Wave-packet Propagation Scheme Research Articles

Quantum wave-packet studies on ion–molecule reaction with and without Coriolis-coupling effect

The time-dependent quantum scattering calculation with Chebyshev wave packet propagation scheme has been carried out based on an accurate electronic potential energy surface of H2O+(X4A″). Due to the influence of the deep potential well, the reaction probability of [Formula: see text] shows resonance structures regardless of the Coriolis-coupling (CC) effect or centrifugal sudden (CS) approximation. In the range of collision energy 0.0–1.0 eV, the integral cross section obtained by the CS approximation calculation is smaller than that by the CC calculation, which indicates that the CC effect plays a significant role in the title reaction.

Fully quantal treatment of nonadiabatic molecular photodynamics: General considerations and application to the benzene cation

The merits and drawbacks of a mixed quantum-classical description of nuclear motion on coupled potential energy surfaces are discussed and compared with a fully quantal treatment. For the latter a particular approach is highlighted in which an efficient wavepacket propagation scheme, the Multiconfiguration Time-Dependent Hartree (MCTDH) method, is combined with a versatile modeling of the Hamiltonian for interacting potential energy surfaces, the linear vibronic coupling (LVC) model. As an illustrative example this fully quantal treatment is applied to the benzene radical cation, where nuclear motion on five multiply intersecting potential energy surfaces with up to eleven nuclear degrees of freedom has been studied. The results for the electronic population dynamics allow to understand recent pump-probe spectra with ultrashort XUV and visible/near IR laser pulses in terms of few-fs population transfer at two consecutive conical intersections.

Efficient Solution of the Electronic Eigenvalue Problem Using Wavepacket Propagation.

We report how imaginary time wavepacket propagation may be used to efficiently calculate the lowest-lying eigenstates of the electronic Hamiltonian. This approach, known as the relaxation method in the quantum dynamics community, represents a fundamentally different approach to the solution of the electronic eigenvalue problem in comparison to traditional iterative subspace diagonalization schemes such as the Davidson and Lanczos methods. In order to render the relaxation method computationally competitive with existing iterative subspace methods, an extended short iterative Lanczos wavepacket propagation scheme is proposed and implemented. In the examples presented here, we show that by using an efficient wavepacket propagation algorithm the relaxation method is, at worst, as computationally expensive as the commonly used block Davidson-Liu algorithm, and in certain cases, significantly less so.

High-Order Harmonic Generation from the Cu(111) surface

SynopsisWe investigate theoretically the origin behind the formation of the plateau and cutoff structures in the high-harmonic spectra produced after the interaction of a near-infrared laser pulse with a metal surface. We use a wave packet propagation scheme and a one dimensional description of the Cu(111) surface.

The creation, destruction and transfer of multipole moments in electron–ion three-body recombination

We use the wave-packet propagation scheme of Goldberger and Watson to define multipole moment creation, destruction, and transfer rates for the three-body recombination (TBR) of electrons with ions. We first assume short-range interaction potentials and then consider Coulomb interactions, for which we use Dollardʼs theory of multichannel scattering. We present the multipole moment rate coefficients in terms of the TBR amplitudes. Finally, we discuss time-reversal invariance and the reciprocity relations, both for the short-range case and for the Coulomb-interaction case, and show that the multipole moment rate coefficients can be expressed in terms of electron-impact ionization amplitudes.

The creation, destruction, and transfer of multipole moments in electron- and proton-impact ionization of atoms and ions

Expanding on previous works that involved elastic and inelastic scattering of electrons by atoms and ions, we use the wave-packet propagation scheme of Dollard to define multipole moment creation, destruction and transfer cross sections for electron- and proton-impact ionization of atoms and ions. The electron-impact cross sections can then be used by defining appropriate rate coefficients for use in Fujimoto’s population-alignment collisional-radiative model for cylindrically symmetric plasmas. Our result for the alignment creation cross section is in agreement with those formulae that were obtained earlier intuitively or by semi-classical collisional methods. The multipole cross sections obtained here can be used also for modelling the relaxation behaviour of laser-excited plasmas under cylindrical symmetry conditions. We have also derived the electron- and proton-impact ionization multipole cross sections in terms of Liouville-space quantities, which then enabled us by using group theoretical methods to obtain the azimuthal-angle dependence of the multipole cross sections and symmetry properties that are results of reflection across a plane over the collisional axis.

