Time-dependent Wave Packet Approach Research Articles

Unveiling Quantum Interference in the D+ + H2 Nonadiabatic Reaction Dynamics at Low Collision Energies.

Fully converged nonadiabatic dynamics calculations of the D+ + H2 → H+ + HD reaction are performed at low temperatures using the time-dependent wave packet approach based on a set of precise 3 × 3 diabatic potential energy surfaces (PESs) ( Phys. Chem. Chem. Phys., 2021, 23, 7735-7747, DOI: 10.1039/D0CP04100A). The D+ + H2 reaction is mediated by a dense manifold of resonances associated with the deep potential well on the ground-state PES. The calculated results show that the nonadiabatic coupling can affect the resonance positions, deviating from the expectation based solely on adiabatic considerations. Furthermore, significant forward-backward asymmetry in total differential cross sections (DCSs) is revealed, which is markedly influenced by nonadiabatic effects. The nonadiabatic effects not only affect the contribution of partial waves in the reaction but also make the interference patterns in the DCSs change significantly.

Time-dependent wave-packet approach to the excited-state intramolecular proton transfer based on relaxed potential energy surfaces of benzimidazole molecule

The wave-packet dynamical approach was used to investigate the excited-state intramolecular proton transfer (PT) of 5′-amino-2-(2′-hydroxyphenyl) benzimidazole (P1) based on the relaxed potential surfaces. For the involved PT process of P1 molecule, the quantum chemical calculation shows that relative to the ground state S0 with a single potential well, the excited state S1 with a double potential well can give much dynamical information. It is also found that because of the existence of a shallow potential barrier on the excited state S1, the PT in it is much easier than that in the ground state S0. When a laser field is used to pump the wave packet and induce the PT process, the external field parameters, such as the frequency and the envelope, also have influences on the PT process because of the impact of both pump time and the energy gap between two states. This kind of external field effect on the PT process gives a specific perspective to examine its dynamical mechanism and provides a reference for exploring the light-induced biophysical processes.

Mode-specific quantum dynamics study of OH + H2S → H2O + SH reaction

The hydrogen abstraction reaction from H2S by OH is of key importance in understanding of the causes of acid rain, air pollution, and climate change. In this work, the reaction OH+H2S → H2O+SH is investigated on a recently developed ab initio-based globally accurate potential energy surface by the time-dependent wave packet approach under a reduced-dimensional model. This reaction behaves like a barrier-less reaction at low collision energies and like an activated reaction with a well-defined barrier at high collision energies. Exciting either the symmetric or antisymmetric stretching mode of the molecule H2S enhances the reactivity more than exciting the bending mode, which is rationalized by the coupling strength of each normal mode with the reaction coordinate. In addition, the modespecific rate constant shows a remarkable non-Arrhenius temperature dependence.

Six-dimensional state-to-state quantum dynamics of H2/D2 scattering from Cu(100): Validity of site-averaging model

Six-dimensional quantum dynamics calculations for the state-to-state scattering of H2/D2 on the rigid Cu(100) surface have been carried out using a time-dependent wave packet approach, based on an accurate neural network potential energy surface fit for thousands of density functional theory data computed with the optPBE-vdW density functional. The present results are compared with previous theoretical and experimental ones regarding to the rovibrationally (in)elastic scattering of H2 and D2 from Cu(100). In particular, we test the validity of the site-averaging approximation in this system by which the six-dimensional (in)elastic scattering probabilities are compared with the weighted average of four-dimensional results over fifteen fixed sites. Specifically, the site-averaging model reproduces vibrationally elastic scattering probabilities quite well, though less well for vibrationally inelastic results at high energies. These results support the use of the site-averaging model to reduce computational costs in future investigations on the state-to-state scattering dynamics of heavy diatomic or polyatomic molecules from metal surfaces, where full-dimensional calculations are too expensive.

An accurate many-body expansion potential energy surface for AlH2 (22A') and quantum dynamics in Al(3P) + H2 (v0 = 0-3, j0 = 0, 2, 4, 6) collisions.

