High-Accurate Transparent Boundary Conditions for Time-Dependent Quantum Wave Packet Method

Complex absorbing potential is usually required in a time-dependent wave packet method to accomplish the calculation in a truncated region. Usually it works effectively but becomes inefficient when the wave function involves translational energy of broad range, particularly involving ultra-low energy. In this work, a new transparent boundary condition (TBC) is proposed for the time-dependent wave packet method. It in principle is of spectral accuracy when typical discrete variable representations are applied. The prominent merit of the new TBC is that its accuracy is insensitive to the translational energy distribution of the wave function, in contrast with the complex absorbing potential. Application of the new TBC is given to one-dimensional particle wave packet scatterings from a barrier with a potential well, which supports resonances states.     

Moving boundary truncated grid method: Multidimensional quantum dynamics

The moving boundary truncated grid (TG) method is used to study wave packet dynamics of multidimensional quantum systems. As time evolves, appropriate Eulerian grid points required for propagating a wave packet are activated and deactivated with no advance information about the dynamics. This method is applied to the Henon-Heiles potential and wave packet barrier scattering in two, three, and four dimensions. Computational results demonstrate that the TG method not only leads to a great reduction in the number of grid points needed to perform accurate calculations but also is computationally more efficient than the full grid calculations.     

Wave packet theory of dynamic stimulated Raman spectra in femtosecond pump-probe spectroscopy

The quantum theory for stimulated Raman spectroscopy from a moving wave packet using the third-order density matrix and polarization is derived. The theory applies, in particular, to the new technique of femtosecond broadband stimulated Raman spectroscopy (FSRS). In the general case, a femtosecond actinic pump pulse first prepares a moving wave packet on an excited state surface which is then interrogated with a coupled pair of picosecond Raman pump pulse and a femtosecond Raman probe pulse and the Raman gain in the direction of the probe pulse is measured. It is shown that the third-order polarization in the time domain, whose Fourier transform governs the Raman gain, is given simply by the overlap of a first-order wave packet created by the Raman pump on the upper electronic state with a second-order wave packet on the initial electronic state that is created by the coupling of the Raman pump and probe fields acting on the molecule. Calculations are performed on model potentials to illustrate and interpret the FSRS spectra.     

Geometric phase effects in the coherent control of the branching ratio of photodissociation products of phenol

Optimal control simulation is used to examine the control mechanisms in the photodissociation of phenol within a two-dimensional, three-electronic-state model with two conical intersections. This model has two channels for H-atom elimination, which correspond to the (2)pi and (2)sigma states of the phenoxyl radical. The optimal pulse that enhances (2)sigma dissociation initially generates a wave packet on the S(1) potential-energy surface of phenol. This wave packet is bifurcated at the S(2)-S(1) conical intersection into two components with opposite phases because of the geometric phase effect. The destructive interference caused by the geometric phase effect reduces the population around the S(1)-S(0) conical intersection, which in turn suppresses nonadiabatic transitions and thus enhances dissociation to the (2)sigma limit. The optimal pulse that enhances S(0) dissociation, on the other hand, creates a wave packet on the S(2) potential-energy surface of phenol via an intensity borrowing mechanism, thus avoiding geometric phase effects at the S(2)-S(1) conical intersection. This wave packet hits the S(1)-S(0) conical intersection directly, resulting in preferred dissociation to the (2)pi limit. The optimal pulse that initially prepares the wave packet on the S(1) potential-energy surface (PES) has a higher carrier frequency than the pulse that prepares the wave packet on the S(2) PES. This counterintuitive effect is explained by the energy-level structure and the S(2)-S(1) vibronic coupling mechanism.     

Scattered wave packet formalism for the energy-resolved reaction probability

The scattered wave packet formalism developed for a quantum subsystem interacting with reservoirs through open boundaries is utilized to calculate the energy-resolved transmission probability. The total wave function is split into incident and scattered components. Markovian outgoing wave boundary conditions are imposed on the scattered or total wave function by the polynomial method. The wave packet correlation function approach is employed to compute the energy-resolved transmission probability for a one-dimensional potential barrier and a one-dimensional model chemical reaction exhibiting a quantum resonance. Accurate results demonstrate that this formalism can significantly reduce the number of grid points required in a dynamical calculation for the reaction probability.     

