Time-dependent Wave Packet Method Research Articles

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

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

Quantum Dynamics Study of the C(1D) + HD Reaction on the ã1A' and b̃1A″ Potential Energy Surfaces.

We present an in-depth theoretical study of the C(1D) + HD (v = 0, j = 0) → CD (CH) (v', j') + H (D) reaction using a time-dependent wave packet method with full Coriolis coupling on the Zhang-Ma-Bian potential energy surfaces (PESs) recently constructed by our group. The integral cross sections (ICS), differential cross sections, CD/CH branching ratios, and product state distributions are calculated over a wide range of collision energies. We find that the vibrational branching ratio defined as ICS(v'=1)/ICS(v'=0) obtained from the b̃1A″ PES is much smaller than that from the ã1A' PES for both product channels, which may be attributed to the dynamical effects of the conical intersection regulated (CI-R) intermediate on the b̃1A″ PES. The collision energy dependence of CD/CH branching ratios displays oscillatory structures, which may be caused by the resonance states supported by the wells on the PESs. The high-temperature rate coefficients are also obtained and compared with previous results. The role of the excited-state PESs is also discussed.

Dynamics studies of the Li(2S) + H2(X1Σg+) → LiH (X1Σ+) + H(2S) reaction by time-dependent wave packet and quasi-classical trajectory methods

Based on the potential energy surface reported by Yuan and co-workers (Phys. Chem. Chem. Phys. 17 (2015) 11732–11739), the specific state (v0 = 0, j0 = 0) dynamics calculations of the Li(2S) + H2(X1Σg+) → LiH(X1Σ+) + H(2S) reaction were performed using the time-dependent wave packet and quasi-classical trajectory methods in the collision energy range from 2.0 to 3.0 eV. The reaction probability, integral cross section, differential cross section, the distribution of LiH product and so on were reported at state-to-state level of theory. The results obtained by quasi-classical trajectory method are in good agreement with quantum values, which indicates that the quantum effect is not very apparent. The differential cross sections results indicate that the abstract reaction mechanism is dominant in the reaction.

Non-adiabatic dynamics studies of the H(2S) + LiH(X1Σ+) reaction by time-dependent wave packet method.

Non-adiabatic dynamics studies of the H + LiH (v0 = 0, j0 = 0) reaction are carried out based on the diabatic potential energy surfaces (PESs) reported by He and co-workers (Sci. Rep., 2016, 6, 25083) in the collision energy range from 0.001 to 1.0 eV. The H(2S) + LiH(X1Σ+) → Li(22S)/Li(22P) + H2(X1Σg+) depletion reactions and the H'(2S) + LiH(X1Σ+) → H(2S) + LiH'(X1Σ+) exchange reaction are studied at the state-to-state level of theory. The dynamics properties, such as reaction probability, integral cross section, differential cross section, the ro-vibrational state distributions of the product and specific-state rate constant are calculated. In addition, the dynamics values of the H(2S) + LiH(X1Σ+) → Li(22S) + H2(X1Σg+) depletion reaction are compared with available theoretical results, which are based on the adiabatic PESs. Large discrepancies are found between the adiabatic and diabatic values, especially at low J values, which indicate that the non-adiabatic effect is very great and cannot be simply ignored. Furthermore, the deviations between adiabatic and diabatic values gradually decrease as the collision energy increases.

Dynamics of the Au + H2 reaction by time-dependent wave packet and quasi-classical trajectory methods

Dynamics of the Au + H2 reaction are studied using time-dependent wave packet (TDWP) and quasi-classical trajectory (QCT) methods based on a new potential energy surface [Int. J. Quantum Chem. 118 e25493 (2018)]. The dynamic properties such as reaction probability, integral cross section, differential cross section and the distribution of product are studied at state-to-state level of theory. Furthermore, the present results are compared with the theoretical studies available. The results indicate that the complex-forming reaction mechanism is dominated in the reaction in the low collision energy region and the abstract reaction mechanism plays a dominant role at high collision energies. Different from previous theoretical calculations, the side-ways scattering signals are found in the present work and become more and more apparent with increasing collision energy.

