Time-dependent Wave Packet Calculations Research Articles

Construction of diabatic potential energy surfaces for the SiH2+ system and dynamics studies of the Si+(2P1/2, 3/2) + H2 reaction.

The construction of diabatic potential energy surfaces (PESs) for the SiH2+ system, related to the ground (12A') and excited states (22A'), has been successfully achieved. This was accomplished by utilizing high-level abinitio energy points, employing a neural network fitting method in conjunction with a specifically designed function. The newly constructed diabatic PESs are carefully examined for dynamics calculations of the Si+(2P1/2, 3/2) + H2 reaction. Through time-dependent quantum wave packet calculations, the reaction probabilities, integral cross sections (ICSs), and differential cross sections (DCSs) of the Si+(2P1/2, 3/2) + H2 reaction were reported. The dynamics results indicate that the total ICS is in excellent agreement with experimental data within the collision energy range studied. The results also indicate that the SiH+ ion is hardly formed via the Si+(2P3/2) + H2 reaction. The results from the DCSs suggest that the "complex-forming" reaction mechanism predominates in the low collision energy region. Conversely, the forward abstraction reaction mechanism is dominant in the high collision energy region.

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).

Bond-selective effect for the dissociative chemisorption of HOD on the Ni(100) surface revealed at the full-dimensional quantum dynamical level.

We present a comprehensive investigation into the dissociative chemisorption of HOD on a rigid Ni(100) surface using an approximate full-dimensional (9D) quantum dynamics approach, which was based on the time-dependent wave-packet calculations on a full-dimensional potential energy surface obtained through neural network fitting to density functional theory energy points. The approximate-9D probabilities were computed by averaging the seven-dimensional (7D) site-specific dissociation probabilities across six impact sites with appropriate relative weights. Our results uncover a distinctive bond-selective effect, demonstrating that the vibrational excitation of a specific bond substantially enhances the cleavage of that excited bond. The product branching ratios are substantially influenced by which bond undergoes excitation, exhibiting a clear preference for the product formed through the cleavage of the excited bond over the alternative product.

Coupled 3D (J ≥ 0) Time-Dependent Wave Packet Calculation for the F + H2 Reaction on Accurate Ab Initio Multi-State Diabatic Potential Energy Surfaces.

We had calculated adiabatic potential energy surfaces (PESs), nonadiabatic, and spin-orbit (SO) coupling terms among the lowest three electronic states (12A', 22A', and 12A″) of the F + H2 system using the multireference configuration interaction (MRCI) level of theory, and the adiabatic-to-diabatic transformation equations were solved to formulate the diabatic Hamiltonian matrix [J. Chem. Phys. 2020, 153, 174301] for the entire region of the nuclear configuration space. The accuracy of such diabatic PESs is explored by performing scattering calculations to evaluate integral cross sections (ICSs) and rate constants. The nonadiabatic and SO effects are studied by utilizing coupled 3D time-dependent wave packet formalism with zero and nonzero total angular momentum on multiple adiabatic/diabatic surfaces calculation. We depict the convergence profiles of reaction probabilities for the reactive as well as nonreactive processes on various electronic states at different collision energies with respect to total angular momentum including all helicity quantum numbers. Finally, total ICSs are calculated as functions of collision energies for the initial rovibrational state (v = 0, j = 0) of the H2 molecule along with the temperature-dependent rate coefficient, where those quantities are compared with previous theoretical and experimental results.

