State-resolved Integral Cross Research Articles

New Potential Energy Surface for the H + Cl2 Reaction and Quantum Dynamics Studies.

The reaction of H + Cl2 → HCl + Cl plays a crucial role in various fields. However, no previous study has investigated this reaction using accurate quantum mechanical methods. In this paper, we construct a global potential energy surface (PES) using the neural network method with more than 20,000 ab initio energies obtained by the MRCI-F12+Q method with the aug-cc-pV5Z basis and extrapolated to the complete basis set limit. The spin-orbit coupling of the Cl atom has been considered in the PES. With this new PES, product state-resolved quantum dynamics calculations for the H + Cl2 (v0 = 0, j0 = 0-2) → HCl + Cl reaction was carried out. Numerical results show that the initial rotational excitation of the Cl2 has negligible effects on the reactivity. Product state-resolved integral cross sections (ICS) and rate constants reveal that the HCl is most favorably produced in its v' = 2 vibrational state. The calculated product vibrational state-resolved and total reaction rate constants suggest that the new global PES is accurate enough, as compared with the available experimental measurements.

Product State-Resolved Reactive Scattering Studies of the H + Cl2 (v0 = 1-3, j0 = 0) → HCl + Cl Reaction by the Time-Dependent Wave Packet Method.

The typical hydrogen atom plus halogen molecule reaction H + Cl2 → HCl + Cl has implications across many fields. In this paper, product state-resolved quantum dynamics calculations for the vibrationally excited reaction H + Cl2 (v0 = 1-3, j0 = 0) → HCl + Cl were conducted using the time-dependent wave packet method on a newly developed accurate potential energy surface. Numerical results indicate that the initial vibrational excitation of Cl2 does enhance the reactivity for this early barrier reaction, although less than the enhancement of the translational energy. The calculated product vibrational state-resolved integral cross sections and rate constants reveal that the product vibrational state distribution and the initial vibrational state of Cl2 are highly correlated. The thermal rate constant in the temperature range from 100 to 1000 K was given and is found to be in reasonable agreement with the experimental measurements.

State-to-State Quantum Dynamics Study of Intramolecular Isotope Effects on Be(1S) + HD (v0 = 2, j0 = 0) → BeH/BeD + H/D Reaction.

The dynamic mechanisms and intramolecular isotope effects of the Be(1S) + HD (v0 = 2, j0 = 0) → BeH/BeD + H/D reaction are studied at the state-to-state level using the time-dependent wave packet method on a high-quality potential energy surface. This reaction can proceed along the indirect pathway that features a barrier and a deep well or the smooth direct pathway. The reaction probabilities, total and state-resolved integral cross sections, and differential cross sections are analyzed in detail. The calculated dynamics results show that both of the products are mainly formed by the dissociation of a collinear HBeD intermediate when the collision energy is slightly larger than the threshold. As the collision energy increases, the BeH + D channel is dominated by the direct abstraction process, whereas the BeD + H channel mainly follows the complex-forming mechanism.

Quantum State-Resolved Nonadiabatic Dynamics of the H+NaF → Na+HF Reaction

The H + NaF reaction is investigated at the quantum state-resolved level using the time-dependent wave-packet method based on a set of accurate diabatic potential energy surfaces. Oscillatory structures in the total reaction probability indicate the presence of the short-lived intermediate complex, attributed to a shallow potential well and exothermicity. Ro-vibrational state-resolved integral cross sections reveal the inverted population distributions of the product. The HF product favors an angular distribution in the forward hemisphere of 30°–60° within the collision energy range from the threshold to 0.50 eV, which is related to the nonlinear approach of the H atom to the NaF molecule. Quantum generalized deflection functions show that the low-J partial waves contribute primarily to the backward scattering, while the high-J partial waves govern the forward scattering. The correlation between the partial wave J and the scattering angle ϑ proves that the reaction follows a predominant direct reaction mechanism.

