Quantum Wave Packet Propagation Research Articles

Shifted-update rotation wavepacket propagation with a laser pulse

SUR is the simplest symplectic propagator applicable to quantum wavepacket propagation in the energy representation. We decompose the algorithm into unimodular modules that allow the implementation of complex, time-varying matrix elements. This allows the algorithm to be applied to the propagation of wavepackets coupled to a time-varying classical external field, without changing the scaling of the computational time with system size. An adaptive time step version of the algorithm is implemented.

Cheating on Complementarity and Interference by Translational – Internal Entanglement

We show that if internal and momentum states of an interfering particle are entangled, then by measuring its internal state we may infer both path (corpuscular) and phase (wavelike) information with practically any precision, without the complementarity constraints of which-path detection. This holds also for multipath---multistate configurations, allowing large amounts of information to be stored in a single particle. We further show that highly complex particles (e.g., molecules or macroscopic bodies) subject to fields that couple (entangle) their internal and translational (momentum) states may undergo an irresversible randomization (diffusion), manifest by the disappearance of the interference pattern, as if they are subject to decoherence. Thus, translational-internal entanglement can give rise to anomalies in quantum wavepacket propagation.

Short-time dynamics through conical intersections in macrosystems. II. Applications

We present several numerical applications based upon the effective-mode formulation for the short-time dynamics through conical intersections in macrosystems, as detailed in the preceding paper and first proposed by Cederbaum et al. [Phys. Rev. Lett. 94, 113003 (2005)]. The macrosystem, containing a vast number of nuclear degrees of freedom (modes), is decomposed into a system part and an environment part. Only three effective environmental modes are needed-together with the system's modes-to accurately calculate the low resolution spectra and the short-time dynamics of the entire macrosystem. For the systems discussed here, results are compared to those of a full quantum wave-packet propagation. Some rules are extracted to provide general tendencies; these rules allow one to understand and predict the dynamical properties in more general situations where the exact quantum dynamics of the macrosystem is out of reach.

Propagation with distributed Gaussians as a sparse, adaptive basis for higher-dimensional quantum dynamics

A simple quantum wavepacket propagation algorithm is presented, designed to produce a very compact, non-direct product representation in higher-dimensional cases. Instead of moving basis functions around, localized basis functions at pre-defined centers are added to and deleted from the representation, generating an active basis function set strictly localized to the region where the moving wavepacket has significantly non-zero values. Simple one-dimensional examples prove this property, as well as the ability of the algorithm to accommodate splitting and rejoining of an arbitrary number of wavefunction pieces, and tunnelling through potential energy barriers. It is argued that future applications to higher-dimensional examples will be less expensive than with traditional direct-product bases, since making the basis adaptive has a lower scaling than the elementary steps necessary for any propagation algorithm itself.

Higher order (A+E)⊗e pseudo-Jahn–Teller coupling

The pseudo-Jahn-Teller (PJT) coupling of a nondegenerate state A with a twofold degenerate state E by a degenerate vibrational mode e is studied for a general system with a C(3) main rotational axis. The PJT coupling terms up to sixth order are derived by symmetry considerations for this general (A+E) multiply sign in circle e case. The obtained expression for the 3 x 3 diabatic potential energy matrix is found to be closely related to the expression recently developed for the higher order Jahn-Teller case [A. Viel and W. Eisfeld, J. Chem. Phys. 120, 4603 (2004)]. The dynamical PJT coupling, which can arise for states of appropriate symmetry if one of the vibrational modes induces a change of the nuclear point group between D(3h), C(3v), C(3h), and C(3), is discussed. The effect of the higher order PJT coupling is tested by a two-dimensional model study based on the e bending mode of NH(3)(+). The models are analyzed by fitting the two-dimensional potential energy surfaces. The significance of the higher order terms on the nonadiabatic dynamics is demonstrated by quantum wave packet propagations.