High Order Split Operators for the Time-Dependent Wavepacket method of Triatomic Reactive Scattering in Hyperspherical Coordinates

Since the introduction of a series of methods for solving the time-dependent Schrödinger equation (TDSE) in the 80s of the last centry, such as the Fourier transform, the split operator (SO), the Chebyshev polynomial propagator, and complex absorbing potential, investigation of the molecular dynamics within quantum mechanics principle have become popular. In this paper, the application of the time-dependent wave packet (TDWP) method using high-order SO propagators in hyperspherical coordinates for solving triatomic reactive scattering was investigated. The fast sine transform was applied to calculate the derivatives of the wave function of the radial degree of freedom. These high-order SO propagators are examined in different forms, i.e., TVT (Kinetic–Potential–Kinetic) and VTV (Potential–Kinetic–Potential) forms with three typical triatomic reactions, H + H , O + O and F + HD. A little difference has been observed among the performances of high-order SO propagators in the TVT and VTV representations in the hyperspherical coordinate. For obtaining total reaction probabilities with 1% error, some of the S class high-order SO propagators, which have symmetric forms, are more efficient than second order SO for reactions involving long lived intermediate states. High order SO propagators are very efficient for obtaining total reaction probabilities.

Describing heavy-ion fusion with quantum coupled-channels wave-packet dynamics

We investigate the fusion of $^{16}\mathrm{O}$ and $^{154}\mathrm{Sm}$ with excited states at Coulomb energies using a theoretical dynamical model. The two-body Schr\odinger equation is solved using the time-dependent wave-packet coupled-channels method. The wave function of the collective motion and excitations are visualized in both position and momentum space, providing a detailed mechanism of the reaction. We benchmark our calculations of the energy-resolved fusion transmission coefficients with those from the time-independent coupled-channels method. The present results are in good agreement with the time-independent results for a wide range of energies and angular momenta, demonstrating both the reliability of the quantum wave-packet dynamical approach for fusion and its usefulness for providing additional insights into fusion dynamics.

Dynamics studies of O+ + D2 reaction using the time-dependent wave packet method

Based on the potential energy surface (PES) reported by Li et al. (Phys. Chem. Chem. Phys. 20, 1039 (2018)), the initial state dynamics calculation of O+ + D2 (v = 0, j = 0) reaction was conducted using the time-dependent wave packet method with a second order split operator. Dynamics properties such as reaction probability, integral cross section, differential cross section, and distribution of products were calculated and compared with available experimental and theoretical results. The present integral cross section values were in good agreement with experimental results. In addition, the differential cross section indicates that the mechanism of the complex-formation reaction plays a dominant role during the reaction.

Full dimensional quantum mechanical calculations of the reaction probability of the H + NH3 collision based on a mixed Jacobi and Radau description.

The collision between hydrogen and ammonia is a benchmark system to study chemical elementary reactions with five atoms. In this work, we present a description of the system based on mixed Jacobi and Radau coordinates combined with the time-dependent wave packet method to study the H + NH3 reaction. The Radau coordinates are used to describe the reactive moiety NH2. A salient feature of this approach is that the present coordinates have a great advantage that a very small number of basis set functions can be used to describe the NH2 group. Potential-optimized discrete variable representation basis is applied for the vibrational coordinates of the reagent NH3. The reaction probabilities for several initial vibrational states are presented in this paper. The role of the different vibrational excitations on the reactivity is thoroughly described.

Non-adiabatic quantum dynamical studies of reaction**Project supported by the National Natural Science Foundation of China (Grant No. 11774043).

Non-adiabatic dynamical calculations are carried out for the reaction on the diabatic potential energy surfaces of Wang et al. (Sci. Rep. 2018, 8, 17960) by using the time-dependent wave packet method. The state-to-state integral cross sections and differential cross sections of two reaction channels (NaH/NaD+D/H) are calculated for collision energy up to 0.4 eV. The cross section branching ratio indicates that the dominant reaction channel changes from NaD+H to NaH+D when the collision energy is larger than 0.227 eV. The products from two reaction channels both prefer to form in vibrationally cold but rotationally hot states, and they both tend to forward scattering.

Studies of the Coriolis coupling effect on reaction dynamics of using the time dependent wave packet method

The time dependent wave packet method is employed to study the reaction on a novel potential energy surface (Phys. Chem. Chem. Phys. 2014 16 23594). Both the centrifugal sudden approximation and Coriolis coupling (CC) effect are utilized to calculate the reaction probabilities and integral cross sections. By comparing the results, it is demonstrated that the CC effect does play a vital role in this reaction.

Non-adiabatic Quantum Dynamics of the Dissociative Charge Transfer He++H2 → He+H+H.