A global 2A″ state potential energy surface for the Al (2P) + O2 (Σg−3) → AlO (2Σ+) + O (3P) reaction based on the doubly hybrid functional XYG3

In this paper, a global and full-dimensional potential energy surface at the 2A″ ground state for the Al + O2 → AlO + O reaction was constructed, for the first time, based on extensive electronic structure calculations using the doubly hybrid functional XYG3 and potential energy surface fittings by neural networks. Details of the reaction paths have been analyzed. It was found that both two intermediates, the cyclic-AlO2 and the linear-OAlO, were able to dissociate to the AlO + O products, and the isomerization process between these two intermediates was controlled by conical intersections between two 2A″ states. Ro-vibrational state resolved integral cross sections have also been calculated at collision energies from 1.0 to 10.0 kcal/mol. The results support the harpooning mechanism in this metal-oxidant-involved reaction.

Dynamical studies for the S+ + D2(v0 = 2, j0 = 0) → SD+ + D reaction by time-dependent wave packet

Using time-dependent wave packet method, the dynamics studies of the S+ + D2(v0 = 2, j0 = 0) → SD+ + D reaction were carried out based on the potential energy surface (PES) reported by Zhu et al., (Phys. Chem. Chem. Phys.23 4757–4767 (2021)). The isotope effect is very obvious. When the H atom is replaced by the D atom, the reaction probability at total angular momentum equal to zero has a threshold of about 0.28 eV and it decreases significantly in the collision energy range studied. The total and rovibrational state-resolved integral cross section were reported and the results indicate that the distribution of integral cross section is mainly concentrated in the ground state. The forward biased differential cross sections show that the stripping mechanism due to high total angular momentum plays a dominant role in the reaction.

Revisiting the oscillator strengths and cross sections of atomic neon by fast electron scattering

The generalized oscillator strengths of the valence-shell excitations from the ground state to the 2p5(3s, 3s′, 3p, 3p′, 4s, 4s′) states of atomic neon have been determined by means of fast electron scattering, with an incident electron energy of 1500 eV and an energy resolution of about 80 meV. The adopted relative flow technique improved accuracy of the experimental measurements prominently. The validity condition of the first Born approximation is clarified by comparing the present measured data with previous experimental and theoretical results. We found that the first Born approximation is not applicable for the monopolar transition in the whole momentum transfer region even at the incident electron energy of 1500 eV. However, the high-order Born terms are found dominating only at the minimum for the dipolar transitions. The good agreement of the present extrapolated optical oscillator strengths with previous available data confirms the reliability of the measurement. With the cross-checked generalized oscillator strengths, the state-resolved integral cross sections in a wide collision energy range have been obtained by adopting the BE-scaling method. The analysis of the feasibility of the BE-scaling method demonstrates that the scaling law applies for the typical dipole-allowed transitions while it would overestimate the cross sections for the dipolar transitions with significant dipole-forbidden components. Present data compilation constitutes a benchmark for developing and testing the theoretical methods or computational codes.

Isotopic effects of the N(2D) + H2 → NH + H reaction: a quantum time-dependent wave packet investigation

Based on the potential energy surface reported by Li and co-workers (J. Comput. Chem. 34 1686–1696 (2013)), the dynamics calculations of N(2D) + H2(v 0 = 0, j 0 = 0) reaction and its isotopic variants HD and D2 are studied using time-dependent wave packet method in the collision energy range of 0.01–1.0 eV. Dynamics properties such as reaction probability, differential cross section, and integral cross section are studied at state-to-state level of theory. Present values are compared with available theoretical and experimental results. The results indicate that the integral cross sections of N(2D) + D2 reaction are in general good agreement with the experimental data at collision energy below 0.15 eV. The rotational state-resolved integral cross sections of N(2D) + H2/HD/D2 reactions are compared with experimental values for the first time, with the obtained values being in good agreement with the experimental data.

Theoretical Study of Barrierless Chemical Reactions Involving Nearly Elastic Rebound: The Case of S(1D) + X2, X = H, D.

