Time-dependent Wave Packet Method Research Articles

State-resolved quantum dynamics and reaction mechanisms of the Ne + HD+(v = 1) reaction

In the work, accurate converged theoretical simulations of the Ne + HD + ( v = 1 ) reaction are presented with the time-dependent wave packet (TDWP) method using the accurate potential energy surface by Lv (J. Chem. Phys. 2010, 132, 014303). In particular, the effect of intramolecular substitution and the translational collision energy on the reactive dynamics is investigated in detail to discern the reaction mechanisms. Total and state-to-state integral cross sections (ICSs) and differential cross sections (DCSs) of the two channels are derived and compared over a wide range of collision energies up to 1.2 eV. The analysis of the ICSs in terms of the total angular momentum contributions shows that the contribution of the J partial wave varies in the two reactive channels at different collision energies. The product state-resolved DCSs reveal that two opposite mechanisms co-exist in the two reactive channels with different ratios at low and high collision energies. Overall, NeH + + D channel appears to form the products via collision complex formation, which survives long enough leading to a forward–backward symmetric total DCS at low collision energies. In comparison, the NeD + + H proceeds through a direct stripping reaction, with predominantly forward scattering in the DCSs.

State-to-State Time-Dependent Quantum Dynamics Studies of the Si(3P) + OH(X 2Π) → OSi(X 1Σg+) + H(2S) Reaction Based on a New HOSi(X2A') Potential Energy Surface.

Quantum and quasi-classical dynamics calculations were conducted for the reaction of Si with OH on the latest potential energy surface (PES), which is obtained by fitting tens of thousands of ab initio energy points by using the many-body expansion formula. To obtain an accurate PES, all energy points calculated with aug-cc-pVQZ and aug-cc-pV5Z basis sets were extrapolated to the complete basis set limit. The accuracy of our new PES was verified by comparing the topographic characteristics and contour maps of potential energy with other works. In addition, the anharmonic vibrational frequencies of HOSi and HSiO based on the present ab initio and PES by means of quantum dynamics methods were calculated. Dynamics information such as reaction probability, integral cross sections (ICS), product distribution, and rate constants was obtained on the new HOSi(X2A') PES. The dynamic information calculated using the quasi-classical trajectory method and time-dependent wave packet method is generally in good agreement, except for the vibrational state-resolved ICSs of product. The calculated differential cross section and capture time reveal that the reaction is primarily governed by the complex formation mechanism.

A quantum investigation of kinetic isotope effects in the Ne + HD[formula omitted](v=0) [formula omitted] NeH[formula omitted]/NeD[formula omitted] + D/H reaction

The exact quantum scattering calculations for the Ne + HD+(v = 0, j = 0) reaction on its electronic ground state have been performed using the time-dependent wave packet method at the state-to-state level. The reaction mechanisms and intramolecular isotope effects have been investigated and analyzed in terms of integral reaction cross section, product internal state distributions and differential cross sections in the 0.4–1.2 eV collision energy interval. Results from the present calculations show that the products NeH+ and NeD+ are associated to different values of the total angular momentum, J. Competing reaction mechanisms that correlate with low and high J values show different preferences for products.

Study on Quantum Dynamics of the Na + Na2 Exchanged Reaction and Lifetime Prediction of Na3 Complex Based on the Neural Network Potential Energy Surface.

A high-precision global potential energy surface (PES) is constructed for the Na3 system based on high-level ab initio calculations and the fundamental invariant neural network (FI-NN) method. The root-mean-square error (RMSE) of the PES is 2.88 cm-1. The state-resolved quantum dynamics of the ground-state Na + Na2 (v = 0, j = 0) → Na2 (v', j') + Na reaction is studied using the time-dependent wave packet (TDWP) method on the new PES. Analysis of the relevant integral cross sections revealed a complicated energy-transfer mechanism during collisions. Similarly, the characteristics of the differential cross sections indicate that the complex-forming mechanism plays a dominant role in the reaction, providing conditions for a comprehensive exploration of the lifetimes of the complexes. Based on the Rice-Ramsperger-Kassel-Marcus (RRKM) theory, the calculated lifetime of the Na3 complex is approximately 3.9 ns.

Ab Initio Neural Network Potential Energy Surface and Quantum Dynamics Calculations on Na(2S) + H2 → NaH + H Reaction.

