Analysis of wave packet motion in frequency and time domain: oxazine 1

Wave packet motion in the laser dye oxazine 1 in methanol is investigated by spectrally resolved transient absorption spectroscopy. The spectral range of 600-690 nm was accessible by amplified broadband probe pulses covering the overlap region of ground-state bleach and stimulated emission signal. The influence of vibrational wave packets on the optical signal is analyzed in the frequency domain and the time domain. For the analysis in the frequency domain an algorithm is presented that accounts for interference effects of neighbored vibrational modes. By this method amplitude, phase and decay time of vibrational modes are retrieved as a function of probe wavelength and distortions due to neighbored modes are reduced. The analysis of the data in the time domain yields complementary information on the intensity, central wavelength, and spectral width of the optical bleach spectrum due to wave packet motion.     

Initial dynamics of the Norrish Type I reaction in acetone: probing wave packet motion

The Norrish Type I reaction in the S(1) (nπ*) state of acetone is a prototype case of ketone photochemistry. On the basis of results from time-resolved mass spectrometry (TRMS) and photoelectron spectroscopy (TRPES) experiments, it was recently suggested that after excitation the wave packet travels toward the S(1) minimum in less than 30 fs and stays there for more than 100 picoseconds [Chem. Phys. Lett.2008, 461, 193]. In this work we present simulated TRMS and TRPES signals based on ab initio multiple spawning simulations of the dynamics during the first 200 fs after excitation, getting quite good agreement with the experimental signals. We can explain the ultrafast decay of the experimental signals in the following manner: the wave packet simply travels, mainly along the deplanarization coordinate, out of the detection window of the ionizing probe. This window is so narrow that subsequent revival of the signal due to the coherent deplanarization vibration is not observed, meaning that from the point of view of the experiment the wave packets travels directly to the S(1) minimum. This result stresses the importance of pursuing a closer link to the experimental signal when using molecular dynamics simulations in interpreting experimental results.     

Time-dependent wave packet propagation using quantum hydrodynamics

A new approach for propagating time-dependent quantum wave packets is presented based on the direct numerical solution of the quantum hydrodynamic equations of motion associated with the de Broglie–Bohm formulation of quantum mechanics. A generalized iterative finite difference method (IFDM) is used to solve the resulting set of non-linear coupled equations. The IFDM is 2nd-order accurate in both space and time and exhibits exponential convergence with respect to the iteration count. The stability and computational efficiency of the IFDM is significantly improved by using a “smart” Eulerian grid which has the same computational advantages as a Lagrangian or Arbitrary Lagrangian Eulerian (ALE) grid. The IFDM is generalized to treat higher-dimensional problems and anharmonic potentials. The method is applied to a one-dimensional Gaussian wave packet scattering from an Eckart barrier, a one-dimensional Morse oscillator, and a two-dimensional (2D) model collinear reaction using an anharmonic potential energy surface. The 2D scattering results represent the first successful application of an accurate direct numerical solution of the quantum hydrodynamic equations to an anharmonic potential energy surface.     

Molecular wave packet interferometry and quantum entanglement

We study wave packet interferometry (WPI) considering the laser pulse fields both classical and quantum mechanically. WPI occurs in a molecule after subjecting it to the interaction with a sequence of phase-locked ultrashort laser pulses. Typically, the measured quantity is the fluorescence of the molecule from an excited electronic state. This signal has imprinted the interference of the vibrational wave packets prepared by the different laser pulses of the sequence. The consideration of the pulses as quantum entities in the analysis allows us to study the entanglement of the laser pulse states with the molecular states. With a simple model for the molecular system, plus several justified approximations, we solve for the fully quantum mechanical molecule-electromagnetic field state. We then study the reduced density matrices of the molecule and the laser pulses separately. We calculate measurable corrections to the case where the fields are treated classically.     

Semiclassical wave packet study of ozone forming reaction

We have applied the semiclassical wave packet method (SWP) to calculate energies and lifetimes of the metastable states (scattering resonances) in a simplified model of the ozone forming reaction. All values of the total angular momentum up to J=50 were analyzed. The results are compared with numerically exact quantum mechanical wave packet propagation and with results of the time-independent WKB method. The wave functions for the metastable states in the region over the well are reproduced very accurately by the SWP; in the classically forbidden region and outside of the centrifugal barrier, the SWP wave functions are qualitatively correct. Prony's method was used to extract energies and lifetimes from the autocorrelation functions. Energies of the metastable states obtained using the SWP method are accurate to within 0.1 and 2 cm(-1) for under-the-barrier and over-the-barrier states, respectively. The SWP lifetimes in the range of 0.5相似文献   

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.     