An accurate potential energy surface is constructed for the excited state of AlH2 by fitting extensive ab initio points calculated at the multi-reference configuration interaction level based on aug-cc-pV(Q+d)Z and aug-cc-pV(5+d)Z basis sets. All the calculated energies are corrected via the many-body expansion method and extrapolated to the complete basis set limit. The various topographic features of the new potential energy surface are investigated to demonstrate the correct behavior of Al(3P) + H2(X1Σg+) and AlH(a3Π) + H(2S) dissociation limits. By employing the time-dependent wave packet approach, the integral scattering cross-sections obtained from the Coriolis coupling calculation and the centrifugal sudden approximation, respectively, are compared in detail and show that the former has a higher effect on the reaction. Moreover, the thermal rate constants for Al(3P) + H2 (v0 = 0-3, j0 = 0, 2, 4, 6) in the temperature range of 0-5000 K are calculated, thereby providing insights into the influence of ro-vibrational quantum numbers on the thermal rate constants.

Dynamical calculations of O(3P) + OH(2Π) reaction on the CHIPR potential energy surface using the fully coupled time-dependent wave-packet approach in hyperspherical coordinates.

We have carried out quantum dynamics calculations for the O + OH → H + O2 reaction on the CHIPR [A. J. C. Varandas, J. Chem. Phys., 2013, 138, 134117] potential energy surface (PES) for ground state HO2 using the fully coupled 3D time-dependent wavepacket formalism [S. Adhikari and A. J. C. Varandas, Comput. Phys. Commun., 2013, 184, 270] in hyperspherical coordinates. Reaction probabilities for J > 0 are calculated for different initial rotational states of the OH radical (v = 0; j = 0, 1). State-to-state as well as total integral cross sections and rate-coefficients are evaluated and compared with previous theoretical calculations and available experimental studies. Using the rate constant for the forward (hereinafter considered to be H + O2 → O + OH) and backward (O + OH → H + O2) reactions of this reactive system, the equilibrium constant of the reversible process [H + O2 ⇌ O + OH] is calculated as a function of temperature and compared with previous experimental measurements.

Coriolis coupling effects on the H(2S) + CH+(X1Σ+) reaction dynamics in the ground electronic state

We investigated the effect of Coriolis coupling (CC) on the initial state-selected dynamics of the H(2S) + CH+() reaction in its electronic ground state () using a time-dependent wavepacket approach. Here, the exact dynamical calculations were carried out by considering the CC terms and the results were compared with our previous study within the centrifugal sudden (CS) approximation. All partial wave contributions up to the total angular momentum J = 60 were required to obtain the converged integral cross section upto collision energy ∼1.0 eV, and the rotational (j) level of CH+ reagent was varied upto 3. The projection quantum number Ω, ], facilitates the coupling between the neighboring substates Ω ± 1. There is no noticeable effect of CC in the dynamics for low-J values when compared to the CS result. As J increases, they effectively reduce the threshold shift observed in the CS probabilities and also vanish the resonance oscillations. The CC treats CH+ destruction (R1) and CH+ retention (R2) channels in the ratio of ∼(3:1), whereas the CS favors only R1 channel even for high-J values. The CC increases the dynamical quantities such as cross sections and rate constants with j-excitations and the values are generally higher than the CS result. Finally, we conclude that neglecting the CC terms generally underestimates the dynamical results for the title reaction which proceeds via the complex-forming mechanism, on the other hand, CC predicts the exact rate constants on par with the experimental results especially at low-T ranges of the astrochemical interest.

Wavepacket golden rule treatment of interparticle Coulombic decay in paired quantum dots.

The interparticle Coulombic decay process in paired quantum dots is studied by electron dynamics calculations. We consider a pair of Coulomb-coupled one-electron charged gallium arsenide quantum dots embedded in a nanowire. The two-electron decay process is approximately described by a single active electron model. Within this model, we employ the time-dependent wavepacket approach to the Fermi golden rule (introduced in the context of vibrational predissociation) to calculate autoionization rates, which are compared to exact rates obtained from fully correlated two-electron dynamics calculations. We found that the approximate decay rates agree well with the exact results in the limit of sufficiently separated quantum dots. Finally, we explore whether the short-range behavior of the new model can be further enhanced by the inclusion of local exchange effects by means of regularization of the Coulomb-potential based on a Jastrow-Slater wavefunction. The proposed method may open a route to study the interparticle Coulombic decay in more intricate systems, e.g., paired metal-nanoparticle-quantum dot systems.

