Three-dimensional Wave Packet Research Articles

Orientation effects in the Coulomb-explosion ionization of anH2+wave packet by short xuv pulses: Applicability of the fixed-nuclei approximation

The Coulomb explosion ionization process of an $\text{H}_{2}{}^{+}$ wave packet in xuv laser fields has been studied by fully three-dimensional ab initio wave packet calculations, with moving nuclei, beyond the Born-Oppenheimer approximation. Both the cases of parallel and perpendicular orientation of the molecule with respect to the laser field have been investigated. Furthermore, we have examined the applicability of the fixed-nuclei approximation method to obtain the kinetic energy distribution of the released nuclei. It is found that the approximation breaks down already at relatively short pulses. We also show that the relative orientation of the internuclear axis and polarization vector has a crucial effect on the kinetic energy spectrum.

Transition in Wall-Bounded Flows

Abstract In this paper, we present direct comparisons of experimental results on transition in wall-bounded flows obtained by flow visualizations, hot-film measurement, and particle-image velocimetry, along with a brief mention of relevant theoretical progresses, based on a critical review of about 120 selected publications. Despite somewhat different initial disturbance conditions used in experiments, the flow structures were found to be practically the same. The following observed flow structures are considered to be of fundamental importance in understanding transitional wall-bounded flows: the three-dimensional nonlinear wave packets called solitonlike coherent structures (SCSs) in boundary layer and pipe flows, the Λ-vortex, the secondary vortex loops, and the chain of ring vortices. The dynamic processes of the formation of these structures and transition as newly discovered by recent experiments include the following: (1) The sequential interaction processes between the Λ-vortex and the secondary vortex loops, which control the manner by which the chain of ring vortices is periodically introduced from the wall region into the outer region of the boundary layer. (2) The generation of high-frequency vortices, which is one of the key issues for understanding both transitional and developed turbulent boundary layers (as well as other flows), of which several explanations have been proposed but a particularly clear interpretation can be provided by the experimental discovery of secondary vortex loops. The ignorance of secondary vortex loops would make the dynamic processes and flow structures in a transitional boundary layer inconsistent with previous discoveries. (3) The dominant role of SCSs in all turbulent bursting, which is considered as the key mechanism of turbulent production in a low Reynolds-number turbulent boundary layer. Of direct relevance to bursting is the low-speed streaks, whose formation mechanism and link to the flow structures in wall-bounded flows can be answered more clearly than before in terms of the SCS dynamics. The observed SCSs and secondary vortex loops not only enable revisiting the classic story of wall-bounded flow transition, but also open a new avenue to reconstruct the possible universal scenario for wall-bounded flow transition.

Barrier Height Effect on Cl+H2(D2) Reaction

Three-dimensional time-dependent quantum wave packet calculation was performed to study the reaction dynamics of Cl+H2(D2) on two potential energy surfaces (CW PESs). The first CW PES is with spin-orbit correction; the second is without spin-orbit correction. The integral cross-section and reaction probability as a function of collision energy are calculated in the collision energy range of 0.1 eV to 1.4 eV. For reaction of Cl with D2, the reaction section with spin-orbit correction has a shift toward the high energy because the barrier height increases. As for the reaction of Cl with H2 at low collision energy, it is more reactive on the PES with spin-orbit correction than on the low barrier height PES without spin-orbit correction, due to the tunnel effect for the reaction of the Cl with H2. When the collision energy is higher than 0.7 eV, the reactivity on the low barrier height PES is larger than that on the high barrier height PES. It is believed that the barrier height plays a very important role in the reactivity of Cl with (H2, D2). For the Cl+H2 reaction the barrier width is also very important because of the tunneling effect.