Dynamics and energetics of the K([formula omitted]) + H[formula omitted] ([formula omitted]) reaction: Significance of orientational and (ro)vibrational contribution

The significance of orientational and (ro)vibrational excitations on the K(2S) + H2 (X1Σg+) reaction dynamics is presented here by performing the exact time-dependent wavepacket calculations using the Coriolis coupling (CC) approach. Employing the new accurate ab initio ground electronic surface 1 2A′ reported by Yuan et al. (2018), the dynamical quantities such as integral cross sections and thermal rate constants are computed within the CC and CS (centrifugal sudden) methods. All partial wave contributions of J (total angular momentum) up to 90 are required to get the convergence in dynamical results up to the collision energy of 3.5 eV. The present study attests that the ground and first vibrational level dynamics is insignificant. For v=2, the reaction probability is monotonically increasing, followed by the onset noted near 1.25 eV, as a function of collision energy up to 3.5 eV. Further, the kinematic effects (replacing H by D atom) on the title system is also performed and found that the KH product formation is more favored than the KD product via HD depletion path.

Six-dimensional quantum dynamics study for the dissociative chemisorption of H2 on pure and alloyed AgAu surfaces.

The 6D time-dependent wave packet calculations were performed to explore H2 dissociation on Ag, Au, and two AgAu alloy surfaces, using four newly fitted potential energy surfaces based on the neural network fitting to density functional theory energy points. The ligand effect resulting from the Ag-Au interaction causes a reduction in the barrier height for H2+Ag/Au(111) compared to H2+Ag(111). However, the scenario is reversed for H2+Au/Ag(111) and H2+Au(111). The 6D dissociation probabilities of H2 on Ag/Au(111) surfaces are significantly higher than those on the pure Ag(111) surface, but the corresponding results for H2 on Au/Ag(111) surfaces are substantially lower than those on the pure Au(111) surface. The reactivity of H2 on Au(111) is larger than that on Ag(111), despite Ag(111) having a slightly lower static barrier height. This can be attributed to the exceptionally small dissociation probabilities at the hcp and fcc regions, which are at least 100 times smaller compared to those at the bridge or top site for H2+Ag(111). Due to the late barrier being more pronounced, the vibrational excitation of H2 on Ag(111) is more effective in promoting the reaction than on Au(111). Moreover, a high degree of alignment dependence is detected for the four reactions, where the H2 dissociation has the highest probability at the helicopter alignment, as opposed to the cartwheel alignment.

Reaction dynamics of C(3P) + Si2(X $^{3}\Sigma ^-_g$ ) → Si(3P) + SiC(X 3Π) on a global CHIPR potential energy surface of the ground state Si2C(X 1A1)

ABSTRACT The dynamics of C(3P) + Si2(X $^{3}\Sigma ^-_g$ ) → Si(3P) + SiC(X 3Π) on its ground state Si2C(X 1A1) are of great significance in carbon-rich interstellar chemistry. Using the combined-hyperbolic-inverse-power-representation method, we construct the first global potential energy surface (PES) for the electronic ground state Si2C(X 1A1) based on a total of 4080 ab initio energy points, which are obtained at the Davidson-corrected internally contracted multireference configuration interaction level of theory. The topographical features of the newly constructed PES are examined in detail and show good agreement with previous theoretical and experimental studies. Finally, we investigate the C(3P) + Si2(X $^{3}\Sigma ^-_g$ ) → Si(3P) + SiC(X 3Π) reaction using the quasi-classical trajectory and time-dependent wave packet calculations, yielding reasonable integral cross sections and rate constants, which are expected to be useful for astrochemical modelling in carbon-rich interstellar environments.

A neural network potential energy surface for the Li + LiNa → Li2 + Na reaction and quantum dynamics study from ultracold to thermal energies.