Molecular isomerization induced by ultrashort infrared pulses. II. Pump-dump isomerization using pairs of time-delayed half-cycle pulses

We investigate population transfer across the barrier in a double-well potential, induced by a pair of time-delayed single-lobe half-cycle pulses. We apply this setup both to a one-dimensional (1D) quartic model potential and to a three-dimensional potential representing HCN-->HNC isomerization. Overall the results for the two systems are similar, although in the 3D system some additional features appear not seen in the 1D case. The generic mechanism of population transfer is the preparation by the pump pulse of a wave packet involving delocalized states above the barrier, followed by the essentially 1D motion of the delocalized part of wave packet across the barrier, and the eventual de-excitation by the dump pulse to localized states in the other well. The correct timing is given by the well-to-well passage time of the wave packet and its recurrence properties, and by the signs of the field lobes which determine the direction and acceleration or deceleration of the wave packet motion. In the 3D system an additional pump-pump-dump mechanism linked to wave packet motion in the reagent well can mediate isomerization. Since the transfer time and the pulse durations are of the same order of magnitude, there is also a marked dependence of the dynamics and the transfer yield on the pulse duration. Our analysis also sheds light on the pronounced carrier envelope phase dependence previously observed for isomerization and molecular dissociation with one-cycle and sub-one-cycle pulses.     

Laser control of electronic transitions of wave packet by using quadratically chirped pulses

An effective scheme is proposed for the laser control of wave packet dynamics. It is demonstrated that by using specially designed quadratically chirped pulses, fast and nearly complete excitation of wave packet can be achieved without significant distortion of its shape. The parameters of the laser pulse can be estimated analytically from the Zhu-Nakamura theory of nonadiabatic transition. If the wave packet is not too narrow or not too broad, then the scheme is expected to be utilizable for multidimensional systems. The scheme is applicable to various processes such as simple electronic excitation, pump-dump, and selective bond breaking, and it is actually numerically demonstrated to work well by taking diatomic and triatomic molecules (LiH, NaK, H(2)O) as examples.     

基于量子波包方法的态-态分辨反应散射动力学计算

本文回顾了最近十几年利用量子波包方法研究气相分子反应散射动力学的工作进展,特别是在态-态分辨水平上的工作进展。比较详细地讨论了目前存在的利用量子波包方法计算态-态微分截面的几种方法。目前态-态分辨的波包动力学计算可以精确地预测三原子和四原子分子反应散射的各种信息,文章最后对几个典型的利用波包方法在态-态分辨水平上研究过的三原子和四原子反应散射体系做了讨论。     

用两束超短乜秒激光脉冲选择控制D2分子的转动波包

通过求解D2分子在飞秒激光场中的含时薛定谔方程,研究了室温下D2分子在超快1s秒激光驱动下的的转动波包动力学．选择用第一束超短飞秒脉冲与温度为300K的D2分子系综相互作用产生一个相干转动波包,用第二束超短匕秒脉冲在波包的1／4和3／4恢复周期选择操纵D2分子取向．研究结果表明,通过选择两束超短飞秒脉冲的延迟时间,可以有效控制D2分子转动波包中奇偶态的相对布居,从而选择性的控制D2分子取向．     

Resonances in three-dimensional H + HLi scattering: a time-dependent wave packet dynamical study

This paper examines the resonances in H + HLi scattering. The signature of these resonances is obtained from the oscillations in its reaction probability versus energy curves. They are identified here from a set of pseudospectra calculated for different initial locations of a stationary Gaussian wave packet on the ab initio potential energy surface (PES) reported by Dunne, Murrel, and Jemmer. The nuclear motion on this PES is monitored with the aid of a time-dependent wave packet method and the pseudospectrum are calculated by Fourier transforming the time autocorrelation function of the initial wave packet. The resonances are further examined and assigned by computing their eigenfunctions through spectral quantization algorithm. Both the linewidth as well as decay lifetimes of the resonances are reported.     