Globally accurate potential energy surface for PH2 + (11 A′) by using the switching function formalism

As an intermediate product of phosphorus compounds in astrophysical chemistry, has great significance in research on the systems. However, as a basis for studying its reaction mechanisms, lacks an accurate global potential energy surface (PES) and related dynamic reports. In this investigation, based on a multi-reference configuration interaction approach with Davidson correction, an accurate global many-body expansion PES for in its ground state was reported by fitting extensive ab initio energies, as calculated with the correlation-consistent basis set aug-cc-pVQZ. Meanwhile, the switching function formalism was adopted to explain and distinguish the transformation between and in one-body energy terms, which ensured the correct dissociation channel in the reaction process of . The topographical characteristics of the title system PES were meticulously contrasted with those in other literature reports, which were consistent with previous experimental and theoretical values. Subsequently, the time-dependent wave packet approach was adopted to calculate the reaction probability and integral cross-section for the reaction to verify the accuracy of the new PES. This dynamics study may help to further explain the thermochemical reactions of phosphorus-containing molecules in interstellar media.

Theoretical study of dissociation dynamics of HD<sup>+</sup> and its quantum control with an intense laser field

The dissociation dynamics of HD<sup>+</sup> molecule in an intense field is investigated by using an accurate three-dimensional time-dependent wave packet approach. When the 790-nm laser pulse interacts with HD<sup>+</sup> molecule, the lowest electronic 1sσ and 2pσ states are coupled. Due to the existence of the permanent electric dipole moment, the transitions in HD<sup>+</sup> molecule involve the direct absorption of an odd and even number of photons, thereby opening different pathways for dissociation. The model of the photon-dressed states is presented to analyze the possible dissociation pathways of HD<sup>+</sup> molecule. The laser-induced dissociation of HD<sup>+</sup> molecule is mainly composed of the four pathways: the direct one-photon absorption, the net two-photon absorption, the direct two-photon absorption, and the direct two-photon absorption. To reveal the dissociation mechanism of HD<sup>+</sup> molecule, the kinetic energy resolved spectra are calculated at the given laser intensities. It is found that the dissociation pathways are strongly dependent on laser intensity, especially for the net one-photon absorption dissociation and direct two-photon absorption dissociation. With further research, the dissociation pathways of HD<sup>+</sup> are controlled by regulating the intensity of laser pulse. At a laser intensity of 4.0 × 10<sup>13</sup> W/cm<sup>2</sup>, the kinetic energy resolved spectrum for the vibrational state <i>ν</i> = 3 includes the contributions from the net two-photon absorption dissociation and the direct two-photon absorption dissociation. For the vibrational state <i>ν</i> = 6, HD<sup>+</sup> molecule is preferentially dissociated via the net one-photon absorption. However, the dissociation mechanism of HD<sup>+</sup> molecule at the vibrational states <i>ν</i> = 3 and <i>ν</i> = 6 have significant changes as the laser intensity increases to 2.0 × 10<sup>14</sup> W/cm<sup>2</sup>. For the vibrational state <i>ν</i> = 3, the branching ratio between the dissociation pathway of the net two-photon absorption and that of the direct two-photon absorption has a dramatic change with the increase of laser intensity. Compared with the kinetic energy resolved spectra at laser energy of 4.0 × 10<sup>13</sup> W/cm<sup>2</sup>, the height of the dissociation peak from the net two-photon absorption decreases, and that of the direct two-photon absorption increases at laser intensity of 2.0 × 10<sup>14</sup> W/cm<sup>2</sup>. For the vibrational state <i>ν</i> = 6, the dissociation process of the net one-photon absorption almost disappears at laser intensity of 2.0 × 10<sup>14</sup> W/cm<sup>2</sup>, and it is replaced by the dissociation pathway of the direct two-photon absorption.

Fully coupled (J > 0) time-dependent wave-packet calculations using hyperspherical coordinates for the H + O2 reaction on the CHIPR potential energy surface.

