Time-dependent Quantum Wave Packet Research Articles

Laser-driven isomerization of HCN → HNC: the importance of rotational excitation.

We report a time-dependent quantum wave packet theory, which is employed to interpret the isomerization dynamics of HCN molecules induced by an intense picosecond infrared laser field. Considering the molecular rotational degrees of the freedom, the wave functions are expanded in terms of molecular rotational bases. Our full-dimensional quantum model includes the full Coriolis coupling in the molecular kinetic energy Hamiltonian and dipole approximation in interaction terms. The numerical results show that the field-induced molecule rotational excitation plays an important role in the isomerization dynamical process. Some phenomena appear such as two-step two-photon absorption and highly oscillatory structure in rotational state distributions. The centrifugal sudden (CS) approximation calculation is also carried out and compared in this work; it is shown that the Coriolis couplings may lead to a significant decrease in the isomerization rate but highly enhanced molecular rotational excitation.

Factors Affecting the Branching Ratio of Photodissociation: Thiophenol Studied through Quantum Wavepacket Dynamics.

The photodissociation dynamics of thiophenol (PhSH) excited to the 1(1) ππ* state was investigated by time-dependent quantum wavepacket propagation within two-dimensional (2D) space consisting of the S-H bond and -SH torsion. We systematically studied the dependence of the branching ratio (Ã/X(~)) between the two electronic states of the phenylthiyl radical (PhS(.) ) on several factors of the 2D potential energy surfaces (PESs). The effect of a reduced initial barrier to the first ππ*/πσ* conical intersection (CI) was found to be marginal, whereas the effects of a reduced torsional barrier of -SH on the excited ππ* state and the mitigated slope of the πσ* PES between the first (ππ*/πσ*) and the second (πσ*/S0 ) CIs were noticeable. The effect of the slope on the branching ratio has never been previously noticed. It was shown that the branching ratio can be sufficiently above unity without pre-excitation of the torsion mode of -SH, which has been assumed so far.

The isotope effect on the photoassociation of X + F → XF (X = H, D)

The photoassociation (PA) reactions of H + F → HF and D + F → DF are investigated by using the time-dependent quantum wave packet method. For each system, we consider four cases, where the target state is set to be ∣ν = 16, 17, 18, 19〉, respectively. The effects of the initial collision momentum and laser parameters, including intensity, pulse duration, and frequency, on the final association probability are calculated and discussed. It is found that the PA probability for H + F → HF (∣ν = 16, 17, 18〉) is significantly greater than that for D + F → DF (∣ν = 16, 17, 18〉), while the PA probability to ∣ν = 19〉 for the latter system is greater than the former one. This isotope effect has been connected with the Franck–Condon overlap integral between the target vibrational state and the collision continuum state.

State-to-state reaction dynamics of (18)O+(32)O2 studied by a time-dependent quantum wavepacket method.

The title isotope exchange reaction was studied by converged time-dependent wave packet calculations, where an efficient 4th order split operator was applied to propagate the initial wave packet. State-to-state differential and integral cross sections up to the collision energy of 0.35 eV were obtained with (32)O2 in the hypothetical j0 = 0 state. It is discovered that the differential cross sections are largely forward biased in the studied collision energy range, due to the fact that there is a considerable part of the reaction occurring with large impact parameter and short lifetime relative to the rotational period of the intermediate complex. The oscillations of the forward scattering amplitude as a function of collision energy, which result from coherent contribution of adjacent resonances, may be a sensitive probe for examining the quality of the underlying potential energy surface. A good agreement between the theoretical and recent experimental integral and differential cross sections at collision energy of 7.3 kcal/mol is obtained. However, the theoretical results predict slightly too much forward scattering and colder rotational distributions than the experimental observations at collision energy of 5.7 kcal/mol.

The role of the shape resonance state in low energy electron induced single strand break in 2'-deoxycytidine-5'-monophosphate.

Low energy electron (LEE) induced single strand break (SSB) has been studied for 2'-deoxycytidine-5'-monophosphate (5'-dCMPH) molecules in the gas phase by means of ab initio electronic structure methods and local complex potential based time-dependent wavepacket quantum mechanical calculations. We have found that the LEE attachment to this cytidine nucleotide results in the formation of a transient metastable anion. The results obtained here show that the electron attachment takes place at the cytosine nucleobase center and within 18-20 fs, the LEE transfers to the σ* orbital of the sugar-phosphate 5' C-O bond. The characteristic electron attachment cross section spectrum is found at ∼1 eV, which is in good agreement with the available experimental observations. Quantum mechanical tunneling of the 5' C-O bound vibrational energy levels may contribute to SSB only above 1.5 eV energy regimes.