For some values of the total angular momentum consistent with reaction, the title processes involve nonreactive trajectories proceeding through a single rebound mechanism during which the internal motion of the reagent diatom is nearly unperturbed. When such paths are in a significant amount, the classical reaction probability is found to be markedly lower than the quantum mechanical one. This finding was recently attributed to an unusual quantum effect called diffraction-mediated trapping, and a semiclassical correction was proposed in order to take into account this effect in the classical trajectory method. In the present work, we apply the resulting approach to the calculation of opacity functions as well as total and state-resolved integral cross sections (ICSs) and compare the values obtained with exact quantum ones, most of which are new. As the title reactions proceed through a deep insertion well, mean potential statistical calculations are also presented. Seven values of the collision energy, ranging from 30 to 1127 K, are considered. Two remarkable facts stand out: (i) The corrected classical treatment strongly improves the accuracy of the opacity function as compared to the usual classical treatment. When the entrance transition state is tight, however, those trajectories crossing it with a bending vibrational energy below the zero point energy must be discarded. (ii) The quantum opacity function, particularly its cutoff, is finely reproduced by the statistical approach. Consequently, the total ICS is also very well described by the two previous approximate methods. These, however, do not predict state-resolved ICSs with the same accuracy, proving thereby that (i) one or several genuine quantum effects involved in the dynamics are missed by the corrected classical treatment and (ii) the dynamics are not fully statistical.

Quantum state-to-state dynamics of O+ + H2(ν = 0, j = 0) → OH+ (ν′, j′) + H reaction on a global potential energy surface

The state-to-state quantum dynamics calculation for the reaction is implemented based on a global potential energy surface. The reaction probabilities, state-resolved integral and differential cross sections are obtained and discussed. Due to the existence of the potential well, the reaction probabilities exhibit obvious oscillating features. And as a typical system of heavy-light-light mass combination, this reaction is more conducive to the occurrence of the product rotational excitation. So when the products are mainly concentrated in and states, the distribution of the product rotational, rather than vibrational, state-resolved integral cross section shows an inversion phenomenon. Furthermore, because of the quantum interference of the rovibrational wave functions, the rotational resolution integral cross section of the product displays a multipeak structure, and this phenomenon becomes less obvious as the collision energy increases. Meanwhile, the total differential cross sections are found to be peaked both forwardly and backwardly, which indicates that there exists a complex-forming mechanism in the reaction. With the increase of collision energy, the feature of differential cross section is from the forward-backward scattering to the forward scattering.

State-to-state quantum dynamics of F(2P)+HO(2Π)→O(3P)+HF(1Σ+) reaction on 13A′ and 23A′′ surfaces

ABSTRACTThe state-to-state dynamics of reaction F + HO() is studied on the potential energy surfaces (PESs) of the and states. The time-dependent wave packet method, which is carried out on the graphics processing units, is used for this accurate calculation. The emphasis is on the exploration of different dynamical behaviours happening on the PESs of two excited states. The obvious vibrational and rotational inversion is found in the state-resolved integral cross section on PES, but the rotational inversion does not appear on PES. Both the total and state-resolved differential cross sections (DCSs) of the reaction on two PESs exhibit the behaviour of sideward and backward scattering, but the backward scattering of is much stronger because of its higher energy barrier, and the sideward scattering is enhanced with the increasing of collision energy. In addition, a multi-peak structure is discovered in the distribution of the product rotational state-resolved integral and DCSs, which is attributed to the quantum interference of the resonance wave functions.

State-to-state dynamics of reaction on potential energy surface**Project supported by the National Natural Science Foundation of China (Grant Nos. 11504206 and 11404049), the China Postdoctoral Science Foundation (CPSF) (Grant No. 2014M561259), and the Ph. D. Research Start-up Fund of Shandong Jiaotong University.

State-to-state time-dependent quantum dynamics calculations are carried out to study reaction on ground potential energy surface (PES). The vibrationally resolved reaction probabilities and the total integral cross section agree well with the previous results. Due to the heavy–light–heavy (HLH) system and the large exoergicity, the obvious vibrational inversion is found in a state-resolved integral cross section. The total differential cross section is found to be forward–backward scattering biased with strong oscillations at energy lower than a threshold of 0.10 eV, which is the indication of the indirect complex-forming mechanism. When the collision energy increases to greater than 0.10 eV, the angular distribution of the product becomes a strong forward scattering, and almost all the products are distributed at . This forward-peaked distribution can be attributed to the larger J partial waves and the property of the F atom itself, which make this reaction a direct abstraction process. The state-resolved differential cross sections are basically forward-backward symmetric for , 1, and 2 at a collision energy of 0.07 eV; for a collision energy of 0.30 eV, it changes from backward/sideward scattering to forward peaked as increasing from 0 to 3. These results indicate that the contribution of differential cross sections with more highly vibrational excited states to the total differential cross sections is principal, which further verifies the vibrational inversion in the products.