The collisions between Na atoms and H2 molecules are of great significance in the field of chemical reaction dynamics, but the corresponding dynamics results of ground-state reactions have not been reported experimentally or theoretically. Herein, a global and high-precision potential energy surface (PES) of NaH2 (12A') is constructed by the neural network model based on 21,873 high-level ab initio points. On the newly constructed PES, the quantum dynamics calculations on the Na(2S) + H2(v0 = 0, j0 = 0) → NaH + H reaction are carried out using the time-dependent wave packet method to study the microscopic reaction mechanism at the state-to-state level. The calculated results show that the low-vibrational products are mainly formed by the dissociation of the triatomic complex; whereas, the direct reaction process dominates the generation of the products with high-vibrational states. The reaction generally follows the direct H-abstraction process, and there is also the short-lived complex-forming mechanism that occurs when the collision energy exceeds the reaction threshold slightly. The PES could be used to further study the stereodynamics effects of isotope substitution and rovibrational excitations on the title reaction, and the presented dynamics data would provide an important reference on the corresponding experimental research at a higher level.

Non-adiabatic dynamics studies of the C+(2P1/2, 3/2) + H2 reaction: Based on global diabatic potential energy surfaces of CH2.

Global diabatic potential energy surfaces (PESs) of CH2+ are constructed using the neural network method with a specific function based on 18 213 abinitio points. The multi-reference configuration interaction method with the aug-cc-pVQZ basis set is adopted to perform the abinitio calculations. The topographical properties of the diabatic PESs are examined in detail. In general, the diabatic PESs provide an accurate quasi-diabatic representation. To validate the diabatic PESs, the dynamics studies of the C+(2P1/2, 3/2) + H2 (v0 = 0, j0 = 0) → H + CH+(X1Σ+) reaction are performed using the time-dependent wave packet method. The reaction probabilities, integral cross sections, differential cross sections, and rate constants are calculated and compared with the experimental and theoretical results. Non-adiabatic dynamics results are in good agreement with experimental data. In addition, the non-adiabatic effect in the C+(2P1/2, 3/2) + H2 reaction is significant due to the non-adiabatic results being obviously larger than adiabatic values. The reasonable non-adiabatic dynamics results indicate that present diabatic PESs can be recommended for any type of dynamics study.

A Globally Accurate Neural Network Potential Energy Surface and Quantum Dynamics Studies on Be+(2S) + H2/D2 → BeH+/BeD+ + H/D Reactions.

Chemical reactions between Be+ ions and H2 molecules have significance in the fields of ultracold chemistry and astrophysics, but the corresponding dynamics studies on the ground-state reaction have not been reported because of the lack of a global potential energy surface (PES). Herein, a globally accurate ground-state BeH2+ PES is constructed using the neural network model based on 18,657 ab initio points calculated by the multi-reference configuration interaction method with the aug-cc-PVQZ basis set. On the newly constructed PES, the state-to-state quantum dynamics calculations of the Be+(2S) + H2(v0 = 0; j0 = 0) and Be+(2S) + D2(v0 = 0; j0 = 0) reactions are performed using the time-dependent wave packet method. The calculated results suggest that the two reactions are dominated by the complex-forming mechanism and the direct abstraction process at relatively low and high collision energies, respectively, and the isotope substitution has little effect on the reaction dynamics characteristics. The new PES can be used to further study the reaction dynamics of the BeH2+ system, such as the effects of rovibrational excitations and alignment of reactant molecules, and the present dynamics data could provide an important reference for further experimental studies at a finer level.

A Neural Network Potential Energy Surface and Quantum Dynamics Study of Ca(1S) + H2(v 0 = 0, j 0 = 0) → CaH + H Reaction.

The reactive collision between Ca and H2 molecules has attracted great interest experimentally due to the key role of the product CaH molecule in the field of astrophysics and cold molecules. However, quantum dynamics calculations for this system have not been reported due to the lack of a global potential energy surface (PES). Herein, a globally accurate PES of the ground-state CaH2 is developed by combining 11365 high-level ab initio points and permutation invariant polynomial neural network method. Based on the newly constructed PES, the state-to-state quantum dynamics calculations for the Ca(1S) + H2 (v 0 = 0, j 0 = 0) → CaH + H reaction are carried out using the time-dependent wave packet method. The dynamic results reveal that the reaction follows the complex-forming mechanism near the reactive threshold, whereas both the indirect insertion mechanism and direct abstraction mechanism have effects at higher collision energies. The newly constructed PES can be used to further study the influence of isotope substitution, rovibrational excitation, and spatial orientation of reactant molecules on reaction dynamics.

Quantum Dynamics Studies of the Li + Na2 (V = 0, j = 0) → Na + NaLi Reaction on a New Neural Network Potential Energy Surface.