We present the non-adiabatic, conical-intersection quantum dynamics of the title collision where reactants and products are in the ground electronic states. Initial-state-resolved reaction probabilities, total integral cross sections, and rate constants of two H2 vibrational states, v0 = 0 and 1, in the ground rotational state (j0 = 0) are obtained at collision energies Ecoll ≤ 3 eV. We employ the lowest two excited diabatic electronic states of and their electronic coupling, a coupled-channel time-dependent real wavepacket method, and a flux analysis. Both probabilities and cross sections present a few groups of resonances at low Ecoll, whose amplitudes decrease with the energy, due to an ion-induced dipole interaction in the entrance channel. At higher Ecoll, reaction probabilities and cross sections increase monotonically up to 3 eV, remaining however quite small. When H2 is in the v0 = 1 state, the reactivity increases by ~2 orders of magnitude at the lowest energies and by ~1 order at the highest ones. Initial-state resolved rate constants at room temperature are equal to 1.74 × 10−14 and to 1.98 × 10−12 cm3s−1 at v0 = 0 and 1, respectively. Test calculations for H2 at j0 = 1 show that the probabilities can be enhanced by a factor of ~1/3, that is ortho-H2 seems ~4 times more reactive than para-H2.

Isotope effect and Coriolis coupling effect for the Li + H(D)Cl LiCl + H(D) reaction**Project supported by the National Natural Science Foundation of China (Grant Nos. 11274096 and 11604083).

A time-dependent quantum wave packet method is used to investigate the dynamics of the Li+ H(D)Cl reaction based on a new potential energy surface (J. Chem. Phys. 146 164305 (2017)). The reaction probabilities of the Coriolis coupled (CC) and centrifugal sudden (CS) calculations, the integral cross sections, the reaction rate constants are obtained. The rate constants of the Li+ HCl reaction are within the error bounds at low temperature. A comparison of the CC and CS results reveals that the Coriolis coupling plays an important role in the Li+ H(D)Cl reaction. The CC cross sections are larger than the CS results within the entire energy range, demonstrating that the Coriolis coupling effect can more effectively promote the Li+ DCl reaction than the Li+ HCl reaction. It is found that the isotope effect has a great influence on the title reaction.

Non-adiabatic state-to-state dynamic studies of Na(3p) + H2(v = 1, 2, 3; j = 0) → NaH + H reactions

Abstract The time-dependent wave packet method is used to study non-adiabatic state-to-state Na(3p) + H2(v = 1, 2, 3, j = 0) → NaH + H reactions, which are sub-processes in the formation of NaH from the collision between Na(3p) and H2. Integral cross section values of the Na(3p) + H2(v) → NaH + H reaction increase significantly when H2 is excited to the v = 2 or v = 3 states. Products from the Na(3p) + H2(v) → NaH + H reaction with three different initial vibrational states all prefer to form in vibrationally cold but rotationally hot states. Regarding the vibrational state distribution of the product from Na(3p) + H2(v > 0) → NaH + H, our theoretical results are consistent with experimental results.

Understanding rotational mode specificity in the O(3P)+CHD3→ OH+CD3 reaction by simple reactant alignment pictures

The mode specificity plays an important role in understanding the fundamental reaction dynamics. This work reports a theoretical study of the rotational mode specificity of the reactant CHD3(JK) in the prototypical hydrocarbon oxidation reaction O(3P)+CHD3→OH+CD3. The time-dependent quantum wave packet method combined with a seven-dimensional reduced model is employed to calculate the reaction probability on an accurate potential energy surface. The obtained reaction probability depends on the values of both K and Ktot with PKtot = K = 0 > PKtot = K = J > PKtot = J,K = 0 = PKtot = 0,K = J. This observation can be well rationalized by the reactant alignment pictures. Rotational excitations of CHD3 up to the angular momentum quantum number J = 4 have a very weak enhancement effect on the reaction except for the state (J = 4, K = 0). In addition, the rotationally excited states of CHD3 with K = 0 promote the reaction more than those with K = J. The quantum dynamics calculations indicate that the K = 0 enhancements are mainly caused by the contributions from the components with K = Ktot = 0. The components correspond to the tumbling rotation of CHD3, which enlarges the range of the reactive initial attack angles.

