Time-dependent Wave Packet Method Research Articles

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.

Quantum dynamics study of C—H stretching vibrational excitation in the F+CHD<sub>3</sub> → HF+CD<sub>3</sub> reaction

In recent decades, significant progress has been made in the precise theoretical investigation of gas-phase chemical reactions. Presently, a major challenge in the field of quantum dynamics is to develop the precise methodologies for studying chemical reactions involving more than four atoms. As a typical multi-atomic reaction system, the F+CH<sub>4</sub> reaction and its isotopic substitution reactions have attracted widespread attention from both experimental and theoretical perspectives in recent years. Experimental studies on the reaction of F+CHD<sub>3</sub> have revealed that the stretching vibration excitation of the C—H bond inhibits the bond dissociation, favoring the formation of DF+CHD<sub>2</sub> product channels. In this study, we use a seven-dimensional quantum time-dependent wave packet method to investigate the dynamics of the F+CHD<sub>3</sub> reaction in both the reactant vibrational ground state and the first stretching excited state of the C—H bond. In this work, the reaction probabilities under different vibrational conditions are analyzed, showing that when the collision energy is below 0.06 eV, the reaction probability curves exhibit numerous fast-oscillating peaks, supporting the experimentally suggested phenomena of dynamic resonance. In a collision energy range from 0.06 eV to 0.3 eV, the reaction probability for the HF product channel in the vibrational excited state is lower than that in the ground state, which is consistent with experimental observation. Through the analysis of the time-independent wave functions of product channels under low-energy collision conditions, it is found that for reactions involving vibrational ground states, the HF products in the product asymptotic region and the reaction transition state region are in the <i>v'</i> = 2 excited state and <i>v'</i> = 3 excited state of stretching vibration, respectively, which are consistent with previous experimental observations and six-dimensional quantum wave packet simulations. For reactions involving the first excited state of C—H stretching vibration, the HF products in the product asymptotic region and the reaction transition state region are both in the <i>v'</i> = 3 excited state of stretching vibration, which are consistent with the results obtained based on energy analysis. Simulation results indicate that in the case of low-energy collisions, the time-independent wave function for the C—H stretching vibrational excited state tends to be closer to the D atom side in the transition state region. This phenomenon is attributed to the more significant energy advantage of the vibrational excited state potential energy surface in the large collision angle region, explaining the inhibitory effect of stretching vibration excitation on the HF product channel. This study offers important theoretical support for explaining experimental results and contributes to a more in-depth understanding of the influence of vibrational mode excitations on the dynamical processes in poly-atomic reactions.

Potential energy surface and quantum dynamics calculation of SH2− (2A′) based on ab initio scaled external correlation correction

An accurate interatomic potential energy surface for ground state of SH2− is reported at the multireference configuration interaction level of theory using aug–cc–pVQZ basis set. The calculated ab initio energy points are utilized, after semi-empirically correcting the dynamical correlation by the many-body expansion-scaled external correlation method. To verify the accuracy of the potential energy surface, molecular reaction dynamics, including the relationship between reaction probability and collision energy, thermal rate constant, and integral scattering cross section are calculated by using the quantum time-dependent wave packet method. The final results show that our potential energy surface is accurate and the molecular reaction dynamics results are satisfactory, and the accurate potential energy surface and its dynamics results can also lay a foundation for the future experimental research of SH−-containing molecules.

A new global potential energy surface for the BH2 molecule and dynamics studies of the B(2p2P) + H2 reaction

A new global potential energy surface (PES) for the ground state of the BH2 system was constructed using permutation invariant polynomial neural network. In ab initio calculation, the AVQZ basis set and multi-reference configuration interaction method was used. The topographic features of the new PES were discussed in detail. To further clarify the accuracy of PES, the dynamics studies of the B(2p2P) + H2 reaction were carried out using time-dependent wave packet method. The dynamics properties such as reaction probabilities, integral cross sections, differential cross sections (DCSs) and rate constants were reported. The DCSs indicated that the “complex-forming” reaction mechanism plays a dominant role at low collision energies and the forward abstraction mechanism dominates the reaction at high collision energies.

Analysis of Ca+(2S) + HD (v0 = 0, j0 = 0) → CaH+/CaD+ + D/H reaction dynamics using time-dependent wave packet method

Using the time-dependent wave packet method on a newly reported potential energy surface, the reaction channels of Ca+(2S) + HD (v0 = 0, j0 = 0) → CaH+/CaD+ + D/H were investigated in the collision energy range of 2.3 eV and 4.0 eV. Our analysis commenced with an investigation of the integral and differential scattering cross sections, as well as the reaction probabilities for both reaction channels. The results reveal that the CaH+ + D reaction channel plays a primary role which is consistent with experimental results. The complex forming mechanism and direct-abstraction reaction mechanism exist in this reaction process.

Significant non-adiabatic effects of the K(4s2S) + H2 reaction

The non-adiabatic dynamical calculations of the K(4s2S) + H2(v 0 = 1, 2, j 0 = 0) reaction are carried out using the time-dependent wave packet method. The non-adiabatic dynamics results, such as reaction probabilities and integral cross sections, are calculated and compared with previous adiabatic values. The adiabatic values are several tens of times larger than those of the non-adiabatic results. The non-adiabatic effect becomes stronger with the increase in the number of excited vibrational states. In addition, the excitation of the vibrational states of H2 can increase the reaction probability of the reaction channel. However, the KH product is still barely formed through the K(4s2S) + H2 reaction, even if the H2 molecule is excited to a high vibrational excited state, which also leads to the opposite conclusion from the adiabatic results. The forward-biased differential cross sections indicate that a direct stripping mechanism plays a dominant role in the 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.

Dynamics studies of the Si+(2P) + D2 reaction by using quantum and quasi-classical methods

The dynamics calculations of the Si+ + D2 (v0 = 0, j0 = 0) → SiD+ + D reaction were carried out by using time-dependent quantum wave packet and quasi-classical trajectory methods. The integral cross sections were calculated and compared with the experimental data in the collision energy range from 1.0 to 10.0 eV. The results indicated that present values are in good agreement with the experimental data. In addition, reaction probabilities, the distribution of the SiD+ product and differential cross sections are also calculated. The differential cross section indicated that the “complex-forming” mechanism plays a dominant role in the low collision energy range and the abstraction mechanism dominates the reaction at high collision energies.

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.