The quantum dynamics of the reactions N+H2(HD,D2) and their vibrational excitation effect

The N(4S)+H2 reaction and its isotopic variants have been investigated by means of time-dependent quantum wave packet with split operator method on the ground state potential energy surface (Zhai and Han, J. Chem. Phys. 2011, 135, 104314). The reaction probabilities, integral cross sections, branching ratio of the integral cross sections, and effect of vibrational excitation of H2, HD, and D2 diatomic molecules are presented and discussed. The results reveal that the intramolecular isotopic effect is greater than the intermolecular one, and that the vibrational excitation of the diatomic molecules can promote the progress of this reaction. In addition, a limited number of rigorous Coriolis coupling calculations of the integral cross sections of the N(4S)+H2 reaction have been carried out. Also shown is that since the Coriolis coupling plays a small part in this accurate quantum calculation, the cheaper centrifugal sudden calculations here reported are effective for this reactive system. © 2014 Wiley Periodicals, Inc.

Efficient fourth-order split operator for solving the triatomic reactive Schrödinger equation in the time-dependent wavepacket approach.

An efficient fourth-order split operator (named 4A6a in the main text), which was presented in the work by Blanes and Moan and was a partitioned Runge-Kutta method ( J. Comput. Appl. Math. 2002 , 142 , 313 ), is recommended for general usage in a reactive scattering calculation by the time-dependent quantum wavepacket method. This 4A6a propagator is constructed in a TVT form, that is, splitting in kinetic-potential-kinetic form, which is an optimal one among a series of higher-order split operators in examining with several typical triatomic reactive scattering processes, H + H2, H + H2(+), H + NH, H + O2, and F + HD reactions. A detailed comparison between the performances of higher-order split operators in the VTV form, that is, splitting in a potential-kinetic-potential, which was reported by Sun et al. ( Phys. Chem. Chem. Phys. 2012 , 14 , 1827 ), and in the TVT form reported in the current work suggests that the recommended 4A6a operator in the TVT form always has good numerical efficiency. This fact may suggest that this fourth propagator in the TVT form can be safely chosen without any further examination, at least among all of the higher-order split operators tested in this work, to apply in an efficient time-dependent wavepacket numerical calculation for describing a triatomic reactive scattering process.

Quantum dynamics study of H + DBr and D + HBr reaction.

Time-dependent quantum wave packet calculations have been performed for the H + DBr and D + HBr reaction using the recent diabatic potential energy surfaces. Reaction probabilities, integral cross sections, and rate constants are obtained. The results show that the isotopic effects have an influence on the nonadiabatic effect which is generally inversely proportional to the atom mass. The calculated rate constants are in good overall agreement with experimental values, indicating that the ab initio surfaces are accurate to describe the isotopic effects.

Coriolis coupling effect of state-to-state quantum dynamics for He + HeH+

To study the Coriolis coupling (CC) effect on the proton transfer reaction He + HeH+ → HeH+ + He on a state-to-state level, a time-dependent quantum wave packet approach is performed based on a new potential energy surface constructed by Liang et al. The CC and centrifugal sudden (CS) approximation state-to-state integral cross section and thermal rate constants are obtained for the first time. The total and the state-to-state differential cross sections (DCSs) are calculated over a collision energy range of 0.01–0.4 eV. Comparisons between the CC and CS results reveal that the CC effect significantly influences the title reaction and that neglecting the CC effect lowers the cross sections and thermal rate constant. The CC effect significantly influences the DCSs, especially at higher product rotational quantum numbers. For the v′ = 0 product states, neglecting the CC effect leads to a much larger relative error in the calculated DCSs than in the v′ = 1 case. Reactant vibrational excitations have more effect in promoting reactivity than the rotational excitations.

Time-dependent quantum wave packet dynamics of S + OH reaction on its electronic ground state.

Initial state-selected dynamics of the S((3)P) + OH (X(2)Π) → SO (X(3)Σ(-)) + H ((2)S) reaction on its electronic ground potential energy surface (X̃(2)A") is investigated here by a time-dependent wave packet propagation (TDWP) approach. Total reaction probabilities for the three-body rotational angular momentum up to J = 138 are calculated to obtain converged integral reaction cross sections and state-specific rate constants employing the centrifugal sudden (CS) approximation. The convergence of the latter quantities is checked by varying all parameters used in the numerical calculations. The cross section and rate constant results are compared with those available in the literature, calculated with the aid of the quasi-classical trajectory method on the same potential energy surface. Reaction probabilities obtained with the TDWP approach exhibit dense oscillatory structures, implying formation of a metastable quasi-bound complex during the collision process. The effect of rotational and vibrational excitations of reagent OH on the dynamical attributes is also examined. While the rotational excitation of reagent OH decreases the reactivity, its vibrational excitation enhances the same.

A Multiwavelet Treatment of the Quantum Subsystem in Quantum Wavepacket Ab Initio Molecular Dynamics through an Hierarchical Partitioning of Momentum Space.