Analysis of the state-to-state dynamics mechanism of H + HBr (v = 0,1, j = 0) → H2 + Br reaction

The dynamics of the H + HBr(v = 0, 1, j = 0) → H2 + Br reaction was investigated in detail at the state-to-state level on a new ab initio potential energy surface (Y Kurosaki and T Takayanagi, private communication). A newly developed graphics processing unit (GPU)-accelerated time-dependent wave packet program was applied to calculate product vibrational state-resolved integral cross sections and differential cross sections for collision energies ranging from 0.05 eV to 1.4 eV. The reaction mechanism was also fully analyzed with respect to the structures of the differential cross sections. The state specific integral cross section and differential cross section of H + HBr(v = 0, j = 0) is remarkably different from that for H + HBr(v = 1, j = 0).

HD +ortho-/para-H2rotational energy transfer non-reactive scattering at low astrophysical temperatures: 2 K ≲ T ≲ 300 K

State-resolved integral cross sections and corresponding thermal rate coefficients are computed for the HD + ortho -/ para -H 2 rotational energy transfer collision at low temperatures of astrophysical interest: 2 K ≲ T ≲ 300 K. A recent original full-dimensional H 2 -H2 potential energy surface (PES) was adopted and appropriately modified for the current non-symmetrical four-atomic system.

Quantum Dynamics of Li+HF/DF Reaction Investigated by a State-to-State Time-dependent Wave Packet Approach

Using the reactant coordinate based time-dependent wave packet method, on the APW potential energy surface, the differential and integral cross sections of the Li+DF/HF(v=0, j=0, 1) reactions were calculated over the collision energy range from the threshold to 0.25 eV. The initial state-specified reaction rate constants of the title reaction were also calculated. The results indicate that, compared with the Li+DF reaction, the product LiF of Li+HF reaction is a little more rotationally excited but essentially similar. The initial rotational excitation from j=0 to 1 has little effect on the Li+DF reaction. However, the rotational excitation of DF does result in a little more rotationally excited product LiF. The different cross section of both reactions is forward biased in the studied collision energy range, especially at relatively high collision energy. The resonances in the Li+HF reaction may be identifiable as the oscillations in the product ro-vibrational state-resolved integral cross sections and backward scattering as a function of collusion energy. For the Li+HF reaction, the rate constant is not sensitive to the temperature and almost has no change in the temperature range considered. For the Li+DF reaction, the rate constant increase by a factor of about 10 in the temperature range of 100–300 K. Brief comparison for the total reaction probabilities and integral cross section of the Li+HF reaction has been carried out between ours and the values reported previously. The agreement is good, and the difference should come from the better convergence of our present calculations.

Quantum State-to-State Dynamics of the H + LiH → H2 + Li Reaction.

State-to-state quantum dynamics calculations for the H + LiH (v = 0-1, j = 0) → H2 + Li reactions are performed based on an ab initio ground electronic state potential energy surface (PES). Total and product state-resolved integral and differential cross sections and rate constants are calculated. The present total integral cross sections and rate constants for the H + LiH (v = 0, j = 0) reaction are found to be in agreement with previous literature results. Product state-resolved integral cross sections and rate constants reveal that the H2 products are preferred to be formed in their rovibrational excited states. The differential cross sections show that the intensity of forward scattering for the H2 products in their rovibrational excited states is stronger than other states. The mechanisms for the v = 0 and v = 1 reactions are found to be highly consistent with each other. Further, the influence of the stripping mechanism on the H + LiH reaction is studied. It is found that the stripping mechanism could be responsible for the decrease of the reactivity, the product state distribution, and scattering direction of the H2 products. It is related to the "attractive" feature of the underlying PES.

