Time-dependent Quantum Wave Packet Method Research Articles

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.

Theoretical investigations of the Au++H2 reactive scattering by the time-dependent quantum wave packet method

Employing the state-to-state time-dependent quantum wave packet method, the Au[Formula: see text]H2 reactive scattering with initial states [Formula: see text], [Formula: see text] and 1 were investigated. Total reaction probabilities, product state-resolved integral cross-sections (ICSs) and differential cross-sections (DCSs) were calculated up to collision energy of 4.5 eV. The numerical results show that total reaction probabilities and ICSs increase with increasing collision energies, and there is little effect to the reactive scattering processes from the rotational excitation of H2 molecule. Below collision energy of around 3.0 eV, the role of the potential well in the entrance channel is significant and the reactive scattering proceeds dominantly by an indirect process, which leads to a nearly symmetric shape of the DCSs. With collision energy higher than 4.0 eV, the reactive scattering proceeds through a direct process, which leads to a forward biased DCSs, and also a hotter rotational distributions of the products. Total ICS agrees with the results by the quasi-classical trajectories theory very well, which suggests that the quantum effects in this reactive process are not obvious. However, the agreement between the experimental total cross-section and our theoretical result is not so good. This may be due to the uncertainty of the experiment or/and the inaccuracy of the potential energy surface.

State-resolved dynamics study of the H + HS reaction on the 3A' and 3A″ states with time-dependent quantum wave packet method.

The quantum dynamics calculations of the H + HS (v = 0, j = 0) reaction on the 3A' and 3A″ potential energy surfaces (PESs) are performed using the reactant coordinate based time-dependent wave packet method. State-averaged and state-resolved results for both channels of the title reaction are presented in the 0.02-1.0 eV collision energy range and compared with those carried out with quasi-classical trajectory (QCT) method. Total integral cross sections (ICSs) for both channels are in excellent agreement with previous quantum mechanical (QM)-Coriolis coupling results while poorly agree with the QCT ICSs of the exchange channel, particularly near the threshold energy region. The product rotational distributions show that for the abstraction channel, the agreement between our QM and the QCT results improves with increasing collision energy. For the exchange channel, our calculations predict colder rotational distributions as compared to those obtained by QCT calculations. Although the QM total differential cross sections (DCSs) are in qualitatively good agreement with the QCT results, the two sets of the state-to-state DCSs with several peaks exhibit great divergences. The origin of the divergences are traced by analyzing the QM DCS for the H + HS (v = 0, j = 0) → H2 (v' = 0, j' = 0) + S reaction on the 3A″ PES at Ec = 1.0 eV. It is discovered that several groups of J partial waves are involved in the reaction and the shape of the DCS is greatly altered by quantum interferences between them.

Coherent phase control of population transfer through ladder system in two laser pulses with ω and nω

The ladder transitions controlled by two harmonic pulses are investigated theoretically using a time-dependent quantum wave packet method for the ground electronic state of HF molecule. By choosing [Formula: see text], [Formula: see text] and [Formula: see text] schemes, the population can be transferred to target states [Formula: see text]. The population distribution can be controlled by the average amplitude of total electric field which depends on the relative phase of two pulses. With the variation of the relative phase between [Formula: see text] and [Formula: see text] pulses, the variation of population has a period of [Formula: see text]. For [Formula: see text] and [Formula: see text] schemes, the population distributions show oscillation behavior with a period of [Formula: see text] by varying the relative phase. The two harmonic pulses can realize a nearly complete population transfer to the target state.

Reactive scattering of an electronically-excited nitrogen atom with H2 and its isotopic variants: [formula omitted

Total reaction probabilities, integral cross sections and total rate constants of the N(2D)+H2 reaction and its isotopic variants were calculated using a time-dependent quantum wave packet method with a centrifugal sudden approximation on the latest reported global potential energy surface. The effect of rotational excitation of the diatoms and its projection quantum number on the behaviour of reaction probabilities was studied. Reaction probabilities were calculated using a flux wave packet method. The results indicate that the reaction kinetics are affected by intermolecular isotope and collision energies.

The extended “ladder” transition controlled by two harmonic pulses

The extended “ladder” transition controlled by two harmonic pulses is investigated by using a time-dependent quantum wave packet method. The molecular population transfers from the state|0, 0> angle to the states|5, 0> angle and|5, 2> angle induced by the fundamental and second-harmonic pulses, and to the states|5, 3> angle and |6, 2> angle induced by the fundamental and third-harmonic pulses. The calculated results show that the two harmonic pulses can induce a nearly 100% of population to transfer to the target state. The relative phase of two pulses can affect the population distribution. The variation of population has a period of π for the fundamental and second-harmonic pulses, and a period of 2π for the fundamental and third-harmonic pulses.

Coherent control of interfering wave packets in dissociating HD+ molecules: the role of phase and delay time

The coherent control of interference between dissociating wave packets of the HD+ molecules generated by a pair of time-delayed and phase-locked femtosecond laser pulses is theoretically studied by using the time-dependent quantum wave packet method. The density function in both coordinate and momentum representation are presented and discussed. It is demonstrated that the interference pattern is observed in both coordinate and momentum density functions. The interference undergoes a π-phase shift when the delay time between the two phase-locked femtosecond laser pulses is changed by half an optical period. In particular, the number of interference fringes, the fringe spacing in the R-dependent density distribution |ψ(R)|2, and the modulation period of the energy-dependent distribution of the fragments P(E) can be tuned by two phase-locked femtosecond pulses.

Molecular alignment effect on the photoassociation process via a pump-dump scheme.