The ultracold reaction offers a unique opportunity to elucidate the intricate microscopic mechanism of chemical reactions, and the Na2Li system serves as a pivotal reaction system in the investigation of ultracold reactions. In this work, a high-precision potential energy surface (PES) of the Na2Li system is constructed based on high-level ab initio energy points and the neural network (NN) method, and a proper asymptotic functional form is adopted for the long-range interaction, which is suitable for the study of cold or ultracold collisions. Based on the new NN PES, the dynamics of the Li + Na2 (v = 0, j = 0) → Na + NaLi reaction are studied in the collision energy range of 10-7 to 80 cm-1. In the high collision energy range of 8 to 80 cm-1, the dynamics of the reaction is studied using the time-dependent wave packet method and the statistical quantum mechanical (SQM) method. Comparing the results of the two methods, it is found that the SQM method provides a rough description of the product ro-vibrational state distribution but overestimates the integral cross-section values. With the decrease of collision energy, the reaction differential cross section gradually changes from forward-backward symmetric scattering to predominant forward scattering. In the low collision energy range from 10-7 to 8 cm-1, the SQM method is used to study the reaction dynamics, and the rate constant in the Wigner threshold region is estimated to be 2.87 × 10-10 cm3/s.

Quantum dynamics of the P(2D) + H2 (X1[formula omitted]) → PH (X3Σ-) + H(2S) reaction

The title reaction is thought to be important for the astronomical PO formation, which may contribute to the generation of bioavailable H3PO3. Using quasi-classical trajectory (QCT) method, the state-specified (v = 0, j = 0) rate constant of this reaction was calculated. The comparison with previous temperature-averaged QCT rate constant shows that the effect of ro-vibrational excitation is relatively small below 2000 K. Then, the time-dependent wave packet (TDWP) method was applied to investigate the quantum reaction mechanisms, obtaining the state-specified (v = 0, j = 0) reaction probability, integral cross sections and rate constants. The number of partial waves and the integral interval of collision energy considered were rigorously tested to ensure the convergence of the TDWP rate constant below 2000 K. The TDWP rate constant agrees better to the latest experimental results at 291 to 685 K than those from the two QCT calculations. Also, the TDWP calculations can produce relatively reliable rate constants at 700 to 2000 K, where the Arrhenius formula fitted by experimental results ignores the temperature dependence of the activation energy. The calculated rate constants are helpful for modelling the phosphorus chemistry and determining the abundances of the P-bearing species in interstellar media (ISM).

A comparative study on adiabatic and nonadiabatic dynamics of the H(2S) + NaH(X1Σ+) reaction

To reveal the influence of nonadiabatic couplings on the H(2S) + NaH(X1Σ+) reaction, a comparative study on adiabatic and nonadiabatic dynamics is conducted by using the time-dependent wave packet method. The dynamics results show that nonadiabatic couplings reduce the reactivity of H2(X1Σg+) forming channel and vibrational state density of the product, while the exchange reaction channel is almost unaffected. Although the nonadiabatic couplings have a great influence on the product state distribution, it has little influence on the scattering direction of the product. For the H2(X1Σg+) forming channels, products tend to forward scattering. For the exchange reaction channel, the NaH(X1Σ+) product exhibits a maximum scattering peak in the backward direction. The study reveals that the effect of nonadiabatic couplings on the ro-vibration distribution of the H2(X1Σg+) forming channel in the H(2S) + NaH(X1Σ+) reaction is significantly different from the effect in the H(2S) + LiH(X1Σ+) reaction.

The influence of stereodynamical control on the nonadiabatic effects in the D + HD (v = 1, j = 2) → D2 + H reaction.

Stereodynamics is a field that studies the influence of the alignment or orientation of colliding partners on the results of collisions. At present, the intersection of nonadiabatic effects and stereodynamics remains to be explored. In this study, we theoretically demonstrate significant stereodynamical effects in the D + HD (v = 1, j = 2) → D2 + H reaction within the collision energy range of 0.01-2.99eV by using the time-dependent wave packet method. It is found that the stereodynamical control not only facilitates the reaction but also allows precise control of the products over a range of different scattering angles. The analysis at the state-to-state level reveals that the nonadiabatic effects are stronger in the parallel configuration than in the perpendicular configuration. By topological approach to separate the two reaction pathways at the conical intersection, the scattering amplitude of the roaming pathway in the parallel configuration is larger than that of the perpendicular configuration, which leads to more dramatic nonadiabatic features in the collision with parallel configuration.