Three-dimensional wave packets in a compressible boundary layer

A three-dimensional wave packet generated by a local disturbance in a two-dimensional hypersonic boundary layer flow is studied with the aid of the previously solved initial-value problem. The solution to this problem can be expanded in a biorthogonal eigenfunction system as a sum of modes consisting of continuous and discrete spectra of temporal stability theory. A specific disturbance consisting of an initial temperature spot is considered, and the receptivity to this initial temperature spot is computed for both the two-dimensional and three-dimensional cases. Using previous analysis of the discrete and continuous spectrum, the inverse Fourier transform is computed numerically. The two-dimensional inverse Fourier transform is calculated for two discrete modes: Mode F and Mode S. The Mode S result is compared with an asymptotic approximation of the Fourier integral, which is obtained using the Gaussian model as well as the method of steepest descent. It is shown that the method of steepest descent provides an excellent approximation to the more computationally intensive numerical evaluation of the inverse Fourier transform. Additionally, the three-dimensional inverse Fourier transform is found using an asymptotic approximation of the Fourier integral. A main feature of the resulting three-dimensional wave packet is its two-dimensional nature, which arises from an association of Mode S with Mack’s second mode.

Effect of Reagent Rotation on Isotopic Branching in (He, HD+) Collisions

A three-dimensional time-dependent quantum mechanical wave packet approach is used to calculate reaction probability (P(R)) and integral reaction cross section (sigma(R)) values for both the channels of the reaction He + HD(+) (v = 1; j = 0, 1, 2, 3) --> HeH(D)(+) + D(H), over a range of translational energy (E(trans)) on the McLaughlin-Thompson-Joseph-Sathyamurthy (MTJS) potential energy surface using centrifugal sudden approximation for nonzero total angular momentum (J) values. The reaction probability plots as a function of translational energy for different J values exhibit several oscillations, which are characteristic of the system. It is shown that HeH(+) is preferred over HeD(+) for large J values and that HeD(+) is preferred over HeH(+) for small J values for all the rotational (j) states studied. The integral reaction cross section for both the channels and therefore the isotopic branching ratio for the reaction depend strongly on j in contrast to the marginal dependence shown by earlier QCT calculations. The computed results are in overall agreement with the available experimental results.

Self-focusing of wave packets and envelope shock formation in nonlinear dispersive media

The self-action of three-dimensional wave packets is analyzed analytically and numerically under the conditions of competing diffraction, cubic nonlinearity, and nonlinear dispersion (dependence of group velocity on wave amplitude). A qualitative analysis of pulse evolution is performed by the moment method to find a sufficient condition for self-focusing. Self-action effects in an electromagnetically induced transparency medium (without cubic nonlinearity) are analyzed numerically. It is shown that the self-focusing of a wave packet is accompanied by self-steepening of the longitudinal profile and envelope shock formation. The possibility of envelope shock formation is also demonstrated for self-focusing wave packets propagating in a normally dispersive medium.

Isotope effects in the dissociation of the B̃A11 state of SiH2, SiHD, and SiD2 using three-dimensional wave packet propagation

Dissociations after the A 1B1-->B 1A1 photoexcitation of SiH2, SiHD, and SiD2 were studied to investigate excited-state dynamics and effects of the initial vibrational state. The cross section (sigma) for the photodissociation relative to SiH2(B)-->Si(1D)+H2 and the rovibrational population of the H2 fragment were computed using the wave packet propagation technique based on the three-dimensional potential energy surfaces (PESs) of the A and B electronic states and the transition dipole surfaces, which were reported in our previous paper [J. Chem. Phys. 122, 144307 (2005)]. The photodissociation spectrum consists of a broadband and a number of sharp peaks. For SiH2 and SiD2, the sharp peaks correspond to the resonance structure of the vibrational levels of the B state and the broadbands are nearly independent of the photon energy. The broadband for SiHD increases steeply with the photon energy above 30,000 cm(-1). The flux leaving the computational grid for SiH2 and SiD2 consists of at least two components, whereas that for SiHD consists of only a faster component. These large isotope effects were discussed based on the valley to the dissociation channel on PES and the difference in the position of the initial wave packet for three isotopomers.

