Time-dependent Wave Packet Method Research Articles

The dynamic studies of the C+ + HD reaction using the time-dependent wave packet method

The dynamic calculations of the C+ + HD (v 0 = 0, j 0 = 0) → D/H + CH+/CD+ reaction in the collision energy range of 0.001–1.80 eV are carried out by using a time-dependent wave packet. The intramolecular isotope effect of the C+ + HD reaction is discussed in detail. Some meaningful dynamic properties of the C+ + HD reaction are reported and compared with available theoretical and experimental results. The results indicated that present values are, in general, in better agreement with experimental data than previous theoretical reports. However, due to the lack of consideration of rotational excitation of reactant and non-adiabatic effect, the present results are always smaller than the experimental results. Differential cross-sections of the D + CH+ and H + CD+ product channels exhibit forward–backward symmetric behaviour, which indicates that the ‘complex-forming’ mechanism plays a dominant role in the reaction. Highlights The dynamic calculations of the C+ + HD (v 0 = 0, j 0 = 0) → D/H + CH+/CD+ reaction are performed using a time-dependent wave packet method based on the newly reported potential energy surface. The dynamicl properties, such as integral cross-sections, rate constants, etc., are calculated and compared with previous theoretical and experimental results. The rovibrational state distributions of the product are reported.

Reaction dynamics of P(4S) + O2(X3Σ−g) → O(3P) + PO(X2Π) on a global CHIPR potential energy surface of PO2(X2A1): implications for atmospheric modelling

Abstract. The reaction dynamics of P(4S) + O2(X3Σg-) → O(3P) + PO(X2Π) are thought to be important in atmospheric and interstellar chemistry. Based on the state-of-the-art ab initio energy points, we analytically constructed a global potential energy surface (PES) for the ground-state PO2(X2A1) using the combined-hyperbolic-inverse-power-representation (CHIPR) method. A total of 6471 energy points were computed by the multireference configuration interaction method with the Davidson correction and aug-cc-pV5Z basis set. The analytical CHIPR PES reproduces ab initio energies accurately with a root-mean-square deviation of 91.5 cm−1 (or 0.262 kcal mol−1). The strongly bound valence region of the PES has complicated topographical features with multiple potential wells and barriers. The attributes of the important intermediates are carefully validated with our geometry optimization results, as well as previous experimental and computational results. Finally, the reaction probability, integral cross sections, and rate constants for P(4S) + O2(X3Σg-) → O(3P) + PO(X2Π) are calculated using the quasi-classical trajectory and time-dependent wave packet methods. The trends of probability and integral cross section versus the collision energy can be divided into three stages, which are governed by the entrance barriers or exothermicity of the reaction. The rate constant demonstrates strong Arrhenius linear behaviour at relatively low temperatures but deviates from this pattern at high temperatures. The calculated cross sections and rate constants are helpful for modelling the phosphorus chemistry in atmospheric and interstellar media.

Non-adiabatic dynamical studies of the Rb(52P) + H2(X1[formula omitted]) → RbH(X1Σ+) + H(2s) reaction based on new diabatic potential energy surfaces

The reaction of Rb(52P) atom with H2 molecule is studied using time-dependent wave packet method based on the newly reported diabatic potential energy surfaces. The dynamics properties such as reaction probabilities, integral cross sections, differential cross sections (DCSs) and so on are calculated at state-to-state level of theory. In addition, the effect of vibrational excitation of reactant is considered in the calculations. The results indicate that the vibrational excitation of reactant can significantly increase the reaction probability and the RbH molecule is hardly formed when the reactant H2 molecule is in the ground state. The vibrational excitation of H2 molecule promotes the reaction more effectively than translational energy. The forward biased DCSs indicate that the stripping mechanism dominates the reaction.

High-Energy Quantum Dynamics of the 15N + o-14N14N Rovibrational Activation and Isotope Exchange Processes.