Long time wave packet dynamics from energy eigenfunctions: nonuniform energy resolution via adaptive bisection fast Fourier transformation

This article presents a new approach to long time wave packet propagation. The methodology relies on energy domain calculations and an on-the-surface straightforward energy to time transformation to provide wave packet time evolution. The adaptive bisection fast Fourier transform method employs selective bisection to create a multiresolution energy grid, dense near resonances. To implement fast Fourier transforms on the nonuniform grid, the uniform grid corresponding to the finest resolution is reconstructed using an iterative interpolation process. By proper choice of the energy grid points, we are able to produce results equivalent to grids of the finest resolution, with far fewer grid points. We have seen savings 20-fold in the number of eigenfunction calculations. Since the method requires computation of energy eigenfunctions, it is best suited for situations where many wave packet propagations are of interest at a fixed small set of points--as in time dependent flux computations. The fast Fourier transform (FFT) algorithm used is an adaptation of the Danielson-Lanczos FFT algorithm to sparse input data. A specific advantage of the adaptive bisection FFT is the possibility of long time wave packet propagations showing slow resonant decay. A method is discussed for obtaining resonance parameters by least squares fitting of energy domain data. The key innovation presented is the means of separating out the smooth background from the sharp resonance structure.     

Nonlinear wave-packet interferometry and molecular state reconstruction in a vibrating and rotating diatomic molecule

We formulate two-color nonlinear wave-packet interferometry (WPI) for application to a diatomic molecule in the gas phase and show that this form of heterodyne-detected multidimensional electronic spectroscopy will permit the reconstruction of photoinduced rovibrational wave packets from experimental data. Using two phase-locked pulse pairs, each resonant with a different electronic transition, nonlinear WPI detects the quadrilinear interference contributions to the population of an excited electronic state. Combining measurements taken with different phase-locking angles isolates various quadrilinear interference terms. One such term gives the complex overlap between a propagated one-pulse target wave packet and a variable three-pulse reference wave packet. The two-dimensional interferogram in the time domain specifies the complex-valued overlap of the given target state with a collection of variable reference states. An inversion procedure based on singular-value decomposition enables reconstruction of the target wave packet from the interferogram without prior detailed characterization of the nuclear Hamiltonian under which the target propagates. With numerically calculated nonlinear WPI signals subject to Gaussian noise, we demonstrate the reconstruction of a rovibrational wave packet launched from the A state and propagated in the E state of Li2.     

Wave packet and quasiclassical trajectory calculations for the N(D) + H2 reaction and its isotopic variants

The N(²D) + H₂(v = 0, j = 0) reaction and its HD and D₂ isotopic variants have been studied by means of quantum mechanical real wave packet and wave packet with split operator and quasiclassical trajectory methodologies on the potential energy surface of Ho et al. [J. Chem. Phys. 119 (2003) 6]. Total initial state-selected and final state-resolved reaction probabilities and product rotational distributions have been calculated for total angular momentum J = 0 in a broad range of collision energies. The real wave packet results are in very good agreement with the corresponding split operator wave packet calculations. A reasonable overall good agreement has been found between the wave packet and quasiclassical trajectory results. Integral cross-sections and thermal rate constants have been calculated from the wave packet reaction probabilities by means of standard J-shifting, refined J-shifting and uniform J-shifting methods in combination with the centrifugal sudden approximation for J > 0. Comparisons with available exact wave packet, quasiclassical trajectory and experimental results are made and discussed.     

Quantum dynamics of solid Ne upon photo-excitation of a NO impurity: A Gaussian wave packet approach

A high-dimensional quantum wave packet approach based on Gaussian wave packets in Cartesian coordinates is presented. In this method, the high-dimensional wave packet is expressed as a product of time-dependent complex Gaussian functions, which describe the motion of individual atoms. It is applied to the ultrafast geometrical rearrangement dynamics of NO doped cryogenic Ne matrices after femtosecond laser pulse excitation. The static deformation of the solid due to the impurity as well as the dynamical response after femtosecond excitation are analyzed and compared to reduced dimensionality studies. The advantages and limitations of this method are analyzed in the perspective of future applications to other quantum solids.     