A new global potential energy surface of CaH2 system constructed with neural network method and dynamics studies of the Ca(4s21S) + H2 reaction

A new global potential energy surface (PES) for the ground state of CaH2 system was constructed by using neural network method. This paper provides a comprehensive discussion on the topographical characteristics of the PES and the spectral properties of stationary points. Furthermore, a time-dependent wave packet method was used to perform the dynamics studies on the Ca(4 s2 1S) + H2 reaction based on the newly constructed PES. Some meaningful dynamics results are reported, including reaction probabilities, integral cross sections and differential cross sections. In addition, the reaction mechanism of the Ca(4 s2 1S) + H2 reaction was discussed in detail.

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.

A globally accurate neural network potential energy surface and quantum dynamics study of Mg+(2S) + H2 → MgH+ + H reaction

A globally accurate ground-state MgH2+ potential energy surface (PES) is constructed by neural network method based on 12,056 high-level ab initio points. On the PES, the dynamics calculations of the Mg+(2S) + H2/HD (v0 = 0, j0 = 0) reaction are performed using the time-dependent wave packet method. The branching ratio (MgD+/MgH+) in the Mg+ + HD reaction is much larger than one in most studied collision energies. The dynamics results imply that the title reaction follows the complex-forming mechanism near the threshold, and the direct abstraction process gradually plays the dominant role as the collision energy increases.

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.

Theoretical Development of the Interaction-Asymptotic Region Decomposition Method for Tetratomic Reactive Scattering.

An accurate and efficient time-dependent wave packet method is proposed for solving the product state-resolved reaction probabilities of the tetratomic reactive system. In this method, the entire scattering process is divided into the interaction region and multiple asymptotic regions, sharing the same spirit as the interaction-asymptotic region decomposition (IARD) approach in a triatomic reactive scattering process. The hyperspherical coordinate is adopted in the interaction region, while the corresponding Jacobi coordinate is employed in each asymptotic region. Therefore, in this IARD method, the "coordinate problem", the difficulty of expressing the wave function in the entire region using a single coordinate system, can be effectively avoided, and only a very small number of the grid points (or the basis functions) are required. For the numerical illustration, the typical tetratomic reaction H2 + OH with zero total angular momentum is calculated, and compared with other quantum wave packet methods. Our proposed IARD method for the tetratomic reactive system is much more efficient and accurate.

A time-dependent quantum wavepacket method on stair-shaped grids for reactive scattering using the hyperspherical coordinates

Development of efficient numerical methods for quantum reactive scattering process by using time-dependent quantum wavepacket method is always necessary in the field of quantum chemistry, due to the complexity of the system, and the large computational efforts required. To perform quantum reactive scattering calculation in hyperspherical coordinates, as the hyper-radial (ρ) increases, the potential well along the angular degree of the freedom (χ) becomes narrower and narrower, which thus requires denser and denser grid points for well describing the diatomic vibrational motion. This makes the time dependent wavepacket packet calculations prohibitively difficult using hyperspherical coordinate when the reaction involves long range interaction potential or requires long absorption potential. In this study, we developed a stair-shaped grid based quantum wavepacket method to overcome this difficulty. In this method, the hyper-radial is partitioned into multidomains in the form of a stair-shape. In each domain, different grid point numbers could be applied for the angular degree of the freedom (χ). In this way, the computational effort could be saved. For numerical example, the stair-shaped grid based quantum wavepacket method is applied to compute the total reaction probability of the F+HCl (v0,j0)→ HF+Cl reaction , which involves long range interaction potential. The results are compared with those calculated with the reactant coordinate-based (RCB) Jacobi coordinate and Interaction Asymptotic Region Decomposition (IARD) method.

A neural network potential energy surface of the Li3 system and quantum dynamics studies for the 7Li + 6Li2 → 6Li7Li + 6Li reaction.

A high-precision global potential energy surface (PES) of the Li3 system is constructed based on high-level ab initio calculations, and the root-mean-square error is 5.54 cm-1. The short-range of the PES is fitted by the fundamental invariant neural network (FI-NN) method, while the long-range uses a function with an accurate asymptotic potential energy form, and the two regions are connected by a switching function. Based on the new PES, the statistical quantum-mechanical (SQM) and the time-dependent wave packet (TDWP) methods are used to study the dynamics of 7Li + 6Li2 (v = 0, j = 0) → 6Li7Li + 6Li reactions in the low collision energy region (10-11 to 10-3 cm-1) and the high collision energy region (8 to 800 cm-1), respectively. In the high collision energy region, the calculation results of the SQM method and the TDWP method are inconsistent, indicating that the reaction dynamics does not follow the statistical behavior in the high collision energy region. In addition, we found that the Coriolis coupling effect plays an important role in this reaction. The symmetric forward-backward scattering in the total DCS indicates that the reaction follows the complex-forming reaction mechanism.