Quantum dynamics of the H + O2→ O + OH reaction has been extensively studied on the adiabatic ground state of CHIPR [A. J. C. Varandas, J. Chem. Phys., 2013, 138, 134117] potential energy surfaces by employing a coupled 3D time-dependent wavepacket approach in hyperspherical coordinates. Calculations have been performed for all non-zero J values for various initial rotational states of the diatom [O2(v = 0, j = 1-5)]. State-to-state and total integral cross sections are calculated using fully converged reaction probabilities, where initial state selected and Boltzmann averaged thermal rate constants are also subsequently calculated. Moreover, a comparison of various reaction attributes obtained by using the fully close coupled approach with the ones obtained from the J-shifting approximation and extrapolation scheme is presented along with other theoretical results and experimental observations.

Delay time dependence of wave packet motion and population transfer of four-level K2 molecule in pump–pump–probe pulses**Project supported by the National Natural Science Foundation of China (Grant Nos. 11704178 and 11764041) and the Scientific Research Fund of Hunan Provincial Education Department, China (Grant No. 15B204).

The effect of delay time on photoelectron spectra and state populations of a four-level ladder K2 molecule is investigated by a pump1–pump2–probe pulse via the time-dependent wave packet approach. The periodical motion of the wave packet leads to the periodical change of the photoelectron spectra. The Autler–Townes triple splitting appears at zero delay time, double splitting appears at nonzero delay time between pump1 and pump2 pulses, and no splitting appears at nonzero delay time between pump2 and probe pulses. The periodical change of the state populations with the delay time may be due to the coupling effect between the two pulses. It is found that the selectivity of the state populations may be attained by regulating the delay time. The results can provide an important basis for realizing the optical control of molecules experimentally.

Dynamical resonances of the deuterated CH2+ complex in the electronic ground state: A quantum wavepacket study.

We here investigate the effects of isotopic substituents on the vibrational energy levels of the CH2+ complex, supported by the electronic ground (1 2A') potential energy surface (PES) of the H + CH+ reaction. We calculate the transition state spectrum by Fourier transforming the time-autocorrelation function of the initial wavepacket (WP) chosen in the interaction region of the PES. Using the time-dependent WP approach, the dynamical resonances are identified as bound and quasibound in nature, and they are characterized in terms of the eigenfunctions and lifetimes. The present work on the isotopic variants [CHD+(CDH+) and CD2+] is compared with our earlier work [P. Sundaram et al., Phys. Chem. Chem. Phys. 19, 20172 (2017)] on the parent CH2+ species. The isotopic variants reveal a large number of peaks in the spectra and the eigenfunctions exhibit the systematic nodal progressions and periodic orbits, the same as in CH2+. While the CD2+ complex exactly mimics the resonance behaviors (local and hyperspherical modes) of the bound and quasibound CH2+ complex, the CHD+(CDH+) complex reveals only the local mode behaviors at low energies and significantly less number of resonance structures at high energies. Lifetime analysis of the isotopic variants implies that the CD2+ complex survives much longer than the CHD+(CDH+) complex and concludes the work by noting the following order in the decay profile of the deuterated CH2+ resonances as CH2+>CHD+(CDH+) >CD2+.

Vibrational and rotational excitation effects of the N(2D) + D2(X1Σg+) → ND(X3Σ+) + D(2S) reaction

ABSTRACTThe effects of the rovibrational excitation of reactants in the N(2D) + D2(X1Σg+) → ND(X3Σ+) + D(2S) reaction are calculated in a collision energy range from the threshold to 1.0 eV using the time-dependent wave packet approach and a second-order split operator. The reaction probability, integral cross-section, differential cross-section and rate constant of the title reaction are calculated. The integral cross-section and rate constant of the initial states v = 0, j = 0, 1, are in good agreement with experimental data available in the literature. The rotational excitation of the D2 molecule has little effect on reaction probability, integral cross-section and the rate constant, but it increased the sideways and forward scattering signals. The vibrational excitation of the D2 molecule reduced the threshold and broke up the forward–backward symmetry of the differential cross-section; it also increased the forward scattering signals. This may be because the vibrational excitation of the D2 molecule reduced the lifetime of the intermediate complex.