An improved fundamental invariant neural network (FI-NN) approach for representing a potential energy surface (PES) involving permutation symmetry is introduced in this work. In this approach, FIs are regarded as symmetric neurons, thus avoiding complex preprocessing of training set data, especially when the training set contains gradient data. In this work, the improved FI-NN method, combined with simultaneous fitting of the energy and gradient strategy, is used for constructing a global accurate PES of a Li2Na system (root-mean-square error of 12.20 cm-1). The potential energies and the corresponding gradients are calculated by a UCCSD(T) method with effective core potentials. Based on the new PES, the vibrational energy levels and the corresponding wave functions of Li2Na molecules are calculated using an accurate quantum mechanics method. To accurately describe the cold or ultracold reaction dynamics of the Li + LiNa(v = 0, j = 0) → Li2(v', j') + Na reaction, the long-range region of the PES in both the reactant and product asymptotes is represented by an asymptotically correct form. A statistical quantum model (SQM) is used to study the dynamics of the ultracold Li + LiNa reaction. The calculated results are in good agreement with the exact quantum dynamics results (B. K. Kendrick, J. Chem. Phys., 2021, 154, 124303), which indicates that the dynamics of the ultracold Li + LiNa reaction can be well described by the SQM approach. The time-dependent wave packet calculations are performed for the Li + LiNa reaction at thermal energies, and the characteristic of differential cross-sections confirms that the reaction follows the complex-forming reaction mechanism.

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.

Accurate time-dependent wave packet calculation for the reaction of Al(2P) + H2[formula omitted] on the AlH2(12A′) surface

The time-dependent wave packet calculation of the Al(2P) + H2X1∑g+ → H(2S) + AlHX1∑+(X1Σ+) reaction is studied on the precise global potential energy surface of AlH2(12A′). The collision energy dependence of reaction probabilities under different total angular momentum is discussed detailedly. The emphasis is on the exploration of different dynamical behaviors calculated by Coriolis coupling and centrifugal sudden approximation, which makes integral scattering cross section calculated by Coriolis coupling has a smaller oscillation intensity clearly. Moreover, the reaction is enhanced strongly by vibration excitation of H2 molecule but only weakly by rotation excitation due to the late barrier.

A globally accurate potential energy surface and quantum dynamics calculations on the Be(1S) + H2(v0 = 0, j0 = 0) → BeH + H reaction

The reactive collision between Be atom and H2 molecule has received great interest both experimentally and theoretically due to its significant role in hydrogen storage, astrophysics, quantum chemistry and other fields, but the corresponding dynamics calculations have not been reported. Herein, a globally accurate ground-state BeH2 PES is represented using the neural network strategy based on 12371 high-level ab initio points. On this newly constructed PES, the quantum time-dependent wave packet calculations on the Be(1S) + H2(v0 = 0, j0 = 0) → BeH + H reaction are performed to study the microscopic dynamics mechanisms. The calculated results indicate that this reaction follows the complex-forming mechanism near the reactive threshold, whereas a direct H-abstraction process gradually plays the dominant role when the collision energy is large enough. The newly constructed PES can be used for further dynamics calculations on the BeH2 reactive system, such as the rovibrational excitations and isotopic substitutions of the H2 molecule, and the presented dynamics data would be of importance in experimental research at a finer level.

State-to-state integral cross sections and rate constants for the N+(3P)+HD→NH+/ND++D/H reaction: Accurate quantum dynamics studies

The reactive collisions of nitrogen ion with hydrogen and its isotopic variations have great significance in the field of astrophysics. Herein, the state-to-state quantum time-dependent wave packet calculations of N+(3P) + HD → NH+/ND+ + D/H reaction are carried out based on the recently developed potential energy surface [Phys. Chem. Chem. Phys. 21 22203 (2019)]. The integral cross sections (ICSs) and rate coefficients of both channels are precisely determined at the state-to-state level. The results of total ICSs and rate coefficients present a dramatic preference on the ND+ product over the NH+ product, conforming to the long-lived complex-forming mechanism. Product state-resolved ICSs indicate that both the product molecules are difficult to excite to higher vibrational states, and the ND+ product has a hotter rotational state distribution. Moreover, the integral cross sections and rate coefficients are precisely determined at the state-to-state level and insights are provided about the differences between the two channels. The present results would provide an important reference for the further experimental studies at the finer level for this interstellar chemical reaction. The datasets presented in this paper, including the ICSs and rate coefficients of the two products for the title reaction, are openly available at https://www.doi.org/10.57760/sciencedb.j00113.00034.