A semiclassical study of wave packet dynamics in anharmonic potentials

Classical and semiclassical methods are developed to calculate and invert the wave packet motion measured in pump-probe experiments. With classical propagation of the Wigner distribution of the initial wave packet created by the pump pulse, we predict the approximate probe signal with slightly displaced recurrence peaks, and derive a set of first-order canonical perturbation expressions to relate the temporal features of the signal to the characteristics of the potential surface. A reduced dynamics scheme based on the Gaussian assumption leads to the correct center of mass motion but does not describe the evolution of the shape of the wave packet accurately. To incorporate the quantum interference into classical trajectories, we propose a final-value representation semiclassical method, specifically designed for the purpose of computing pump-probe signals, and demonstrate its efficiency and accuracy with a Morse oscillator and two kinetically coupled Morse oscillators. For the case of one-color pump probe, a simple phase-space quantization scheme is devised to reproduce the temporal profile at the left-turning point without actual wave packet propagation, revealing a quantum mechanical perspective of the nearly classical pump-probe signal.     

The perfect revival time of localized wave packet consisting of superposition of bound states with an arbitrary energy spectrum

A study is made of the long-term evolution of the wave packet, which is initially well localized in a one-dimensional confined potential. The wave packet consists of a linear superposition of bound states with an arbitrary energy spectrum. An exact analytical expression is derived, which predicts all revival times in any time scale. The perfect revival time is also calculated. The Pöschl–Teller oscillator has been considered as a simple example.     

Effective chromophore potential, dissipative trajectories, and vibrational energy relaxation: Br2 in Ar matrix

The intramolecular wave packet dynamics on the electronic B (3pi0) potential of Br2 in solid argon is induced and interrogated by femtosecond pump-probe spectroscopy. An effective potential of the chromophore in the solid is derived from the wave packet period for different excitation photon energies. Deep in the potential well, it is consistent with vibrational energies from wavelength-resolved spectra. It extends to higher energies, where the vibrational bands merge to a continuum, and even beyond the dissociation limit, thus quantifying the cage effect of the argon matrix. This advantage of pump-probe spectroscopy is related to a reduced contribution of homogeneous and inhomogeneous line broadenings. The vibrational energy relaxation rates are determined by a variation of the probe window spatial position via the probe quantum energy. A very large energy loss in the first excursion of the wave packet is observed near the dissociation limit. This strong interaction with the argon matrix is directly displayed in an experimental trajectory.     

Positioning of bound electron wave packets in molecules revealed by high-harmonic spectroscopy

By solution of the time-dependent two-electron Schr?dinger equation, we demonstrate that strong-field ionization in combination with electron correlation can localize bound electron wave packets in molecules. The wave packet creation is revealed by the emission spectrum in high-order harmonic generation, which is sensitive to the ionization and recombination phase difference between different ionization channels. For hydrogen molecules at stretched internuclear distance, we find that the ionization phase difference between the gerade and ungerade channels is in the range from π and 1.5π, indicating that the bound wave packet either is initially on the same side as the outgoing electron or is delocalized.     

Juxtaposing density matrix and classical path-based wave packet dynamics

In many physical, chemical, and biological systems energy and charge transfer processes are of utmost importance. To determine the influence of the environment on these transport processes, equilibrium molecular dynamics simulations become more and more popular. From these simulations, one usually determines the thermal fluctuations of certain energy gaps, which are then either used to perform ensemble-averaged wave packet simulations, also called Ehrenfest dynamics, or to employ a density matrix approach via spectral densities. These two approaches are analyzed through energy gap fluctuations that are generated to correspond to a predetermined spectral density. Subsequently, density matrix and wave packet simulations are compared through population dynamics and absorption spectra for different parameter regimes. Furthermore, a previously proposed approach to enforce the correct long-time behavior in the wave packet simulations is probed and an improvement is proposed.