Accurate Quantum Wave Packet Study of the Deep Well D+ + HD Reaction: Product Ro-vibrational State-Resolved Integral and Differential Cross Sections.

The H+ + H2 reaction and its isotopic variants as the simplest triatomic ion-molecule reactive system have been attracting much interests, however there are few studies on the titled reaction at state-to-state level until recent years. In this work, accurate state-to-state quantum dynamics studies of the titled reaction have been carried out by a reactant Jacobi coordinate-based time-dependent wave packet approach on diabatic potential energy surfaces constructed by Kamisaka et al. Product ro-vibrational state-resolved information has been calculated for collision energies up to 0.2 eV with maximal total angular momentum J = 40. The necessity of including all K-component for accounting the Coriolis coupling for the reaction has been illuminated. Competitions between the two product channels, (D+ + HD' → D'+ + HD and D+ + HD' → H+ + DD') were investigated. Total integral cross sections suggest that resonances enhance the reactivity of channel D+ + HD'→ H+ + DD', however, resonances depress the reactivity of the another channel D+ + HD' → D'+ + HD. The structures of the differential cross sections are complicated and depend strongly on collision energies of the two channels and also on the product rotational states. All of the product ro-vibrational state-resolved differential cross sections for this reaction do not exhibit rigorous backward-forward symmetry which may indicate that the lifetimes of the intermediate resonance complexes should not be that long. The dynamical observables of this deuterated isotopic reaction are quite different from the reaction of H+ + H2 → H2 + H+ reported previously.

H/D + Li2 LiH/LiD + Li reactions studied by quantum time-dependent wave packet approach

The isotopic effect is a significant way to further understand the reaction mechanism without greatly changing the system. However, the isotopic effect of the H + Li2 reaction has received little attention in previous theoretical studies. Furthermore, as a deep potential well exists on the reaction path, obtaining convergent result is very time-consuming. So some approximate methods were used in previous theoretical calculations. However the Coriolis coupling effect plays an important role in the reaction, and thus whether these approximate methods are reasonable needs further testing. Based on the potential energy surface (PES) reported by Song et al., the dynamical calculations of H/D + Li2 LiH/LiD + Li reactions are carried out by time dependent quantum wave packet method with second order split operator in a collision energy range from 0 to 0.4 eV. In order to obtain the convergent results, lots of convergence tests are carried out and because the Coriolis coupling effect plays an important role in the reaction, all the number of projections of total angular momentum J are included in the present calculation. The dynamical properties such as reaction probability, integral cross section, differential cross section are calculated and compared with previous theoretical values. Large discrepancies are found between present results and the values obtained from Gao et al. especially at high collision energies. Owing to the fact that the same PES is applied to the calculation and Gao's results of total angular momentum J=0 accord well with the present values, we suppose that the parameters used in the calculation have little influence on the final results and the main discrepancies are attributed to the number of projections of total angular momentum which are cut off in Gao et al.'s calculation. In order to verify our speculation, the numbers of projections of total angular momentum which are 1, 5, 10, 15, 20, and 25, are considered in the calculation, respectively. The results indicate that the main discrepancy between present values and the results obtained from Gao et al. can be attributed to the number of projections of total angular momentum used in Gao et al.'s calculation that is not convergent, and that the present values are more accurate than previous theoretical studies for all the numbers of projections of total angular momentum which are included in the calculation. Furthermore, when the H atom is substituted by the heavy isotope D atom, the reaction probability and integral cross section become large. However, it does not generate large effect on the reaction mechanism. The forward and backward symmetry differential cross section signals indicate that the complex forming reaction mechanism dominates the reaction.

3D time-dependent wave-packet approach in hyperspherical coordinates for the H + O2 reaction on the CHIPR and DMBE IV potential energy surfaces.

We perform quantum dynamics calculations for the reaction H + O2 → O + OH on the ground-state potential energy surfaces CHIPR [Varandas, J. Chem. Phys., 2013, 138, 134117] and DMBE IV [Pastrana et al., J. Phys. Chem. 1990, 94, 8073] using a three-dimensional time-dependent wave packet formalism based on hyperspherical coordinates. Initial rovibrational state [O2(v = 0-4, j = 1-5)] dependent reaction probabilities are calculated for the case J = 0. The J-shifting scheme is employed to estimate initial state selected integral cross-sections as well as thermal rate coefficients, which is verified using a realistic extrapolation scheme. The calculated total and state-to-state rate coefficients are compared with the findings of recent experimental studies and previous theoretical calculations.