Extracting photoelectron spectra from the time-dependent wave function. II. Validation of two methods: Projection on plane waves and time-dependent surface flux

Extraction of the photoelectron spectrum (PES) from the time-dependent wave-packet calculations is a fundamental requirement for studying strong-field ionization. To analyze the PES, one needs to extract the physical observables from the time-dependent wave function at the end of the laser pulse. The exact PES can be obtained by projecting this wave function onto the continuum states of the same binding potential, which have to obey the incoming boundary condition. This means that the continuum states at large distances from the atomic or molecular targets have to be localized in momentum space so that asymptotically the continuum states can be approximated by plane waves. In this paper, we extend our previous analysis [B. Feti\ifmmode \acute{c}\else \'{c}\fi{}, W. Becker, and D. B. Milo\ifmmode \check{s}\else \v{s}\fi{}evi\ifmmode \acute{c}\else \'{c}\fi{}, Extracting photoelectron spectra from the time-dependent wave function: Comparison of the projection onto continuum states and window-operator methods, Phys. Rev. A 102, 023101 (2020)] and investigate two alternative methods of the PES extraction: projecting the time-dependent wave function onto plane waves as well as the so-called time-dependent surface flux (tSURFF) method. A thorough analysis is performed to check the reliability of these methods in comparison with the exact method. The time integral, which appears in the tSURFF ionization amplitude, is divided into smaller time intervals. Analyzing the corresponding partial amplitudes and their interference we relate these time intervals to particular parts of the PES. The method is applied to analyze the high-energy PES as well as the low-energy and very-low-energy structures in the PES.

A neural network potential energy surface and quantum dynamics studies for the Ca+(2S) + H2 → CaH+ + H reaction.

Reactive collisions of Ca+ ions with H2 molecules play a crucial role in ultracold chemistry, quantum information and other cutting-edge fields, and have been widely studied experimentally, but the corresponding theoretical studies have not been reported due to the lack of an applicable potential energy surface (PES). Herein, a globally accurate PES of the ground-state CaH2+ is constructed using the permutation invariant polynomial neural network method based on 27 780 ab initio points calculated at the multi-reference configuration interaction level. On the new PES, the quantum time-dependent wave packet calculations are performed to study the dynamics mechanisms of the Ca+(2S) + H2(ν0 = 0, j0 = 0) → CaH+ + H reaction. The calculated results suggest that the reaction follows a direct abstraction process when the collision energy is below 5.0 eV. The dynamics results would have a great reference significance for the experimental research of this reactive system at a finer level, and further dynamics studies, such as the effects of isotope substitution and rovibrational excitations of the reactant molecule, could be carried out on this newly constructed PES.

Quantum Wave Packet Study of the H + Br2 → HBr + Br Reaction on a New Ab Initio Potential Energy Surface.

An accurate global potential energy surface (PES) for the HBr2 system has been constructed using the fundamental invariant neural network fitting method based upon 11 698 ab initio energies at the UCCSD(T)/CBS level of theory, with the spin-orbit coupling of the 2P3/2 orbit of the Br atom properly included. The time-dependent wave packet calculations have been performed to study the H + Br2 → HBr + Br reaction on the new PES. The total reaction probabilities for total angular momentum J = 0 for the ground initial state show no threshold due to the submerged barrier height (-0.351 kcal/mol) of the PES. The total integral cross sections (ICS) for reactant Br2 in ro-vibrational states (v0 = 0, j0 = 0, 10, 20, 30; v0 = 1-5, j0 = 0) were calculated for collision energy of up to 0.5 eV. It is found that the initial rotational excitation has a negligible effect on the ICS, and the initial vibrational excitation depresses the reactivity to some extent. The thermal rate constants for the title reaction in the temperature range of 100-1000 K were calculated from the Boltzmann averaging of the v0 = 0-5 rate constants, which overestimated the experimental results to some extent.