Multi-state vibronic interactions in the 1,2,3-trifluorobenzene radical cation

The multi-state and multi-mode vibronic interactions between the five lowest electronic states of the title compound are investigated theoretically by an ab initio quantum dynamical approach. The well-established linear vibronic coupling scheme is adopted, augmented by quadratic coupling terms for the totally symmetric modes. The pertinent system parameters are obtained from outer valence Greens function and equation-of-motion coupled-cluster ab initio calculations. Large-scale quantum dynamical simulations are performed employing a powerful wavepacket propagation scheme. The band shapes and line structures (as far as available) of the experimental photoelectron spectra are well reproduced. Time-dependent electronic populations reveal ultrafast internal conversion processes and allow for important insight into the fluorescence properties of the radical cation. The relation to other fluoro derivatives of the benzene radical cation is discussed.

The creation, destruction and transfer of multipole moments in electron scattering by ions

Expanding on previous works that involved the scattering of electrons by atoms, we use the wave-packet propagation scheme of Dollard to define multipole moment creation, destruction and transfer cross sections for elastic and inelastic scattering of electrons by ions. We find that our cross section formulae for inelastic scattering agree with those obtained by Fujimoto and coworkers, who used semi-classical collision theory and the impact approximation, but differ from the expressions obtained by them for elastic scattering cross sections. This latter result is due to the fact that Dollard’s theory takes into account the concept that, in the case of electron–ion scattering, the incident and scattered electrons are asymptotically not free. In addition, we apply the Gell-Mann–Goldberger (‘two-potential’) formula in order to provide an unambiguous definition of elastic cross sections, as well as to provide a convenient way of obtaining practical expressions associated with well-established methods, such as the Coulomb–Born and distorted-wave approximations. The present theoretical framework will be the basis for numerical calculations considering specific examples in a future work.

Photodetachment–photoelectron spectroscopy of HS−·H2S and DS−·D2S: the transition states of the SH + H2S and SD + D2S reactions

The transition state region for neutral hydrogen transfer reactions can be accessed by photodetachment of a stable negative ion with a geometry similar to that of the neutral transition state. In this work the SH + H(2)S and SD + D(2)S reactions are investigated by photodetachment-photoelectron spectroscopy of HS(-) x H(2)S and DS(-) x D(2)S. The spectra exhibit vibrational structure which is attributed to the antisymmetric stretching mode (H-atom motion) of the neutral transitions state for H-atom transfer. The spectra are compared to one-dimensional simulations performed using a wave packet propagation scheme. Electronic structure calculations of the anionic, neutral and transition-state geometries and calculations of the vertical detachment energy at different levels of theory are used to support the analysis of the spectra. A vertical detachment energy VDE of 3.06 eV has been determined.

Revivals of quantum wave packets in graphene

We investigate the propagation of wave packets on graphene in a perpendicular magnetic field and the appearance of collapses and revivals in the time evolution of an initially localized wave packet. The wave-packet evolution in graphene differs drastically from the one in an electron gas and shows a rich revival structure similar to the dynamics of highly excited Rydberg states. We present a novel numerical wave-packet propagation scheme in order to solve the effective single-particle Dirac–Hamiltonian of graphene and show how the collapse and revival dynamics is affected by the presence of disorder. Our effective numerical method is of general interest for the solution of the Dirac equation in the presence of potentials and magnetic fields.

Exact two-electron wave packet dynamics of H2 in an intense laser field: Formation of localized ionic states H+H−

We have developed an efficient grid method that can accurately deal with the electronic wave packet dynamics of two-electron systems in three-dimensional (3D) space. By using the dual transformation technique, we remove the numerical difficulties arising from the singularity of the attractive Coulomb potential. Electron–electron repulsion is incorporated into the wave packet propagation scheme without introducing any approximations. The exact electronic dynamics of H2 is simulated for the first time. At small internuclear distances (e.g., R=4 a.u.), an ionic component characterized by the structure H+H− is created in an intense laser field E(t) (intensity>1013 W/cm2 and λ≈720 nm) because an electron is transferred from the nucleus around which the dipole interaction energy for the electron becomes higher with increasing |E(t)|. The localized ionic structure is identified with the H− anion at the nucleus around which the dipole interaction energy becomes lower. Tunneling ionization proceeds via the formation of such a localized ionic structure, and direct ionization from the covalent structure is much smaller; the localized ionic structure plays the dominant doorway state to ionization of H2.

