Time-dependent Quantum Wave Packet Method Research Articles

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.

The global potential energy surface of the RbH2 system and dynamics studies of the H + RbH → Rb + H2 reaction

A new global potential energy surface of the ground state of the RbH2system is constructed by using the permutation invariant polynomial neural network method.In the ab initiocalculations, the aug-cc-pVQZ basis set for H, Def2-QZVPP basis set for Rb, and multi-reference configuration interaction method with Davidson correction are used. The topographical features of the new PES are discussed in detail, and no wells and barriers in the minimum energy path are found. Thereafter, specific initial-state dynamics calculations of the H + RbH (v = 0 ∼ 2,j = 0) → Rb + H2reaction are carried out based on the new PES by means of the time-dependent quantum wave packet method with a second-order split operator. The dynamics results indicate that the vibrational excitation of RbH molecules reduces and increases the reaction probability when the collision energy is below 0.4 eV and above 0.4 eV, respectively.

Control of molecular-field-free orientation steered by asymmetric phase-jump laser pulses

• The molecular orientation with phase-jump laser pulse is investigated by time-dependent quantum wave packet method. • The asymmetry of laser pulse has a significant influence on the orientation. • The molecular orientation is effected by the laser pulse parameters. A theoretical scheme used for manipulating the orientation of LiH molecules with phase-jump laser pulse is proposed. The time-dependent quantum wave packet method is used to numerically compute the wave-function of molecules by including both vibrational and rotational degrees of the freedom. The effect of asymmetric phase jump pulses on molecular orientation can be well understood by a train of HCPs kicking the molecule. The effective orientation of molecules can be achieved by phase-jump laser pulse. The maximal orientation degree, 0.757, and the longest orientation duration, 0.365 ps, are given by optimizing the parameters of phase-jump laser pulse. The molecular orientation is influenced significantly by phase and phase-jump time. Also the molecular orientation is dependent on pulse frequency, peak intensity and system temperature.

Control of photodissociation of the molecular ion HD+ with two completely overlapping laser pulses

The dissociation dynamics of molecular ion HD+ in two completely overlapping THz and infrared pulses are investigated by using the time-dependent quantum wave packet method. The angular distribution of fragments depends on the carrier-envelope phase (CEP) of the THz pulse. The infrared pulse is employed to control the dissociation probability and the direction of the products D+H+. When the intensity of infrared pulse is 2.0×1014 W/cm2, the molecule HD+ is pre-oriented by the THz pulse and most of products D+H+ and H+D+ are distributed in the same direction. When the intensity is increased to 4.6×1014 W/cm2, the angular distribution is mainly generated by the THz pulse after molecular ions are dissociated, and the direction of products D+H+ is opposite to that of products H+D+.

Theoretical investigation of pump–probe photoelectron spectroscopy on KLi

Based on the time-dependent quantum wave packet method, the ionization dynamics of the KLi molecule are theoretically simulated using the pump–probe technique. The Autler–Townes splitting phenomenon of photoelectron spectroscopy is analyzed by changing the laser pulse width, the intensity of the probe laser pulse, and the delay time between the pump and probe pulses. It has been found that the height difference between the splitting peaks becomes larger as the width of the pump pulse increases under the resonant condition. Furthermore, the probe laser with large pulse width has little effect on the peak height difference compared with the pump pulse, but it results in multi-splitting of the photoelectron spectroscopy. Meanwhile, the effect of delay time on the splitting peaks in photoelectron spectroscopy is investigated.

State-to-state dynamics of reactions H + DH’(ν = 0,j = 0) → HH’(ν’,j’) + D/HD(ν’,j’) + H’ with time-dependent quantum wave packet method* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11504206 and 12004216), the Ph. D. Research Start-up Fund of Shandong Jiaotong University (Grant No. BS2020025), and the Shandong Natural Science Foundation, China (Grant Nos.

State-to-state time-dependent quantum dynamics calculations have been carried out to study H + DH’ → HH’ + D/HD + H’ reactions on BKMP2 surface. The total integral cross sections of both reactions are in good agreement with earlier theoretical and experimental results, moreover the rotational state-resolved reaction cross sections of H + DH’ → HH’ + D at collision energy E C = 0.5 eV are closer to the experimental values than the ones calculated by Chao et al. [J. Chem. Phys. 117 8341 (2002)], which proves the higher precision of the quantum calculation in this work. In addition, the state-to-state dynamics of H + DH’ → HD’ + H reaction channel have been discussed in detail, and the differences of the micro-mechanism of the two reaction channels have been revealed and analyzed clearly.