Influence of centrifugal forces on the development of wave packets in boundary layers with a uniformly valid model

The behavior of three-dimensional wave packets in the boundary layer on curved surfaces is analyzed in this study based on a modification of the triple-deck theory referred to as the “criss-cross” interaction model. The equations of the criss-cross interaction describe a particular type of boundary layer instability mode that possesses underlying properties of both the Tollmien–Schlichting waves and Taylor–Görtler vortices. Previous analysis of the criss-cross interaction regime suggests a possibility for upstream propagation of perturbations in the boundary layer and possible absolute instability of the flow. However, these results cannot be considered as conclusive because the initial-value problem for the criss-cross interaction equations is ill-posed. In a recent work [Turkyilmazoglu M, Ruban AI. A uniformly valid well-posed asymptotic approach to the inviscid–viscous interaction theory. Stud Appl Math 2002;108:161–85] a regularized non-asymptotic model to describe criss-cross interaction has been proposed. Whereas in the original version of the theory, perturbations have an unbounded growth rate as the longitudinal wave number ∣ k∣ → ∞, in the new model of [Turkyilmazoglu M, Ruban AI. A uniformly valid well-posed asymptotic approach to the inviscid–viscous interaction theory. Stud Appl Math 2002;108:161–85], as physically expected the amplification rate remains bounded for both spatially growing and temporally growing waves. A Fourier transform method is used in the present study to solve the linearized equations for the flow over concave roughness and humps and it is found that disturbances develop and are convected downstream as wave packets. The behavior of the wave packets is consistent with convective instability, and the upstream influence is no longer present at large times.

Selective excitation of the OClO molecule with femtosecond laser pulse

The three-dimensional time-dependent quantum wave packet dynamics $(J=0)$ using a Hamiltonian for a triatomic molecule in Radau coordinates is employed to study laser pulse excitation of the OClO molecule. The fast Fourier transform (FFT) and the split operator methods are applied to propagate the wave packet. The vibronic excitations $A\phantom{\rule{0.2em}{0ex}}^{2}A_{2}({\ensuremath{\nu}}_{1},{\ensuremath{\nu}}_{2},{\ensuremath{\nu}}_{3})\ensuremath{\leftarrow}X\phantom{\rule{0.2em}{0ex}}^{2}B_{1}(0,0,0)$ of the triatomic molecule OClO using femtosecond laser pulses of varying intensities are investigated. With an ultrashort laser pulse of certain FWHM (full width at half maximum), the vibrational level can be selectively excited. The changes in the vibrational population distributions caused by simple variation of the pulse are remarkable.

Initial-value problem for three-dimensional disturbances in a compressible boundary layer

An initial-value problem is formulated for a three-dimensional wave packet in a compressible boundary layer flow. The problem is solved using a Laplace transform with respect to time and Fourier transforms with respect to the streamwise and spanwise coordinates. The solution can be presented as a sum of modes consisting of continuous and discrete spectra of temporal stability theory. Two discrete modes, known as mode S and mode F, are of interest in high-speed flows since they may be involved in a laminar-turbulent transition scenario. The continuous and discrete spectrum are analyzed numerically for a hypersonic flow with Mach number M=5.6. The following features are revealed: (1) The synchronism of mode S with acoustic waves at a streamwise wave number α→0 is primarily two-dimensional; (2) at high angles of disturbance propagation, mode F is no longer synchronized with entropy and vorticity waves; (3) at high angles of disturbance propagation, the synchronism between mode S and mode F is not accompanied by a mode S instability, and at even higher angles of disturbance propagation, mode S and mode F are not synchronized.

Self-action dynamics of ultrashort electromagnetic pulses

The self-action dynamics of three-dimensional wave packets whose width is on the order of the carrier frequency is studied under fairly general assumptions concerning the dispersion properties of the medium. The condition for the wave field collapse is determined. Self-action regimes in a dispersion-free medium and in media with predominance of anomalous or normal group velocity dispersions are numerically investigated. It is shown that, for extremely short pulses, nonlinearity leads not only to the self-compression of the wave field but also to a “turn-over” of the longitudinal profile. In a dispersionless medium, the formation of a shock front within the pulse leads to the nonlinear dissipation of linearly polarized radiation and to self-focusing stabilization. For circularly polarized radiation, the wave collapse is accompanied by the formation of an envelope shock wave.