We report full quantum reaction probabilities, computed within the framework of time-independent quantum mechanics using hyperspherical coordinates, for the 15N + 14N14N inelastic and reactive collision processes, restricted to total angular momentum J = 0, for kinetic energies up to 4.5 eV. We take advantage of the nonzero (i = 1) nuclear spin of 14N, leading to the existence of two nuclear spin isomers of 14N14N, namely, ortho- and para-14N14N, to restrict the study to the ortho molecular nitrogen species, with even rotational quantum number j = 0, 2, ... states. Specifically, we start with diatomic reagents ortho-14N14N in the initial rotational state j = 0. A comparison with similar works previously published by other groups using time-dependent wave packet and quasi-classical trajectory methods for the 14N + 14N14N fully symmetric collision is given. We find that reactive processes 15N + 14N14N involving atom exchange do not happen for collision energies less than 2.2 eV. Collisions at energies of around 2.0 eV are most effective for populating reactants' rovibrational states, that is, for inelastic scattering, whereas those at energies close to 5.0 eV yield a newly formed 14N15N isotopologue in a wide variety of excited vibrational levels.

A time-dependent quantum approach to dissociative recombination, associative ionization, and Penning ionization.

A time-dependent wave packet method is introduced for calculating the integral and differential cross sections for the dissociative recombination (DR), associative ionization (AI), and Penning ionization (PI) processes. This method is demonstrated for DR/AI of the N + O ↔ NO+ + e- system and PI for the He* + Ar → He + Ar+ + e- system. Good agreement with previous theoretical and experimental results is obtained for these DR, AI, and PI processes. This method has the potential to provide a quantitative characterization of polyatomic ionization-involved processes on multidimensional potential energy surfaces.

An accurate many-body expansion potential energy surface for HO2 (X 2A″) by extrapolation to the complete basis set limit and quantum dynamics of the related reaction O(3P) + OH(2Π)

A new global many-body expansion potential energy surface (PES) for the ground electronic state of HO2 is constructed. All ab initio energy points are employed using aug-cc-pV(Q+ d)Z and aug-cc-pV(5+ d)Z basis sets at the multi-reference conformational interaction level and then extrapolated to the complete basis set limit. The topographic characteristics of the global PES for HO2 (X 2A″) are discussed in detail and compared with experimental results, showing good agreement. We subsequently consider the O(3P) + OH(2Π) → O2(3 ) + H(2S) reaction using the time-dependent wave packet method and calculate dynamics behaviors, including the vibration–rotation distribution and reaction probabilities. The results indicate that the new PES is suitable for dynamics investigations of O(3P) + OH(2Π) → O2(3 ) + H(2S) and can be used as a component for PESs to construct larger oxygen/hydrogen containing systems.

Dynamics of C(3P) + OH(X 2Π) reaction on the new global HCO(X2A') potential energy surface.

A precise analytical potential energy surface (PES) of HCO(X2A') is fitted from a great quantity of abinitio energy points computed with the multi-reference configuration interaction method and aug-cc-pV(Q/5)Z basis sets. The whole energy points extrapolated to the complete basis set limit are fitted by the many-body expansion formula. The calculated topographic characteristics are analyzed and compared with the existing work to prove the precision of the present HCO(X2A') PES. By utilizing the time-dependent wave packet and quasi-classical trajectory methods, the reaction probabilities, integral cross sections, and rate constants are computed. The results are compared in detail with the former results carried out on the other PES. Moreover, the provided information on stereodynamics leads to an in-depth understanding of the role of collision energy in product distribution.

Globally Accurate Gaussian Process Potential Energy Surface and Quantum Dynamics Studies on the Li(2S) + Na2 → LiNa + Na Reaction at Low Collision Energies.

The LiNa2 reactive system has recently received great attention in the experimental study of ultracold chemical reactions, but the corresponding theoretical calculations have not been carried out. Here, we report the first globally accurate ground-state LiNa2 potential energy surface (PES) using a Gaussian process model based on only 1776 actively selected high-level ab initio training points. The constructed PES had high precision and strong generalization capability. On the new PES, the quantum dynamics calculations on the Li(2S) + Na2(v = 0, j = 0) → LiNa + Na reaction were carried out in the 0.001-0.01 eV collision energy range using an improved time-dependent wave packet method. The calculated results indicate that this reaction is dominated by a complex-forming mechanism at low collision energies. The presented dynamics data provide guidance for experimental research, and the newly constructed PES could be further used for ultracold reaction dynamics calculations on this reactive system.