Beyond Born-Oppenheimer theory for ab initio constructed diabatic potential energy surfaces of singlet H3+ to study reaction dynamics using coupled 3D time-dependent wave-packet approach.

The workability of beyond Born-Oppenheimer theory to construct diabatic potential energy surfaces (PESs) of a charge transfer atom-diatom collision process has been explored by performing scattering calculations to extract accurate integral cross sections (ICSs) and rate constants for comparison with most recent experimental quantities. We calculate non-adiabatic coupling terms among the lowest three singlet states of H3+ system (11A', 21A', and 31A') using MRCI level of calculation and solve the adiabatic-diabatic transformation equation to formulate the diabatic Hamiltonian matrix of the same process [S. Mukherjee et al., J. Chem. Phys. 141, 204306 (2014)] for the entire region of nuclear configuration space. The nonadiabatic effects in the D+ + H2 reaction has been studied by implementing the coupled 3D time-dependent wave packet formalism in hyperspherical coordinates [S. Adhikari and A. J. C. Varandas, Comput. Phys. Commun. 184, 270 (2013)] with zero and non-zero total angular momentum (J) on such newly constructed accurate (ab initio) diabatic PESs of H3+. We have depicted the convergence profiles of reaction probabilities for the reactive non-charge transfer, non-reactive charge transfer, and reactive charge transfer processes for different collisional energies with respect to the helicity (K) and total angular momentum (J) quantum numbers. Finally, total and state-to-state ICSs are calculated as a function of collision energy for the initial rovibrational state (v = 0, j = 0) of the H2 molecule, and consequently, those quantities are compared with previous theoretical and experimental results.

Global X2 A′ potential energy surface of Li2 H and quantum dynamics of H + Li2 (X1 Σg + ) → Li + LiH (X1 Σ+ ) reaction

A global potential energy surface (PES) for the electronic ground state of Li2H system is constructed over a large configuration space. About 30 000 ab initio energy points have been calculated by MRCI-F12 method with aug-cc-pVTZ basis set. The neural network method is applied to fit the PES and the root mean square error of the current PES is only 1.296 meV. The reaction dynamics of the title reaction has been carried out by employing time-dependent wave packet approach with second order split operator on the new PES. The reaction probability, integral cross section and thermal rate constant are obtained from the dynamics calculation. In most of the collision energy regions, the integral cross sections are in well agreement with the results reported by Gao et al. The rate constant calculated from the new PES increases in the temperature range of present investigation.

Time-Dependent Quantum Wave Packet Study of the Si + OH → SiO + H Reaction: Cross Sections and Rate Constants.

The dynamics of the Si(3P) + OH(X2Π) → SiO(X1Σ+) + H(2S) reaction is investigated by means of the time-dependent wave packet (TDWP) approach using an ab initio potential energy surface recently developed by Dayou et al. ( J. Chem. Phys. 2013 , 139 , 204305 ) for the ground X2A' electronic state. Total reaction probabilities have been calculated for the first 15 rotational states j = 0-14 of OH(v=0,j) at a total angular momentum J = 0 up to a collision energy of 1 eV. Integral cross sections and state-selected rate constants for the temperature range 10-500 K were obtained within the J-shifting approximation. The reaction probabilities display highly oscillatory structures indicating the contribution of long-lived quasibound states supported by the deep SiOH/HSiO wells. The cross sections behave with collision energies as expected for a barrierless reaction and are slightly sensitive to the initial rotational excitation of OH. The thermal rate constants show a marked temperature dependence below 200 K with a maximum value around 15 K. The TDWP results globally agree with the results of earlier quasi-classical trajectory (QCT) calculations carried out by Rivero-Santamaria et al. ( Chem. Phys. Lett. 2014 , 610-611 , 335 - 340 ) with the same potential energy surface. In particular, the thermal rate constants display a similar temperature dependence, with TDWP values smaller than the QCT ones over the whole temperature range.