An adaptive pseudospectral method for wave packet dynamics

We solve the time-dependent Schro?dinger equation for molecular dynamics using a pseudospectral method with global, exponentially decaying, Hagedorn basis functions. The approximation properties of the Hagedorn basis depend strongly on the scaling of the spatial coordinates. Using results from control theory we develop a time-dependent scaling which adaptively matches the basis to the wave packet. The method requires no knowledge of the Hessian of the potential. The viability of the method is demonstrated on a model for the photodissociation of IBr, using a Fourier basis in the bound state and Hagedorn bases in the dissociative states. Using the new approach to adapting the basis we are able to solve the problem with less than half the number of basis functions otherwise necessary. We also present calculations on a two-dimensional model of CO(2) where the new method considerably reduces the required number of basis functions compared to the Fourier pseudospectral method.     

Atomic wave motion in molecular nanostructures

In large-scale molecular objects (nanostructures) such as dendromers, supramolecules, polymers, nanotubes, etc. external perturbations may have local character. When the perturbation is removed, atomic wave motions of a rather complex type may arise in the nanostructure. They can not only transfer signals inside the nanoobject, but also generate standing waves and antinodes and accumulate energy in other domains of the nanostructure, i.e., give rise to energy traps. These problems have not been addressed before. In this paper we propose a method to calculate the time-dependent evolution of these phenomena for large-scale molecular structures of arbitrary structure and size.     

Coriolis-coupled wave packet dynamics of H + HLi reaction

We investigated the effect of Coriolis coupling (CC) on the initial state-selected dynamics of H+HLi reaction by a time-dependent wave packet (WP) approach. Exact quantum scattering calculations were obtained by a WP propagation method based on the Chebyshev polynomial scheme and ab initio potential energy surface of the reacting system. Partial wave contributions up to the total angular momentum J=30 were found to be necessary for the scattering of HLi in its vibrational and rotational ground state up to a collision energy approximately 0.75 eV. For each J value, the projection quantum number K was varied from 0 to min (J, K(max)), with K(max)=8 until J=20 and K(max)=4 for further higher J values. This is because further higher values of K do not have much effect on the dynamics and also because one wishes to maintain the large computational overhead for each calculation within the affordable limit. The initial state-selected integral reaction cross sections and thermal rate constants were calculated by summing up the contributions from all partial waves. These were compared with our previous results on the title system, obtained within the centrifugal sudden and J-shifting approximations, to demonstrate the impact of CC on the dynamics of this system.     

Plane wave packet formulation of atom-plus-diatom quantum reactive scattering

We recently interpreted several reactive scattering experiments using a plane wave packet (PWP) formulation of quantum scattering theory [see, e.g., S. C. Althorpe, F. Fernandez-Alonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N. Zare, and E. Wrede, Nature (London) 416, 67 (2002)]. This paper presents the first derivation of this formulation for atom-plus-diatom reactive scattering, and explains its relation to conventional time-independent reactive scattering. We generalize recent results for spherical-particle scattering [S. C. Althorpe, Phys. Rev. A 69, 042702 (2004)] to atom-rigid-rotor scattering in the space-fixed frame, atom-rigid-rotor scattering in the body-fixed frame, and finally A+BC rearrangement scattering. The reactive scattering is initiated by a plane wave packet, describing the A+BC reagents in center-of-mass scattering coordinates, and is detected by projecting onto a series of AC+B (or AB+C) plane wave "probe" packets. The plane wave packets are localized at the closest distance from the scattering center at which the interaction potential can be neglected. The time evolution of the initial plane wave packet provides a clear visualization of the scattering into space of the reaction products. The projection onto the probe packets yields the time-independent, state-to-state scattering amplitude, and hence the differential cross section. We explain how best to implement the PWP approach in a numerical computation, and illustrate this with a detailed application to the H+D2 reaction.     

Time-dependent wave packet study on trans-cis isomerization of HONO

Using a full six-dimensional ab initio potential energy surface and nuclear motion Hamiltonian, time-dependent computations were performed for the cis-trans isomerization of HONO. The multiconfiguration time-dependent Hartree method was used to propagate the six-dimensional wave packets. The initial excitations were chosen to be excitations of the local stretch modes and the HON local bend mode. The energy redistribution within 2 to 5 ps in the energy region of the OH stretching modes in both isomers was analyzed. The Fourier transformed frequency domain spectra were attributed to the eigenstates calculated previously by the time-independent variational approach. The results are also compared with classical trajectory computations of Thomson et al. on empirical surfaces. In agreement with matrix experiments, the cis-->trans isomerization was found to be much faster than the opposite interconversion. The intramolecular dynamics were found to be very complex involving numerous weakly excited delocalized eigenstates and anharmonic resonances. Particularly in the cis-isomer, the excitation of the HON bending local mode leads to fast energy redistribution in cis-trans delocalized modes. Neither the excitation of the OH stretching local mode in the cis nor in the trans form produces a fast isomerization, in agreement with the strongly localized characters of the corresponding eigenstates calculated variationally by Richter et al. and the gas phase spectra of HONO.     