The state-to-state dynamics of the N + NH(3Σ−) → N2(X1 Σg +) + H reaction: based on a new global potential energy surface

A new global potential energy surface (PES) of the ground state of the HN2 system is built using the neural network method. The aug-cc-pVQZ basis set for the H atom, cc-pwCVQZ basis set for the N atom and multi-reference configuration interaction method are employed in the ab initio calculations. The topographic features of the PES are discussed and compared with available theoretical studies. In addition, the initial state (v 0 = 0, j 0 = 0) dynamic studies of the N + NH(3Σ−) → N2(X1 ) + H reaction are performed using a time-dependent wave packet method, based on the newly constructed PES. The dynamics properties, such as reaction probabilities, integral cross-sections, differential cross-sections, the rovibrational state distribution of product and rate constants, are calculated at the state-to-state level of theory and compared with available theoretical and experimental results. The differential cross-section indicates that the forward abstraction mechanism dominates the reaction with the increase of collision energy. Highlights A new global potential energy surface of the ground state of the HN2 system was constructed using the neural network method. Quantum state-resolved dynamical calculations for the N + NH(3Σ−)(v 0 = 0, j 0 = 0) → N2(X1 ) + H reaction were carried out using a time-dependent wave packet method based on the newly constructed potential energy surface. Some meaningful dynamic properties were reported and compared with available theoretical and experimental data.

The impact of non-adiabatic effects on reaction dynamics: a study based on the adiabatic and non-adiabatic potential energy surfaces of CaH2.

The two-state non-adiabatic potential energy matrices of the CaH2+ system are calculated via a diabatization approach by using a neural network model. Subsequently, the adiabatic and non-adiabatic potential energy surfaces (PESs) are constructed based on these non-adiabatic potential energy matrices. Furthermore, based on the adiabatic and non-adiabatic PESs, the Ca+(4s2S) + H2(X1Σ+g) → H(2S) + CaH+(X1Σ+) reaction is studied using the time-dependent wave packet method. Comparative analysis of the experimental and theoretical integral reaction cross-sections (ICSs) indicates that the maximum deviation between the results obtained from the adiabatic PES and the corresponding experimental value is 12.7 bohr2; in contrast, the maximum discrepancy between the theoretical result derived from the non-adiabatic PES and the experimental value is merely 0.42 bohr2. The potential well along the reaction path acts as a 'filter', selectively guiding intermediates with longer lifetimes in the potential well back to the reactant channel. This phenomenon indicates that the non-adiabatic effects significantly influence the reaction dynamics of the CaH2+ system.

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.

Comparative study of the H and D abstraction in the H + CH3D reaction with a ten-dimensional quantum dynamics model.

The mode selectivity in the prototypical H + CH3D reaction is investigated by the initial state selected time-dependent wave packet method within a ten-dimensional quantum dynamics model. The model is a novel reduced dimensional model for the X + YCZ3 reaction, which allows the CZ3 to break C3V symmetry. The calculated reaction probabilities initially from different reactant vibrational states show that the CH3 stretching modes excitations obviously promote the H-abstraction reaction but have a slight influence on the D-abstraction reaction. In contrast, the CD stretching mode excitation significantly enhances the D-abstraction reaction. For both H- and D-abstraction reactions, the excitation of either the CH3 umbrella bending mode or the CH3 rocking mode shows a promotional effect on the reactivity, while fundamental excitation of the CH3 bending mode has a negligible effect. Impressively, the first-overtone excitation of CH3 bending mode remarkably promotes the H-abstraction reaction, resulting from the 1:2 Fermi coupling between the CH3 symmetric stretching mode and the first overtone of CH3 bending mode. In addition, translational energy is more efficient than vibrational energy in promoting the H-abstraction reaction at low energy, while vibrational energy becomes more efficient for the D-abstraction reaction.