Exact Nondipole Kramers-Henneberger Form of the Light-Atom Hamiltonian: An Application to Atomic Stabilization and Photoelectron Energy Spectra

The exact nondipole minimal-coupling Hamiltonian for an atom interacting with an explicitly time- and space-dependent laser field is transformed into the rest frame of a classical free electron in the laser field, i.e., into the Kramers-Henneberger frame. The new form of the Hamiltonian is used to study nondipole effects in the high-intensity, high-frequency regime. Fully three-dimensional nondipole ab initio wave packet calculations show that the ionization probability may decrease for increasing field strength. We identify a unique signature for the onset of this dynamical stabilization effect in the photoelectron spectrum.

Nonadiabatic Time-Dependent Wave Packet Study of the D+ + H2 Reaction System

A theoretical investigation on the nonadiabatic processes of the D(+) + H(2) reaction system has been carried out by means of exact three-dimensional nonadiabatic time-dependent wave packet calculations with an extended split operator scheme (XSOS). The diabatic potential energy surface newly constructed by Kamisaka et al. (J. Chem. Phys. 2002, 116, 654) was employed in the calculations. This study provided quantum cross sections for three competing channels of the reactive charge transfer, the nonreactive charge transfer, and the reactive noncharge transfer, which contrasted markedly to many previous quantum theoretical reports on the (DH(2))(+) system restricted to the total angular momentum J = 0. These quantum theoretical cross sections derived from the ground rovibrational state of H(2) show wiggling structures and an increasing trend for both the reactive charge transfer and the nonreactive charge transfer but a decreasing trend for the reactive noncharge transfer throughout the investigated collision energy range 1.7-2.5 eV. The results also show that the channel of the reactive noncharge transfer with the largest cross section is the dominant one. A further investigation of the v-dependent behavior of the probabilities for the three channels revealed an interesting dominant trend for the reactive charge transfer and the nonreactive charge transfer at vibrational excitation v = 4 of H(2). In addition, the comparison between the centrifugal sudden (CS) and exact calculations showed the importance of the Coriolis coupling for the reactive system. The computed quantum cross sections are also compared with the experimental measurement results.

A 2 A 2 ←X 2 B 1 absorption and Raman spectra of the OClO molecule: A three-dimensional time-dependent wave packet study

Time-dependent wave packet calculations of the (A (2)A(2)<--X (2)B(1)) absorption and Raman spectra of the OClO molecule are reported. The Fourier grid Hamiltonian method in three dimensions is employed. The X (2)B(1) ground state ab initio potential energy surface reported by Peterson is used together with his corresponding A (2)A(2) state surface or the revised surface of the A (2)A(2) state by Xie and Guo. Radau coordinates are used to describe the vibrations of a nonrotating OClO molecule. The split-operator method combined with fast Fourier transform is applied to propagate the wave function. We find that the ab initio A (2)A(2) potential energy surface better reproduces the detailed structures of the absorption spectrum at long wavelength, while the revised surface of the A (2)A(2) state, consistent with the work of Xie and Guo, better reproduces the overall shape and the energies of the vibrational levels. Both surfaces of the A (2)A(2) state can reasonably reproduce the experimental Raman spectra but neither does so in detail for the numerical model employed in the present work.

Stable spatial Langmuir solitons

We study localized two- and three-dimensional Langmuir solitons in the framework of model based on generalized nonlinear Schrödinger equation that accounts for local and nonlocal contributions to electron–electron nonlinearity. General properties of solitons are investigated analytically and numerically. Evolution of three-dimensional localized wave packets has been simulated numerically. The additional nonlinearities are shown to be able to stabilize both azimuthally symmetric two-dimensional and spherically symmetric three-dimensional Langmuir solitons.

Time-dependent Quantum Scattering Calculation of the O(&lt;sup&gt;3&lt;/sup&gt;P)+HBr(DBr) Reaction

An exact three-dimensional time-dependent quantum wave packet was employed to calculate the o(p-3) + hbr(dbr) reaction using a generalized london-ering-polanyi-sato(leps) potential energy surface. the results showed that vibrational excitation is effective for the reaction, and rotational excitation has an orientational effect in definite energy range. the rate constants and the reaction cross sections for the tide reactions have been computed, the calculated rate constants kappa(o+hbr) agreed well with experimental data. by comparing with relevant results, it can be found that the kinetic isotopic effects of the reaction are relatively obvious.