The photoassociation processes via the pump-dump scheme for the heternuclear (Na + H → NaH) and the homonuclear (Na + Na → Na2) molecular systems are studied, respectively, using the time-dependent quantum wavepacket method. For both systems, the initial atom pair in the continuum of the ground electronic state (X(1)Σ(+)) is associated into the molecule in the bound states of the excited state (A(1)Σ(+)) by the pump pulse. Then driven by a time-delayed dumping pulse, the prepared excited-state molecule can be transferred to the bound states of the ground electronic state. It is found that the pump process can induce a superposition of the rovibrational levels |v, j〉 on the excited state, which can lead to the field-free alignment of the excited-state molecule. The molecular alignment can affect the dumping process by varying the effective coupling intensity between the two electronic states or by varying the population transfer pathways. As a result, the final population transferred to the bound states of the ground electronic state varies periodically with the delay time of the dumping pulse.

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.

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.

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.

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.

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.

Accurate Study on the Quantum Dynamics of the He + HeH+ (X1Σ+) Reaction on A New ab Initio Potential Energy Surface for the Lowest 11A′ Electronic Singlet State

A time-dependent quantum wave packet method is used to investigate the dynamics of the He + HeH(+)(X(1)Σ(+)) reaction based on a new potential energy surface [Liang et al., J. Chem. Phys.2012, 136, 094307]. The coupled channel (CC) and centrifugal-sudden (CS) reaction probabilities as well as the total integral cross sections are calculated. A comparison of the results with and without Coriolis coupling revealed that the number of K states N(K) (K is the projection of the total angular momentum J on the body-fixed z axis) significantly influences the reaction threshold. The effective potential energy profiles of each N(K) for the He + HeH(+) reaction in a collinear geometry indicate that the barrier height gradually decreased with increased N(K). The calculated time evolution of CC and CS probability density distribution over the collision energy of 0.27-0.36 eV at total angular momentum J = 50 clearly suggests a lower reaction threshold of CC probabilities. The CC cross sections are larger than the CS results within the entire energy range, demonstrating that the Coriolis coupling effect can effectively promote the He + HeH(+) reaction.

CONTROLLING ABOVE-THRESHOLD DISSOCIATION BRANCHING RATIOS OF HD+ WITH FEMTOSECOND LASER PULSE TRAIN

Above-threshold dissociation (ATD) process of the molecular ions HD+ steered by a femtosecond laser pulse train (LPT) is investigated theoretically using the time-dependent quantum wave packet method. Energy-dependent distributions of ATD fragments are analyzed by using an asymptotic-flow expression in the momentum space. It is found that fragment kinetic energy spectra shift to low energy region with increasing pulse number of LPT. The photofragment branching ratio between the 1sσg and 2pσu dissociation channels is sensitive to the pulse number of LPT. The momentum distribution of the ATD fragments is discussed in detail.

UV Photolysis of N2O Isotopomers: Isotopic Fractionations and Product Rotational Quantum State Distributions

The time-dependent quantum wave packet method is used to study the dynamics of the photodissociation processes for the isotopomers 14N14N16O, 14N15N16O, 15N14N16O, 15N15N16O, 14N14N17O, and 14N14N18O. In general, the computed isotopic fractionation factors derived from the absorption cross sections of five heavy isotopomers are in good agreement with the experimental results. Relative to the 14N14N16O isotopomer, the N2 rotational state distributions for the isotopically nitrogen substituted N2O are found to be entirely shifted to higher rotational states. Similar to its isotopic fractionation factors, the N2 rotational state distributions for the asymmetric isotopomers 14N15N16O and 15N14N16O are found to be observably different.

The Coriolis effect in the N + ND → N 2 + D reaction

In this paper, we employ the time-dependent quantum wave packet method to explore the Coriolis couplings effects and ro-vibrational excitation of reagent on the two coupled potential energy surfaces (PESs) (1 2A′ and 2 2A′) [V.C. Mota, P. Caridade, A.J.C. Varandas, J. Theor. Comput. Chem. 8 (2009) 849] for the title reaction. It is found that the effect of Coriolis coupling for the title reaction is considerable and its neglect remarkably underestimates the integral cross sections. Moreover, it turns out that vibrational and rotational excitation generally increases the reaction probabilities on both, the 1 2A′ and 2 2A′ states, and the effect of vibrational excitation for 1 2A′ PES is more pronounced.

Above threshold dissociation in HD+ using frequency chirped laser pulses

We have theoretically studied the dynamics of above threshold dissociation (ATD) in molecular ions HD+ using frequency chirped femtosecond laser pulses from numerical solutions of the time-dependent Schrödinger equation by using the three-dimensional time-dependent quantum wave packet method. Energy-dependent distributions of ATD fragments are analyzed by an asymptotic-flow expression in momentum space. Linearly positive and negative frequency chirped laser pulses are adopted. It is found that varying frequency chirped parameters can change branching ratios of the 1sσ g and 2pσ u dissociations channels. The concept of a light-induced potential is used to interpret the ATD process. The angular resolved energy distributions of the photofragments are also illustrated.

Multiphoton association reaction He + H+ → HeH+ steered by ultra-short laser pulse

The multiphoton association reaction He + H+ → HeH+ in the electronic ground state is investigated using the time-dependent quantum wave packet method. It is shown that the collision pairs He + H+ in continuum state transfer into ν = 0 state and then produce stable molecules HeH+ through emission of two or three photons. The multiphoton transition takes place via intermediate states, and the transfer probability is determined by the collision energy and the intermediate states. The populations of the intermediate states and ν = 0 state can be controlled by the laser duration. The three-photon transition is more efficient than the two-photon transition for producing the molecule HeH+ in ν = 0 state. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011