Scattering of water from graphite: simulations and experiments

The scattering of water molecules from a graphite (0001) surface has been studied experimentally and using molecular dynamics simulations. Model potentials for the gas–solid interaction have been developed and tested by comparing experimental and simulated angular distributions for different translational energies (0.09–0.8 eV), incident angles (30–75°) and surface temperatures (300–1200 K). Good agreement is found for both scattering intensities and angular resolved average velocities, supporting the main features of the model potentials. The importance of trapping at low incident energy is discussed as well as the possibility of vibrational excitation at high collision energy. The latter phenomenon is investigated using purely classical trajectory calculations, a forced oscillator model and a wavepacket propagation scheme. The results indicate that meaningful estimates of the vibrational excitation can be obtained using classical simulations, supporting previously reported results on the CF 3Br/graphite system [M.B. Någård, N. Marković, J.B.C. Pettersson, J. Chem. Phys. 109 (1998) 10350].

Tunnel ionization of H_{2} in a low-frequency laser field: A wave-packet approach

The dynamics of multielectron dissociative ionization (MEDI) of ${\mathrm{H}}_{2}$ in an intense IR laser pulse are investigated using a wave-packet propagation scheme. The electron tunneling processes corresponding to the successive ionizations of ${\mathrm{H}}_{2}$ are expressed in terms of field-free Born-Oppenheimer (BO) potential energy surfaces (PES) by transforming the tunnel shape resonance picture into a Feshbach resonance problem. This transformation is achieved by defining a new, time-dependent electronic basis in which the bound electrons are still described by field-free BO electronic states while the ionized ones are described by Airy functions. In the adiabatic, quasistatic approximation, these functions describe free electrons under the influence of the instantaneous electric field of the laser and such an ionized electron can have a negative total energy. As a consequence, when dressed by the continuous ejected electron energy, the BO PES of an ionic channel can be brought into resonance with states of the parent species. This construction gives a picture in which wave packets are to be propagated on a continuum of coupled electronic manifolds. A reduction of the wave-packet propagation scheme to an effective five-channel problem has been obtained for the description of the first dissociative ionization process in ${\mathrm{H}}_{2}$ by using Fano's formalism [U. Fano, Phys. Rev. 124, 1866 (1961)] to analytically diagonalize the infinite, continuous interaction potential matrix and by using the properties of Fano's solutions. With this algorithm, the effect that continuous ionization of ${\mathrm{H}}_{2}$ has on the dissociation dynamics of the ${\mathrm{H}}_{2}^{+}$ ion has been investigated. In comparison with results that would be obtained if the first ionization of ${\mathrm{H}}_{2}$ was impulsive, the wave-packet dynamics of the ${\mathrm{H}}_{2}^{+}$ ion prepared continuously by tunnel ionization are markedly nonadiabatic. The continuous ionization appears to give rise to a population in the dissociative continuum that is localized at small internuclear distances throughout the action of the laser pulse, and is released only when the laser pulse is over, yielding a complex fragment kinetic energy spectrum. Comparison with available experimental data is made.

Time-dependent treatment of scattering. II. Novel integral equation approach to quantum wave packets

The time-dependent form of the Lippmann–Schwinger integral equation is used as the basis for a novel wave-packet propagation scheme. The method has the advantage over a previous integral equation treatment in that it does not require extensive matrix inversions involving the potential. This feature will be important when applications are made to systems where in some degrees of freedom the potential is expressed in a basis expansion. As was the case for the previous treatment, noniterated and iterated versions of the equations are given; the iterated equations, which are much simpler in the present new scheme than in the old, eliminate a matrix inversion that is required for solving the earlier noniterated equations. In the present noniterated equations, the matrix to be inverted is a function of the kinetic energy operator and thus is diagonal in a Bessel function basis set (or a sine basis set, if the centrifugal potential operator is incorporated into an effective potential). Transition amplitudes for various orbital angular momentum quantum numbers can be obtained from: (1) Fourier transform of the amplitude density from the time to the energy domain, and (2) direct analysis of the scattered wave packet. The approach is illustrated by an application to a standard potential scattering model problem.