Transition state dynamics of OHF on several electronic states: Photodetachment spectrum of OHF− and conical intersections

Wave packet simulations of the photodetachment spectrum of OHF(-) are performed on several electronic adiabatic states, two triplets and four singlets of neutral OHF. The transition moments to these six states have been approximated using the ab initio electronic wave functions of OHF(-) and OHF calculated at the equilibrium configuration of the parent anion. In a first step, two-dimensional simulations of the spectrum are performed on new two-dimensional potential energy surfaces (PESs) of the neutral in a OHF collinear geometry. The resulting simulated spectrum is in rather good agreement with the experimental one, reproducing all the structures from 0 to 2.5 eV electron kinetic energies. At energies below 0.5 eV, all calculated states, singlets and triplets, contribute to the total spectrum. At higher energies, however, only the triplet states participate. In a second step, to improve the description of the spectrum, three-dimensional wave packet simulations of the spectrum are performed, getting an excellent agreement with the experiment. The collinear (3)Sigma(-) and (3)Pi states split in two (3)A(") and one (3)A('). New adiabatic PESs are used in this work for the 2 (3)A(") and 1 (3)A(') states, while the one recently proposed was used for the ground 1 (3)A("). It is found that the minimum energy paths of the (3)Sigma(-) and (3)Pi states cross twice at collinear geometry, so that at the transition state the ground state corresponds to (3)Pi, while (3)Sigma(-) is the lowest state otherwise. Such conical intersections are expected to give rise to important Sigma-Pi vibronic effects, requiring a complete three-dimensional model of coupled diabatic states to improve our understanding of the reaction dynamics in this kind of systems.

Higher order nonlinear evolution equations for a three-dimensional electromagnetic wave packet in a plasma

Starting from the full set of governing equations including the weak relativistic effect, three coupled nonlinear equations with higher older nonlinear and dispersive terms are derived, which describe the nonlinear evolution of a three-dimensional electromagnetic wave packet propagating in a plasma. Two particular cases are considered, where the space dependence of the dependent variables is either on the space coordinate along the direction of propagation of the wave or on that along an arbitrary fixed direction. In both cases the three coupled equations reduce to a single equation. This single equation is used to study the modulational instability of a uniform electromagnetic wave train. It is found that due to the inclusion of the weak relativistic effect there is always modulational instability, and a higher order nonlinear term in the evolution equation has a stabilizing influence.

Quantum dynamics of H2 formation on a graphite surface through the Langmuir Hinshelwood mechanism.

We have studied the formation of the H2 molecule on a graphite surface, when both H atoms are initially physisorbed. The graphite surface is assumed to be planar, and a model potential is obtained in a semiempirical way to reproduce the experimental properties of H physisorption on graphite. The reaction probability has been computed in the case when the angular momentum of the relative H-H motion lies parallel to the surface plane. Three-dimensional wave packet calculations have been performed for collision energies ranging from 2 to 50 meV. It is shown that the reaction occurs with a significant probability and produces the H2 molecule with a considerable amount of vibrationnal energy. A simple mechanical model is presented, where desorption of the nascent H2 molecule results from two successive binary elastic collisions.

Quantum scattering calculation of the O(1D)+HBr reaction.

Three-dimensional time-dependent quantum wave packet calculation for the O((1)D)+HBr reaction has been carried out using an accurate ab initio global potential energy surface [K. A. Peterson, J. Chem. Phys. 113, 4598 (2000)]. The calculations show that the initial state-selected reaction probabilities are dominated by resonance structures, and the lifetime of the resonance is generally in the subpicosecond time scale. The energy dependence of the reaction cross section is computed, which manifests still resonance structures, and is a decreasing function of the translational energy. The thermal rate constants are also computed, which are nearly independent on the temperature. The calculation results are discussed and compared to similar reaction with deep well.