Competition between adiabatic and nonadiabatic fragmentation pathways in the unimolecular decay of the ArI2(B) van der Waals complex

The competition between vibrational and electronic predissociations of the ArI2(B) van der Waals complex has been studied using several dynamical computational methods: exact quantum wave-packet propagation, time-dependent golden rule, and quasiclassical trajectory with quantum jumps model. Five electronic states are considered using recent three-dimensional coupled surfaces obtained with a perturbative diatoms-in-molecules method. Final vibrational and electronic populations, predissociation rates, and absorption spectra have been computed for I2(B,v=18-24)<--I2(X,v=0) excitations within the complex. The contribution of vibrational predissociation into the total decay oscillates as a function of vibrational excitation due to intramolecular vibrational relaxation in a sparse-intermediate regime, which induces irregular variations of the total decay rate. Franck-Condon oscillations control the branching ratios of the individual electronic predissociation channels. However, since these oscillations are out of phase as a function of vibrational excitation, they have limited effect on the oscillatory behavior of the total predissociation rate. Comparison between exact quantum and perturbative golden rule calculations shows that vibrational predissociation has some impact on the electronic predissociation process and affects the final electronic distributions. On the contrary, vibrational product distributions are not significantly affected by the electronic predissociation. A classical description of the ArI2 dynamics provides an averaged picture of the competing predissociation processes, being better adapted for treating intermolecular vibrational relaxation in the statistical limit.

Theoretical study of the time-resolved photoelectron spectrum of Na 2 F: effects of thermal initial conditions

The excited state dynamics of the Na2F cluster initiated by a femtosecond laser pulse is studied considering a thermally excited initial sample. Within a pump-probe set-up, the time-dependent photoelectron spectrum is calculated, which is shown to be a sensitive tool to study intramolecular motion of the cluster. Temperature effects are taken into account through thermal averaging over the time-dependent spectra obtained from different initial vibrational states of the cluster. The nuclear motion upon laser excitation is described by full-dimensional quantum wavepacket propagation using explicit, realistic pump and probe pulses. The characteristic features of the time-resolved photoelectron spectra of the Na2F cluster, identified as due to periodic bending motion of the cluster as well as to the excitation of the stretching mode, are found to be robust against increasing vibrational temperature of the cluster beam. This finding is important for possible future experiments.

Time-resolved photoelectron spectra as probe of excited state dynamics: A full quantum study of the Na2F cluster

The excited state dynamics of the Na2F cluster initiated by a femtosecond laser pulse is studied by quantum wave packet propagation within a pump–probe setup. The probe pulse is supposed to ionize the system to yield a photoelectron spectrum that depends on the time delay between the pump- and probe pulse. It is shown that the time dependence of the photoelectron spectrum is an extremely sensitive tool to study intramolecular motion of the cluster like the energy flow between different internal modes. The potential energy surfaces involved in the photoinduced process are calculated from a pseudopotential model with repulsive and Coulomb potentials for the ions and a quantum description of the excess electron via electron-Na+ and electron-F− pseudopotentials, polarization of the ionic cores as well as electron-ion correlation being added perturbatively. The nuclear motion upon laser excitation is described by full-dimensional quantum wave packet propagation using realistic laser pulse parameters. We find that the pump–probe signal is essentially dominated by the bending motion of the cluster with a periodicity of 180 fs. In addition, we also report detailed structures in the photoelectron spectrum which can be attributed to the excitation of the stretching mode. The possibility of experimental observation of the predicted dynamical behavior is discussed.

Intramolecular energy flow and nonadiabaticity in vibrationally mediated chemistry: Wave packet studies of Cl+H2O

Time-dependent and time-independent quantum scattering methods are used to investigate state-to-state inelastic and reactive collision dynamics for a three-dimensional (3D) atom+triatom model of Cl+H2O→HCl+OH. The results elucidate the role of (i) intramolecular vibrational energy transfer and (ii) vibrational nonadiabaticity on the time scale of a reactive encounter in systems with nearly degenerate stretching “local modes.” Adiabatic two-dimensional (2D) vibrational eigenfunctions [ψn(r1,r2,R)] and eigenvalues [En(R)] are first obtained in OH bond coordinates (r1,r2) as a function of Cl–H2O center-of-mass separation (R), which then provides the requisite adiabatic potential energy curves and nonadiabatic coupling matrix elements for full 3D quantum wave packet propagation. Inspection of these 2D vibrational eigenfunctions indicates that near degeneracy between H2O symmetric |01+〉 and antisymmetric |01−〉 states is systematically lifted as R decreases, causing vibrational energy to flow into local-mode OH excitations pointing either toward (“proximal”) or away from (“distal”) the approaching Cl atom, respectively. This suggests a simple yet powerful physical model for mode-specific reactive scattering dynamics, the predictions of which are confirmed by full 3D quantum wave packet calculations over a range of collision velocities.