We present an hierarchical scheme where the propagator in quantum dynamics is represented using a multiwavelet basis. The approach allows for a recursive refinement methodology, where the representation in momentum space can be adaptively improved through additional, decoupled layers of basis functions. The method is developed within the constructs of quantum-wavepacket ab initio molecular dynamics (QWAIMD), which is a quantum-classical method and involves the synergy between a time-dependent quantum wavepacket description and ab initio molecular dynamics. Specifically, the current development is embedded within an "on-the-fly" multireference electronic structural generalization of QWAIMD. The multiwavelet treatment is used to study the dynamics and spectroscopy in a small hydrogen bonded cluster. The results are in agreement with previous calculations and with experiment. The studies also allow an interpretation of the shared proton dynamics as one that can be modeled through the dynamics of dressed states.

Time-dependent quantum wave packet and quasiclassical trajectory studies of the Au(2S) + H2(X1∑+g) → AuH(X1∑+g) + H(2S) reaction

The time-dependent quantum wave packet (TDWP) and quasiclassical trajectory calculations (QCT) are carried out for the Au(2S) + H2(X1∑+g) → AuH(X1∑+g) + H(2S) reaction on a global potential energy surface. The reaction probabilities at a series of J values, integral cross sections (ICSs) and differential cross sections of the title reaction are calculated by the TDWP method. For reaction probabilities, there are a mass of sharp oscillations at low collision energy, which can be attributed to resonances supported by the potential well. Due to the endothermicity of the title reaction, the total ICS shows a threshold about 1.53 eV. In order to further investigate the reactive mechanism, the lifetime of complex is calculated by QCT method. At the low collision energy, most intermediate complexes are long lived, which implies that the reaction is governed by indirect reactive mechanism. With the collision energy increasing, the direct reactive mechanism occupies the dominant position. Due to the change of the reactive mechanism, the angular distribution shifts toward the forward direction with collision energy increasing. The isotopic variant, Au + D2→AuD + D reaction, is also calculated by TDWP method. The calculated reaction probabilities and ICSs show that the isotope effect reduces the reactivity.

Branching Ratio between Proton Transfer and Electron Transfer Channels of a Bidirectional Proton-Coupled Electron Transfer.

Rigorous quantum dynamical study of concerted proton-coupled electron transfer (PCET) on the time scale of a few femtoseconds (fs) has been rarely reported. Herein, a time-dependent quantum wavepacket propagation method was applied to the dynamics of the charge-transfer excited electronic state of FHCl corresponding to F(+)HCl(-). The dynamics corresponds to a bidirectional PCET with two dissociation channels: the electron transfer (ET, generating FH+Cl) and proton transfer (PT, generating F+HCl) paths. The calculated branching ratio (Cl/F), 0.78, implies a surprising fact: PT prevails over ET. A detailed analysis of the proton movement and electron readjustment suggests that the proton movement starts ∼3 fs earlier than the electron movement, and the electron readjustment is triggered by the initial movement of the proton. The branching ratio drastically inverts to 1.24 because of a reduced nonadiabatic effect in the isotope-substituted system, FDCl.

Intense attosecond pulse generated from a molecular harmonic plateau of H2+ in mid-infrared laser fields

High-order harmonic generation from the molecular ion H2+ exposed to intense laser fields is investigated by the time-dependent quantum wave packet method. Molecular and atomic plateaus of harmonic spectra are effectively distinguished at large internuclear distances, where the harmonic efficiency of the molecular plateau is several orders of magnitude higher than that of the latter. We report on a physical model of the origin of the molecular supercontinua and reveal that the creation of this plateau directly results from the interference of the intramolecular electronic wave packet localized in two potential wells following the laser field. This is our first effort in utilizing the efficient molecular plateau to generate intense isolated attosecond pulses by controlling the dynamics of the nucleus and electrons with a mid-infrared laser. Further, we show that the harmonic plateau is enhanced at the macroscopic level by solving the Maxwell wave equation coupled with the Schrödinger equation.

Theoretical Study of the H+ClO Reaction

We present a theoretical study of the H+OCl system on an accurate ab initio potential energy surface (PES) investigated by Peterson et al.[J. Chem. Phys. 113 (2000) 6186]. Both the exact time-dependent quantum wave packet (TDWP) and quasi-classical trajectory (QCT) methods are employed. The results of reaction probabilities for total angular momentum J = 0 and the integral cross section calculated by the TDWP are in good agreement with the QCT ones. Additionally, the nearly forward-backward symmetric product scattering angular distributions and the weak products' rotational alignment effect obtained by the QCT calculations are attributed to a long-lived intermediate reaction process.