Dynamics studies of O<sup>+</sup> + H<sub>2</sub>→ OH<sup>+</sup> + H reaction

In the present work, the long-range interaction potential part of potential energy surface (PES) of OH<sub>2</sub><sup>+</sup> system is revised and the new resulting PES apparently is more reasonable than the old one in the long-range part. Based on the new PES, the dynamics calculations of O<sup>+</sup> +H<sub>2</sub>→ OH<sup>+</sup> + H reaction are carried out at a state-to-state level of theory by using time-dependent quantum wave packet method with second order split operator in a collision energy range from 0.01 to 1.0 eV. The dynamic properties such as reaction probability, ro-vibrational resolved statereaction probability, integral cross section, differential cross section, and state specific rate constant are calculated and compared with available theoretical and experimental results. The results of ro-vibrational resolved state reaction probability reflect some dynamic properties such as resonances which is attributed to the deep well located on the reaction path. The vibrational resolved state reaction probability indicates that the excitation efficiency of the OH<sup>+</sup> product is relatively low. The results of integral cross sections indicate that the present results are in better agreement with the experimental values than with previous theoretical calculations, especially in the low collision energy region. However, the state specific rate constant results underestimate the experimental values. The comparison betweenour calculations and the experimental results indicates that the contribution of the rotational excitation of H<sub>2</sub> molecule should be included in the calculations. However, only the initial state <i>v</i> = 0, <i>j</i> = 0 is calculated in the present work. We suppose that the deviation of the present results from the experimental data is due to the fact that the rotational excitation of reactant isnot included in the present calculation. The differential cross section signals indicate that the complex-forming reaction mechanism isdominated in the case of low collision energy, but it transforms into abstract reaction mechanism as the collision energy further increases.

Mode-specific quantum dynamics and kinetics of the hydrogen abstraction reaction OH + H2O → H2O + OH.

Hydrogen abstraction processes are prevalent in a wide range of chemically active environments. In this work, the prototypical hydrogen exchange reaction OH + H2O → H2O + OH is investigated on an accurate ab initio based potential energy surface using an initial state-selected time-dependent wave packet method. Exciting either the symmetric stretching mode or the antisymmetric stretching mode of the reactant H2O promotes the reaction more than exciting the bending mode. The vibrational energy initially deposited in H2O is more efficient than the translational energy in promoting the reaction. There exists a remarkable synergistic effect between the stretching mode and the bending mode as the efficacy for the combination band excitation is larger than the sum of individual excitations. The mode-specific dynamics is partially rationalized by the sudden vector projection model. Besides, the mode-specific rate constants apparently exhibit a strong non-Arrhenius behavior at low and moderate temperatures.

An ab initio-based global potential energy surface for the SH3 system and full-dimensional state-to-state quantum dynamics study for the H2 + HS → H2 S + H reaction.

An accurate potential energy surface for the ground electronic state of SH3 system has been constructed with 41,882 high level ab initio energy points and the neural network fitting method. The time-dependent wave packet method has been used to calculate the first state-to-state differential cross sections for the title reaction up to 1.2 eV in full dimensions, based on the reactant-product decoupling scheme. It is found that the majority of H2 S are produced in the ground vibrational state, with a large fraction of available energy for the reaction ending up as product translational motion. The differential cross sections at the threshold energy are dominated by a very narrow peak in the backward direction. With the increase of collision energy, the width of the angular distribution increases considerably, which is a typical feature of a direct reaction via abstract mechanism, similar to the H2 + OH → H2 O + H reaction. © 2018 Wiley Periodicals, Inc.

Quantum dynamics calculation of the annihilation spectrum for positron–proline scattering

The annihilation spectrum for positron scattering by the amino acid proline was calculated using local complex potential theory combined with the time-dependent quantum wave packet method. Two nuclear degrees of freedom associated with the motion of the carboxyl group proton were considered in the dynamics. The positronic potential energy surface and positron–electron contact densities were calculated using ab initio multi-component molecular orbital theory. The calculated annihilation spectrum contained several vibrational resonance peaks, which allowed the positron binding energies to be estimated. We also observed a resonance with a very small contribution of zwitterionic proline via proton transfer.

Adiabatic population transfer between electronic states of LiH molecule in two picosecond laser pulses

The population transfer of stimulated Raman adiabatic passage (STIRAP) is investigated using a time-dependent quantum wave packet method. The population is transferred from an initial state to a target state through the interaction of the external laser field with the permanent dipole moment and the transition dipole moment. The laser field is composed of an infrared pulse and a near ultraviolet pulse. The two pulses with small detunings are more efficient to achieve the STIRAP transition. The process of STIRAP is sensitive to the detunings of the two pulses. When the two detunings are the same in a Λ transition or the positive detuning of the pump pulse is equal to the negative detuning of the Stokes pulse in a ladder transition, the final population in the intermediate state can be eliminated and the target population is increased.