Pulse length control of Na+2 photodissociation by intense femtosecond lasers

Fragmentation dynamics of the molecular ion Na+2 irradiated by an intense femtosecond pulse laser is studied using quantum wave packet propagations. It is demonstrated that the pulse duration (20–250 fs) can be used as a control parameter for both the total dissociation probability and the branching ratio between different dissociation channels. This pulse length effect is important when the duration of the pulse is shorter than the vibrational period of the molecular ion in the ground state. The effects of laser intensity (1011–3×1012 W/cm2), wavelength (680–780 nm) and initial vibrational level on the dissociation dynamics are also studied.

Multiple Time Scale Quantum Wavepacket Propagation: Electron−Nuclear Dynamics

We have developed a multiple time scale (MTS) quantum wavepacket propagation algorithm for the electron−nuclear dynamics in which the electron and nuclear motions are followed simultaneously. The large mass disparity between the electron and the nuclear degrees of freedom poses a problem when one propagates the total wavefunction using a single time step. The standard split operator propagation method requires a small time step to be used for stable propagation of the fast electronic degrees of freedom, which leads to an unnecessarily large number of propagations for slow nuclear motions. A new factorization of the time evolution operator based on the decomposition of the total Hamiltonian into the nuclear part and the electronic Hamiltonian is proposed. The MTS factorization allows one to choose the spatial grid size and the time step appropriate for each subsystem separately. The MTS algorithm is applied to a charge-transfer model for the evaluation of optical spectra and thermal rate constants. It is s...

Coherent control of photodissociation in intense laser fields

The fragmentation dynamics of the hydrogen molecular ion H2+ and of its isotopic derivate HD+subjected to an intense pulsed laser radiation are studied using quantum wave packet propagations. It is shown that bichromatic optical excitations are subject to a high degree of control through the variation of the relative phase between the two fields. A phase-locked (ω,2ω) laser pulse is used to induce asymmetry in the angular distribution of the emitted fragments. In addition, an appreciable isotope separation in the fragmentation of HD+ is predicted. The critical role of quantum molecular interferences in such phase-controllable processes is demonstrated.

Time-dependent discrete variable representations for quantum wave packet propagation

We present an efficient method for exact wave function propagation with several degrees of freedom based on time-dependent discrete variable representations (TD-DVR) of the evolution operator. The key idea is to use basis sets that evolve in time according to appropriate reference Hamiltonians to construct TD-DVR grids. The initial finite basis representation is chosen to include the initial wavefunction and thus the evolution under the bare zeroth order Hamiltonian is described at each time by a single DVR point. For this reason TD-DVR grids offer optimal representations in time-dependent calculations, allowing significant reduction of grid size and large time steps while requiring numerical effort that (for systems with several degrees of freedom) scales almost linearly with the total grid size. The method is readily applicable to systems described by time-dependent Hamiltonians. TD-DVR grids based on the time-dependent self-consistent field approximation are shown to be very useful in the study of intramolecular or collision dynamics.

Time-dependent treatment of vibrational predissociation within the golden rule approximation

The time-dependent formulation for vibrational predissociation of weakly bound complexes within the golden rule treatment is presented. The quantum wave packet propagation in this formulation eliminates the difficulty of strenuous long time propagation of the full wave function due to long-lived resonance which occurs in the more exact time-dependent treatment. As a result, the new time-dependent treatment of vibrational predissociation essentially parallels that of direct photodissociation and therefore requires only short time propagation of the wave function. The wave packet propagation is efficiently carried out in the interaction picture and numerical calculations of rotational state distributions and the total decay width are presented for vibrational predissociation of HeCl2. Correct rotational state distribution can be obtained with only a few time propagation steps owing to the use of large step size allowed in the interaction picture. Our approach provides an efficient method for the calculation of vibrational predissociation for more complex systems such as those with more than three atoms.

Multichannel quantum wave packet propagation in the interaction picture: application to gas-surface scattering

Propagation of quantum wave packet in the interaction picture substantially improves the efficiency of time-dependent quantum mechanical (TDQM) methods for solving various scattering or half scattering problems. This paper generalizes the idea in a straightforward manner to treat coupled channel quantum wave packet propagation when basis set expansions of the total wavefunction in certain degrees of freedom are desired.