Testing wave packet dynamics in computing radiative association cross sections

A time-dependent wave packet method is used to compute cross sections for radiative recombination reactions using the Li((2)S)+H(+)-->LiH(+)(X (2)Sigma(+))+gamma as a test case. Cross sections are calculated through standard time-to-energy mapping of the time-dependent transition moment and a useful method is introduced to deal with the low collision energy regime. Results are in quantitative agreement over the whole energy range 10(-4)-5 eV with previous time-independent results for the same system [I. Baccarelli, L. Andric, T. Grozdanov, and R. McCarroll, J. Chem. Phys. 117, 3013 (2002)], thereby suggesting that the method can be of help in computing radiative association cross sections for more complicated systems.     

Semiclassical wave packet study of anomalous isotope effect in ozone formation

We applied the semiclassical initial value representation method to calculate energies, lifetimes, and wave functions of scattering resonances in a two-dimensional potential for O+O2 collision. Such scattering states represent the metastable O3* species and play a central role in the process of ozone formation. Autocorrelation functions for scattering states were computed and then analyzed using the Prony method, which permits one to extract accurate energies and widths of the resonances. We found that the results of the semiclassical wave packet propagation agree well with fully quantum results. The focus was on the 16O16O18O isotopomer and the anomalous isotope effect associated with formation of this molecule, either through the 16O16O+18O or the 16O+16O18O channels. An interesting correlation between the local vibration mode character of the metastable states and their lifetimes was observed and explained. New insight is obtained into the mechanism by which the long-lived resonances in the delta zero-point energy part of spectrum produce the anomalously large isotope effect.     

Nonadiabatic interactions in wave packet dynamics of the bromoacetyl chloride photodissociation

The competitive photodissociation of bromoacetyl chloride BrCH2COCl in the first 1A" state (S1) by 248 nm photons is investigated by nonadiabatic wave packet simulations. We show that the preferential breaking of the stronger C-Cl bond (alpha to the excited carbonyl) over the weaker C-Br bond (beta) could be explained by a diabatic trapping or nonadiabatic recrossing as previously proposed. Our energy resolved flux analysis agrees fairly well with the experimental branching ratio (C-Cl:C-Br=1.0:0.4). Even if this does not prove the mechanism, this at least prevents to discard it. A reduced dimensionality approach based on constrained Hamiltonian is used. The nonadiabatic dissociation is studied in the two C-O/C-X (X=Br, Cl) subspaces to emphasize the role of the C-O vibration upon [nO-->piCO*] excitation. The internal torsion and wagging dihedral angles are frozen at their Franck-Condon value, according to preliminary dynamical tests. The other inactive coordinates are optimized at the trans and Cs constrained geometry in the first excited state. Corresponding 2D cuts in the potential energy surfaces have been computed at the CASSCF level. The nonadiabatic kinetic couplings are highly peaked along an avoided crossing seam in both cases. A two-state diabatic model with a constant potential coupling is proposed in the two C-O/C-X subspaces. The inclusion of the C-O stretching in the active coordinates improves the value of the branching ratio over our previous 1D computation.     

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.     

A wave packet based statistical approach to complex-forming reactions

A wave packet based statistical model is suggested for complex-forming reactions. This model assumes statistical formation and decay of the long-lived reaction complex and computes reaction cross sections and their energy dependence from capture probabilities. This model is very efficient and reasonably accurate for reactions dominated by long-lived resonances, as confirmed by its application to the C((1)D)+H(2) reaction.     

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.     

Exact three-dimensional time-dependent wave packet calculations on the Connection Machine

Summary In this paper, we report our massively parallel implementation of grid techniques for the solution of the time-dependent Schrödinger equation in three spatial dimensions on the Connection Machine, which is a Single Instruction Multiple Data (SIMD) computer. Most of the operations involved in this calculation may be executed independently for each grid point. The few operations which cannot be executed independently are implemented using parallel communication algorithms. In addition, we report a simple modification of the multidimensional FFT, which provides an estimated 15% reduction in computational complexity relative to the standard 2-D FFT. It is suggested that this modification may be very well suited to hypercube communication topologies.