An analytic global potential energy surface of the CsH2 system and the dynamic calculations of the H + CsH reaction

ABSTRACT Based on 17,326 ab initio points, a global potential energy surface (PES) of the ground state of the CsH2 system was constructed using the neural network method. In ab initio calculations, the AVQZ basis set was used for the H atom, the def2-QZVP basis set was adopted for the Cs atom, and a multi-reference configuration interaction method was employed. The topographical characteristics of the newly developed PES were discussed in detail and no wells or barriers were detected. In addition, the dynamical calculations of the H + CsH reaction were performed using the time-dependent wave packet method, based on the new PES. Dynamics properties, such as reaction probability, integral cross section and differential cross-section were examined. The differential cross-section results indicated that the forward abstraction mechanism dominated the abstraction channel, and the ‘rebound' reaction mechanism played a primary role in the exchange channel. Highlights Using the PIP-NN method, A global potential energy surface for the ground state of the CsH2 system was built based on 17,326 ab initio points. Dynamic calculations for the abstraction and exchange channels of the H + CsH reaction were performed using the time-dependent wave packet method and the dynamic properties of these two channels were discussed in detail. The direct abstraction mechanism plays a dominant role in the abstraction channel and the ‘rebound' mechanism dominates the exchange channel.

State-to-state dynamics of the C+(2P) + SH(X2Π) → H(2S) + CS+(X2Σ+) reaction using a time-dependent wave packet and quasi-classical trajectory methods

The time-dependent quantum wave packet (TDWP) and quasi-classical trajectory (QCT) are the basic research methods of reaction dynamics. Utilizing these two methods, the total reaction probability (J = 0), integral cross section (ICS), and rate parameter for the C+(2P) + SH(X2Π)(v = 0, 1, 2, 3) → H(2S) + CS+(X2Σ+) reactions are calculated on an accurate potential energy surface [Zhang et al. Phys. Chem. Chem. Phys. 2022, 24, 1007]. The results of QCT are slightly different from those of the TDWP in value, but the trend is consistent. They are also weakly dependent on the initial vibrational excitation of SH. The state-to-state reaction probability and ICS at fixed collision energies (0.1, 0.3, 0.5, and 0.7 eV) are first calculated using QCT methods. It is hoped that our work can attract experimentalists to study the dynamics of this interesting but rarely discussed system.

Correction: Umer et al. High Order Split Operators for the Time-Dependent Wavepacket method of Triatomic Reactive Scattering in Hyperspherical Coordinates. Entropy 2019, 21, 979

The authors would like to update the affiliations for Umair Umer and Syed Kazim Usman in the published publication [...]

Effect of the reactant vibration on quantum dynamics of the reaction H + CH(v = 0,1,2, j = 0) → H2 + C based on a new CH2(X3A″) potential energy surface

Based on the new ab initio potential energy surface of CH2 (X3A″) system, the influence of the reactant vibration on the H + CH → H2 + C reaction has been studied by using quantum time-dependent wave packet method. The results show that for the collision energy lower than 0.47 eV, the vibrational excitation of reactants inhibits the abstraction reaction H + CH → H2 + C, but promotes the exchange reaction H + CH → HC + H. In addition, the vibrational excitation of reactants has also a certain influence on the Coriolis coupling effect. Finally, because of the wider collision energy range (0.010–1.0 eV) in CC and QCT calculations in this work, the calculated reaction rate constants of H + CH(v = 0, j = 0) → H2 + C reaction in the temperature range of 1500–2000 K are much closer to the experimental center value than the existing theoretical results, which shows that the calculation results in this work are more reasonable and accurate.

State-to-state dynamical studies of the C+ + H2(v = 0, j = 0) → CH+ + H reaction using time-dependent wave packet method

The quantum state-resolved dynamics studies of the C+ + H2(v = 0, j = 0) → CH+ + H reaction were carried out using time-dependent wave packet method based on the potential energy surface (PES) reported by Li et al. The dynamics properties such as reaction probability, integral cross section, differential cross section, the rovibrational state distribution of product and rate constant were calculated and compared with available theoretical and experimental values. The results indicated that present values are in general good agreement with the experimental data. The forward–backward symmetry scattering signals shows that the “complex-forming” reaction mechanism dominates the title reaction. The rate constants of the initial state (v = 0, j = 0) were studied in the temperature range from 10 to 5000 K. The results indicated that the rate constant sharply increases with the increase of temperature.

