H

Quantum scattering calculations of the O((3)P)+OH((2)Π)⇌O2((3)Σg (-))+H((2)S) reactions are presented using the combined-hyperbolic-inverse-power-representation potential energy surface [A. J. C. Varandas, J. Chem. Phys. 138, 134117 (2013)], which employs a realistic, ab initio-based, description of both the valence and long-range interactions. The calculations have been performed with the ABC time-independent quantum reactive scattering computer program based on hyperspherical coordinates. The reactivity of both arrangements has been investigated, with particular attention paid to the effects of vibrational excitation. By using the J-shifting approximation, rate constants are also reported for both the title reactions.

Development of efficient time-evolution method based on three-term recurrence relation

The advantage of the real-time (RT) propagation method is a direct solution of the time-dependent Schrödinger equation which describes frequency properties as well as all dynamics of a molecular system composed of electrons and nuclei in quantum physics and chemistry. Its applications have been limited by computational feasibility, as the evaluation of the time-evolution operator is computationally demanding. In this article, a new efficient time-evolution method based on the three-term recurrence relation (3TRR) was proposed to reduce the time-consuming numerical procedure. The basic formula of this approach was derived by introducing a transformation of the operator using the arcsine function. Since this operator transformation causes transformation of time, we derived the relation between original and transformed time. The formula was adapted to assess the performance of the RT time-dependent Hartree-Fock (RT-TDHF) method and the time-dependent density functional theory. Compared to the commonly used fourth-order Runge-Kutta method, our new approach decreased computational time of the RT-TDHF calculation by about factor of four, showing the 3TRR formula to be an efficient time-evolution method for reducing computational cost.

Electronic nonadiabatic effects in low temperature radical-radical reactions. I. C(3P) + OH(2Π)

The formation of collision complexes, as a first step towards reaction, in collisions between two open-electronic shell radicals is treated within an adiabatic channel approach. Adiabatic channel potentials are constructed on the basis of asymptotic electrostatic, induction, dispersion, and exchange interactions, accounting for spin-orbit coupling within the multitude of electronic states arising from the separated reactants. Suitable coupling schemes (such as rotational + electronic) are designed to secure maximum adiabaticity of the channels. The reaction between C((3)P) and OH((2)Π) is treated as a representative example. The results show that the low temperature association rate coefficients in general cannot be represented by results obtained with a single (generally the lowest) potential energy surface of the adduct, asymptotically reaching the lowest fine-structure states of the reactants, and a factor accounting for the thermal population of the latter states. Instead, the influence of non-Born-Oppenheimer couplings within the multitude of electronic states arising during the encounter markedly increases the capture rates. This effect extends up to temperatures of several hundred K.

Relative efficacy of vibrational vs. translational excitation in promoting atom-diatom reactivity: rigorous examination of Polanyi's rules and proposition of sudden vector projection (SVP) model

To provide a systematic and rigorous re-examination of the well-known Polanyi's rules, excitation functions of several A + BC(v = 0, 1) reactions are determined using the Chebyshev real wave packet method on accurate potential energy surfaces. Reactions with early (F + H2 and F + HCl), late (Cl + H2), and central (H∕D∕Mu + H2, where Mu is a short-lived light isotope of H) barriers are represented. Although Polanyi's rules are in general consistent with the quantum dynamical results, their predictions are strictly valid only in certain energy ranges divided by a cross-over point. In particular, vibrational excitation of the diatomic reactant typically enhances reactivity more effectively than translational excitation at high energies, while reverse is true at low energies. This feature persists irrespective of the barrier location. A sudden vector projection model is proposed as an alternative to Polanyi's rules. It is found to give similar, but more quantitative, predictions about mode selectivity in these reactions, and has the advantage to be extendible to reactions involving polyatomic molecules.

Chemical reaction versus vibrational quenching in low energy collisions of vibrationally excited OH with O

Quantum scattering calculations are reported for state-to-state vibrational relaxation and reactive scattering in O + OH(v = 2 - 3, j = 0) collisions on the electronically adiabatic ground state (2)A'' potential energy surface of the HO2 molecule. The time-independent Schrödinger equation in hyperspherical coordinates is solved to determine energy dependent probabilities and cross sections over collision energies ranging from ultracold to 0.35 eV and for total angular momentum quantum number J = 0. A J-shifting approximation is then used to compute initial state selected reactive rate coefficients in the temperature range T = 1 - 400 K. Results are found to be in reasonable agreement with available quasiclassical trajectory calculations. Results indicate that rate coefficients for O2 formation increase with increasing the OH vibrational level except at low and ultralow temperatures where OH(v = 0) exhibits a slightly different trend. It is found that vibrational relaxation of OH in v = 2 and v = 3 vibrational levels is dominated by a multi-quantum process.

State-to-state quantum dynamics of the N(4S) + CH(X2Π) → CN(X2Σ+,A2Π) + H(2S) reactions

The reactions between N((4)S) and CH(X(2)Π) lead to H((2)S) plus CN in its two lowest electronic states (X(2)Σ(+) and A(2)Π), which are responsible for the interstellar CN formation. Accurate quantum dynamics of these reactions are investigated on new global potential energy surfaces of the two lowest-lying triplet states of HCN (1(3)A' and 1(3)A") fitted to more than 37,000 points at the internally contracted multi-reference configuration interaction level with the Davidson correction. The pathways for these highly exothermic and barrierless reactions feature both the HCN and HNC wells. Long-lived resonances supported by these wells manifest in reaction probabilities as numerous oscillations, particularly for low J partial waves. The 1(3)A" state is found to be more reactive than the 1(3)A' state, due apparently to its more attractive nature in the entrance channel. The CN products in both electronic states are highly excited in both vibrational and rotational degrees of freedom. The near forward-backward symmetric differential cross sections are consistent with a complex-forming mechanism.