Quantum control of the dissociation of LiH molecules with two intense laser pulses

The dissociation dynamics of LiH molecules induced by two overlapping femtosecond pulses is investigated based on the time-dependent quantum wave packet method. The first pulse induces population transfer from the ground state $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ to the excited state $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ which is coupled with the repulsive state $B{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ and the state $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ by the second pulse. The two products $\mathrm{Li}(2p)$ and $\mathrm{Li}(2s)$ can be obtained via the ladder and $\mathrm{\ensuremath{\Lambda}}$ transitions, respectively, and the branching ratio of the products can be controlled by varying the second pulse frequency $\ensuremath{\hbar}{\ensuremath{\omega}}_{2}$. The choice of the intermediate state can affect the dissociation probability and angular distribution of fragments. As the second pulse intensity is increased, more products occur in other directions besides the directions $\ensuremath{\theta}={0}^{\ensuremath{\circ}}$ and ${180}^{\ensuremath{\circ}}$. The delay time of two pulses also has influence on the angular distribution.

Enhancement of molecular orientation with two super-Gaussian pulses

A theoretical scheme is presented to realize effective molecular orientation driven by two super-Gaussian pulses (SGPs). As an applied example, the orientation dynamics of LiH molecule is studied by using the time-dependent quantum wave packet method. The calculations are performed including both the molecular vibrational and rotational degrees of freedom. It is shown that the efficient molecular orientation can be achieved by two SGPs, and the maximal orientation degree is 0.823, which is obviously better than those by the Gaussian pulse and a single SGP. The orientation degree and orientation duration time are dependent on the laser frequency, field intensity and delay time between two SGPs. The pulse shaped parameter N characterizing the SGP has effects on molecular orientation and rotational population. Furthermore, the molecular orientation degree and orientation duration time decrease with the increase of temperature. A long-lived molecular orientation duration time and high orientation degree can be achieved in the range of temperature from 0 to 100 K.

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.

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.

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.

State-to-state quantum dynamics studies of the H + LiH+ → Li+ + H2 reaction

ABSTRACTQuantum dynamical calculations of the H + LiH+ → Li+ + H2 reaction were performed based on the potential energy surface (PES) reported by Dong et al. (RSC Adv. 7, 7008 (2017)) using the time-dependent quantum wave packet method in collision energy range from 0.01 to 1.0 eV. Dynamics properties such as reaction probability, integral cross section, differential cross section (DCS), and thermal rate constant of the H + LiH+ → Li+ + H2 reaction were reported at the state-to-state level of theory and compared with available theoretical calculations. The results indicated that present values are in good agreement with results obtained from the quasi-classical trajectory method. However, large differences can be found between present values and previous quantum results. This can be attributed to the different PESs used in the calculation and the CS approximation was adopted in previous theoretical studies. In addition, the ‘rebound’ reaction mechanism was proposed in previous theoretical studies in a high collision energy range. However, the DCS scattering signals calculated in the present work indicated that complex-forming and direct abstract reaction mechanisms are dominant in low and high collision energies, respectively.

Mode specific dynamics in bond selective reaction O'(3P) + HOD → O'H + OD/O'D + OH.

Taking advantage of bond selectivity and mode specificity has long been realized to control the outcome of chemical reactions. The mode-specific dynamics in the bond selective abstraction reaction O'(3P) + HOD are investigated using a full-dimensional time-dependent quantum wave packet method. Integral cross sections and product branching ratios from several low-lying vibrational states of the reactant HOD are calculated on an accurate global potential energy surface describing the lowest triplet state of the HOOH system. Both the H-abstraction reaction and the D-abstraction reaction prefer the vibrational energy to the translational energy, satisfying the prediction of Polanyi rules for a late-barrier reaction. The observed strong bond selectivity can be rationalized by the sudden vector projection model as well. The bias to the D-abstraction channel for the reaction O'(3P) + HOD from the reactant ground state can be partially attributed to the different mass combination in comparison to the H + HOD reaction, in which the H-abstraction channel is more favored.