A study on the non-adiabatic dynamics of the Li(2p) + H2 → Li(2 s) + H2 quenching reaction calculated by time-dependent wavepacket method

A non-adiabatic time-dependent wave packet calculations of the quenching reaction Li(2p) + H2 → Li(2 s) + H2 are carried out based on a diabatic potential energy surface (PES). The integral cross sections (ICSs) and reaction probabilities are calculated at the state-to-state level. In addition, the ICSs and reaction probabilities of the abstraction reaction are compared with the quenching reaction. According to the ICSs with different vibrational state of H2, we argue that the potential well along the reaction path has an important influence on the non-adiabatic transition.

Dynamic study of the H + AuH reaction based on a new ground potential energy surface

Time-dependent wave packet (TDWP) calculations were performed for the title reaction on a new ground potential energy surface (PES) (2A′) constructed by Yuan et al. The reaction probability, integral cross-section (ICS), and differential cross-section (DCS) were obtained for both the PES. The ICSs on the Yuan PES were smaller than those on the Zanchet PES. The direct mechanism was dominant in the abstraction reaction, while the indirect mechanism was dominant in the exchange reaction. Another observation was that the collision energy is readily transferred into the internal energy (vibration of H2 and rotation of HAu).

An efficient way to incorporate the geometric phase in the time-dependent wave packet calculations in a diabatic representation.

We present a new approach to incorporate the geometric phase in the time-dependent wave packet calculations based on the analytic diabatic potential energy matrices for two-state systems connecting via a conical intersection. The approach only requires information on the location of the conical intersection and the adiabatic potential energy surface of the ground electronic state and merely takes the same computational cost as a diabatic calculation. Demonstrations of the benchmark H + H2/HD reactions show that the new approach can accurately include the geometric phase in dynamics calculation and can be easily extended to the cold regime where the GP effects become more pronounced. Due to its simplicity and numerical efficiency, the new approach has the potential to extend the dynamics study of the geometric effects to a wide range of reaction systems.

A time-dependent quantum dynamical study of H + AuH reaction

We performed the first time-dependent wave packet calculations on H + HAu → Au + H2/ H + HAu reaction using the ground potential energy surface (2A') constructed by Zanchet' et al. For studying the mechanism of the title reaction, the reaction probabilities, integral and differential cross sections are calculated. The direct mechanism plays an important role in the abstraction reaction, while the indirect mechanism plays an important role in exchange reaction. The energy transfer goes essentially to vibration and rotation of H2 products. However, the translation to vibration energy transfer is not efficient in the exchange reaction.

Six-dimensional potential energy surfaces for the dissociative chemisorption of HCl on rigid Ag(100) and Ag(110) surfaces.

The dependence of reactivity on different facets of a surface is an interesting subject in dynamics at gas-surface interfaces. Here, we constructed new six-dimensional (6D) potential energy surfaces (PESs) for the dissociative chemisorption of HCl on rigid Ag(100) and Ag(110) surfaces, using the neural network method based on extensive density functional theory (DFT) calculations with the Perdew-Burke-Ernzerhof (PBE) functional, and compared the two PESs with the previously fitted PES of HCl/Ag(111). Time-dependent wave packet calculations show that the new PESs are very well converged with respect to the fitting procedure as well as to the number of DFT data points. The 6D dissociation probabilities for HCl initially in the ground rovibrational state decrease gradually for HCl/Ag(110), HCl/Ag(100), and HCl/Ag(111), consistent with the increasing barrier heights for the three reactions. The validity of the site-averaging approximation for HCl/Ag(110) does not hold well as compared with HCl/Ag(100) and HCl/Ag(111), in particular, at low kinetic energies, due to the strong steering effect this reaction exhibits if it is modeled with the semilocal PBE functional, which results in a low reaction barrier and a deep physisorption well.