State-to-state quantum dynamics of the N(4S) + H2(X1Σ+) → NH(X3Σ−) + H(2S) reaction and its reaction mechanism analysis**Project supported by the National Natural Science Foundation of China (Grant No. 11074151) and the Natural Science Foundation of Shandong Province, China (Grant No. ZR2014AM022).

Quantum state-to-state dynamics of the N(4S) + H2 (X1Σ+) → NH(X3Σ−) + H(2S) reaction is reported in an accurate novel potential energy surface constructed by Zhai et al. (2011 J. Chem. Phys. 135 104314). The time-dependent wave packet method, which is implemented on graphics processing units, is used to calculate the differential cross sections. The influences of the collision energy on the product state-resolved integral cross sections and total differential cross sections are calculated and discussed. It is found that the products NH are predominated by the backward scattering due to the small impact parameter collisions, with only minor components being forward and sideways scattered, and have an inverted rotational distribution and no inversion in vibrational distributions; both rebound and stripping mechanisms exist in the case of high collision energies.

Quantum state-to-state dynamics for the quenching process of Br(2P1/2) + H2(v i = 0, 1, j i = 0)

Quantum state-to-state dynamics for the quenching process Br((2)P(1/2)) + H(2)(v(i) = 0, 1, j(i) = 0) → Br((2)P(3/2)) + H(2)(v(f), j(f)) has been studied based on two-state model on the recent coupled potential energy surfaces. It was found that the quenching probabilities have some oscillatory structures due to the interference of reflected flux in the Br((2)P(1/2)) + H(2) and Br((2)P(3/2)) + H(2) channels by repulsive potential in the near-resonant electronic-to-vibrational energy transfer process. The final vibrational state resolved integral cross sections were found to be dominated by the quenching process Br((2)P(1/2)) + H(2)(v) → Br((2)P(3/2)) + H(2)(v+1) and the nonadiabatic reaction probabilities for Br((2)P(1/2)) + H(2)(v = 0, 1, j(i) = 0) are quite small, which are consistent with previous theoretical and experimental results. Our calculated total quenching rate constant for Br((2)P(1/2)) + H(2)(v(i) = 0, j(i) = 0) at room temperature is in good agreement with the available experimental data.

Time-dependent wave packet and quasiclassical trajectory study of the C(P3)+OH(X Π2)→CO(X Σ1+)+H(S2) reaction at the state-to-state level

The first calculations of state-to-state reaction probabilities and product state-resolved integral cross sections at selected collision energies (0.05, 0.1, 0.5, and 1.0 eV) for the title reaction on the ab initio potential energy surface of [Zanchet et al. J. Phys. Chem. A 110, 12017 (2006)] with the OH reagent in selected rovibrational states (v = 0-2, j = 0-5) have been carried out by means of the real wave packet (RWP) and quasiclassical trajectory (QCT) methods. State-selected total reaction probabilities have been calculated for total angular momentum J = 0 in a broad range of collision energies. Integral cross sections and state-specific rate coefficients have been obtained from the corresponding J = 0 RWP reaction probabilities for initially selected rovibrational states by means of a capture model. The calculated RWP and QCT state-selected rate coefficients are practically temperature independent. Both RWP and QCT reaction probabilities, integral cross sections, and rate coefficients are almost independent of the initial rotational excitation. The RWP results are found to be in an overall good agreement with the corresponding QCT results. The present results have been compared with earlier wave packet calculations carried out on the same potential energy surface.

Nonadiabatic effects in D + + H 2 and H + + D 2

Using time-dependent nonadiabatic and adiabatic wave packet methods, we investigate nonadiabatic effects in collisions of D +(H +) with H 2(D 2) for collision energies from 1.7 to 2.5 eV. A new accurate diabatic potential energy surface [L.P. Viegas, A. Alijah, A.J.C. Varandas, J. Chem. Phys. 126 (2007) 74309] of the H 3 + system fitted from full multireference configuration interaction calculations with a cc-pV5Z basis set is incorporated into the quantum calculations of initial state resolved integral cross sections. Comparison with previous calculations and experimental measurements are used to give insight on the nonadiabatic charge transfer process and isotope effect.