A new global analytical potential energy surface of NaH2+ system and dynamical calculation for H(2S) + NaH+(X2Σ+) → Na+(1S) + H2(X1Σg+) reaction

A new global potential energy surface (PES) of the NaH2+ system is constructed by fitting 27,621 ab initio energy points with the neural network method. The root mean square error of the new PES is only 4.1609 × 10−4 eV. Based on the new PES, dynamical calculations have been performed using the time-dependent quantum wave packet method. These results are then compared with the H(2S) + LiH+(X2Σ+) → Li+(1S) + H2(X1Σg+) reaction. The direct abstract mechanism is found to play an important role in the reaction because only forward scattering signals on the differential cross section results for all calculated collision energies.

Photoassociation reaction of OH molecules through reverse ladder transition

Photoassociation via reverse ladder transition controlled by two and four laser pulses is investigated using the time-dependent quantum wave packet method. The calculated results show that the amplitudes of the pulses have an enormous effect on the target population and total yield of association. For the target state with a high energy level, the population of background states can reduce the state-selectivity. Although, the total yield of association is decreased, the four pulses can induce the population transferring to low vibrational levels, and the state-selectivity of the target state is high.

Global diabatic potential energy surfaces for the BeH2 + system and dynamics studies on the Be+(2P) + H2(X1Σg +) → BeH+(X1Σ+) + H(2S) reaction.

The Be+(2P) + H2(X1Σg+) → BeH+(X1Σ+) + H(2S) reaction has great significance for studying diabatic processes and ultracold chemistry. The first global diabatic potential energy surfaces (PESs) which are correlated with the lowest two adiabatic states 12A′ and 22A′ of the BeH2+ system are constructed by using the neural network method. Ab initio energy points are calculated using the multi-reference configuration interaction method with the Davidson correction and AVQZ basis set. The diabatic energies are obtained from the transformation of ab initio data based on the dipole moment operators. The topographical characteristics of the diabatic PESs are described in detail, and the positions of crossing between the Vd11 and Vd22 are pinpointed. On new diabatic PESs, the time-dependent quantum wave packet method is carried out to study the mechanism of the title reaction. The results of dynamics calculations indicate the reaction has no threshold and the product BeH+ is excited to high vibrational states easily. In addition, the product BeH+ tends to backward scattering at most collision energies.

Effect of phase coherence on population transfer in three harmonic laser pulses

The population transfer controlled by fundamental, 2nd-harmonic and 3rd-harmonic pulses is investigated by using the time-dependent quantum wave packet method. By varying the phase of the fundamental pulse, it can be coherent with the 2nd-harmonic and 3rd-harmonic pulses. Compared with two harmonic pulses, the phase in three harmonic pulses is more efficient in controlling population transfer. Molecular orientation can be controlled by the phases of the three pulses. The value of molecular orientation mainly depends on the phase coherence between the fundamental and 2nd-harmonic pulses.

Above-threshold dissociation of the molecular ion HD+ in a moderate-intensity femtosecond laser field from the calculation of time-of-flight spectra

The dissociation of the molecular ion ${\mathrm{HD}}^{+}$ in moderate-intensity laser pulses is studied using the time-dependent quantum wave-packet method. Simulations of the time-of-flight (TOF) neutral atom spectra produced from dissociation of the $v=10$ vibrational state at a laser intensity of ${10}^{12}\phantom{\rule{0.16em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$ and from $v=0$ at the intensity of $5\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.16em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$ are calculated. Good agreement is found with previous experimental results [P. A. Orr et al., Phys. Rev. Lett. 98, 163001 (2007) and J. D. Alexander et al., J. Phys. B 42, 154027 (2009)]. Furthermore, the kinetic energy distribution of the dissociated fragments of molecular ion ${\mathrm{HD}}^{+}$ is studied within the moderate laser-intensity region from ${10}^{12}$ to $5\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.16em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$ by considering initial vibrational states from $v=0$ to 15. It is found that the above-threshold dissociation could be more obviously observed from the TOF spectra when the initial vibrational state is set as $v=6$ for a moderate-intensity femtosecond laser field.