Electronically Nonadiabatic Effects on the Quantum Dynamics of the Ha + BeHb+ → Be+ + HaHb; Hb + BeHa+ Reactions.

Nonadiabatic effects are ubiquitous and play an important role in many chemical processes. Here, the adiabatic and nonadiabatic quantum scattering calculations of the H + BeH+ reaction are performed using the time-dependent wave packet method based on an accurate diabatic potential energy matrix that includes the lowest two electronic states and their couplings. The resulting integral cross sections reveal that the nonadiabatic effect significantly inhibits the reactivity of the BeH+-depletion channel but enhances that of the H-exchange channel. The vibrational excitation is suppressed, but the translational excitation is promoted for the H2 product in the BeH+-depletion channel when the nonadiabatic coupling is included. However, the nonadiabatic coupling has a mild effect on the H-exchange product-state distribution. When the nonadiabatic effect is considered, the differential cross sections of the H2 product become less polarized because of the formation of an excited-state complex, whereas the corresponding results of the H-exchange channel only present an increase in the magnitude at the backward region.

Full quantum time-dependent simulations for the two-body breakups of H2Ar2+ and N2Ar2+

We developed a full quantum time-dependent wave-packet evolution method to simulate the multibody breakups of polyatomic molecular ions. The interaction picture theory was used to propagate the wave packet, where the effects of strong and long-range interactions are considered by basis functions and the weak and short-range interactions are included in the perturbation term. In this method, the Coulomb interactions, polycentric interactions, vibration-rotation coupling of molecular fragments, and the rotation-rotation coupling between molecular fragment and parent molecule are considered accurately. Using this method, we simulate the two-body breakups of ${\mathrm{H}}_{2}{\mathrm{Ar}}^{2+}$ and ${\mathrm{N}}_{2}{\mathrm{Ar}}^{2+}$. The simulated results show that the ultrafast rotation of the molecular fragment generally exists in the breakup of the polyatomic molecular ion. For ${\mathrm{H}}_{2}{\mathrm{Ar}}^{2+}, {\mathrm{H}}_{2}^{+}$ can rotate from an initial broad distribution around ${35}^{\ensuremath{\circ}}$ and ${145}^{\ensuremath{\circ}}$ to a narrow distribution around ${75}^{\ensuremath{\circ}}$ and ${105}^{\ensuremath{\circ}}$ within 30 fs. For ${\mathrm{N}}_{2}{\mathrm{Ar}}^{2+}$, the initial sine-shaped angular distribution ($j$ = 0) shrinks to a narrow range (${90}^{\ensuremath{\circ}}\ifmmode\pm\else\textpm\fi{}{20}^{\ensuremath{\circ}}$) within 120 fs and then spreads to an approximately random distribution within 300 fs. Such ultrafast rotations are dominated by the polycentric interaction between fragments and impacted by the vibration-rotation and rotation-rotation couplings.

The quenching processes of the Na(3p) + H2 → Na(3s) + H2 reaction studied using the time-dependent wave packet method

The quenching reaction Na(3p) + H2 → Na(3s) + H2 calculations were performed using the time-dependent wave packet method based on the nonadiabatic potential energy surface (PES) reported by Wang et al. The dynamical properties, such as reaction probability, integral cross-section and rate constants, are calculated at the state-to-state level of theory and compared with the reaction and non-reaction processes. The results indicated that the potential well on the V 22 PES has a great influence on the oscillation structures on the reaction probability. In addition, the vibrational state-resolved reaction probability and integral cross-section show that the products are mainly distributed in the vibrationally excited state of Na(3s) + H2 (v′ = 3). The quenching efficiency increases slightly with the increase of temperature. Highlights The quenching reaction Na(3p) + H2 → Na(3s) + H2 is studied using the quantum mechanical method, and the dynamics properties, such as reaction probability, integral cross-section and rate constant, are reported. The oscillation structures on the reaction probability curves are analysed in detail. The vibrational state distribution of the product is reported.