Time-Dependent Wave Packet Quantum Scattering and Quasi-Classical Trajectory Calculations of the H + FCl(v=0,j=0) → HF + Cl/HCl + F Reaction

The dynamics of the title reaction are investigated using both time-dependent wave packet quantum scattering and quasi-classical trajectory (QCT) methods on adiabatic ground 1(2)A' potential energy surface (PES). Compared with the quantum results of reaction probabilities of H + FCl(J=0) → HF + Cl/HCl + F, the QCT method is proven feasible and further employed to produce integral cross sections and rate constants. Significant resonance structures are observed in the reaction probabilities using the quantum method; however, there are some undulations in the calculated QCT integral cross sections for both product channels. A comparison between the quantum mechanical coupled-channel (CC) calculation and centrifugal sudden approximation calculation reveals the very important role of Coriolis coupling effects in the quantum calculation. Comparisons between the calculated thermal rate constants for both reactions and the previous theoretical and experimental results have been done. HCl product formation is favored over the HF product in the reactive system. Finally, the HF products are found to be mainly forward scattering, and the HCl products are mainly backward scattering.

Manifestation of external field effect in time-resolved photo-dissociation dynamics of LiF

The photo-dissociation dynamics of LiF is investigated with newly constructed accurate ab initio potential energy curves (PECs) using the time-dependent quantum wave packet method. The oscillations and decay of the wave packet on the adiabats as a function of time are given, which can be compared with the femtosecond transition-state (FTS) spectroscopy. The photo-absorption spectra and the kinetic-energy distribution of the dissociation fragments, which can exhibit the vibration-level structure and the dispersion of the wave packet, respectively, are also obtained. The investigation shows a blue shift of the band center for the photo-absorption spectrum and multiple peaks in the kinetic-energy spectrum with increasing laser intensity, which can be attributed to external field effects. By analyzing the oscillations of the wave packet evolving on the upper adiabat, an approximate inversion scheme is devised to roughly deduce its shape.

INVESTIGATION OF THE EXCHANGE REACTIONH + H′S → HS + H′ON THE1A′STATE POTENTIAL ENERGY SURFACE

The quantum time dependent wave packet (TDWP) and quasiclassical trajectory (QCT) calculations were carried out to study the exchange reaction H(2S) + H′S(2Π) → HS(2Π) + H′(2S) on the1A′potential energy surface (PES). The integral cross sections of the H + H′S (v = j = 0) → HS + H′reaction calculated by the two methods were presented. The results reveal that the integral cross sections (ICS) decrease with the collision energy increasing. The result of the QCT calculations is reasonably consistent with the time-dependent wave packet. Moreover, the differential cross sections (DCS) were calculated by the QCT method at the four different collision energies, which display a forward–backward symmetry. A long-lifetime H2S intermediate complex of the exchange reaction was found according to the trajectories. In the stereodynamics investigation, the polar and dihedral angle distribution functions were calculated, which have the distinct oscillations. The oscillations could be attributed to the deep well on the1A′PES. However, based on the polar-angle and dihedral angle distribution functions, it could be predicted that the main product rotational angular momentum preferentially point to the positive or negative direction of y-axes.

Time-dependent quantum wave packet study of the Ar+H2+→ArH++H reaction on a new ab initio potential energy surface for the ground electronic state (12A′)

A new global potential energy surface for the ground electronic state (1(2)A') of the Ar+H2(+)→ArH(+)+H reaction has been constructed by multi-reference configuration interaction method with Davidson correction and a basis set of aug-cc-pVQZ. Using 6080 ab initio single-point energies of all the regions for the dynamics, a many-body expansion function form has been used to fit these points. The quantum reactive scattering dynamics calculations taking into account the Coriolis coupling (CC) were carried out on the new potential energy surface over a range of collision energies (0.03-1.0 eV). The reaction probabilities and integral cross sections for the title reaction were calculated. The significance of including the CC quantum scattering calculation has been revealed by the comparison between the CC and the centrifugal sudden approximation calculation. The calculated cross section is in agreement with the experimental result at collision energy 1.0 eV.

Time-dependent quantum wave packet dynamics of the C + OH reaction on the excited electronic state

Quantum state-selected dynamics of C((3)P) + OH (X(2)Π) → CO(a(3)Π) + H ((2)S) reaction on its first excited electronic potential energy surface (1(2)A(")) is examined here using a time-dependent wave packet propagation approach. All partial wave contributions for the total angular momentum, J = 0-95, are included to obtain the converged cross sections and initial state-selected rate constants in the temperature range of 10-500 K. The reaction probability, as a function of collision energy, exhibits dense oscillatory structures owing to the formation of resonances during collision. These resonance structures also persist in reaction cross sections. The effect of reagent rotational and vibrational excitation on the dynamical attributes is examined and discussed. Reagent rotational excitation decreases the reactivity whereas, vibrational excitation of the reagent has minor effects on the reactivity. The results presented here are in good accord with those obtained using the time-independent quantum mechanical and quasi-classical trajectory methods.