Classical Trajectory Method Research Articles

Generation of attosecond pulses of recombination radiation in two-colour laser fields

The possibility of generation of attosecond pulses of recombination radiation upon the above-threshold tunnel ionisation of atoms (ions) in two-colour laser fields is studied. The method of classical photoelectron trajectories in the continuum is used to determine the laser field parameters minimising the duration of recombination radiation. It is shown that pulses of duration of several tens of attoseconds can be generated in such fields. The principal possibility of generation of coherent electromagnetic pulses of duration τg≲1 as is also shown.

Peculiarities of atom–quasidiatom collision complex formation: classical trajectory study

General peculiarities in the formation of quasibound complexes (QC) in collisions of an atom with a rigid diatomic or linear polyatomic molecule are studied using the method of classical trajectories. The CO2–Ar system is taken as an example. Statistical distributions of parameters characterizing either the formation of QC or those appropriate to rotational relaxation cross-sections are simulated and analyzed. Various factors are examined as far as their role in the formation of the QC is concerned: (1) the complexity of a trajectory approach (exact classical, planar, coplanar); (2) the selection of intermolecular potential energy surface (ab initio Parker–Snow–Pack potential; empirical Berreby–Dayan potential); (3) the departure of the initial CO2 rotational distribution from equilibrium. The cross-sections and bimolecular thermal rates for QC formation are obtained using the modified Sorbie–Murrell model. The use of derived analytical expressions makes the computations of QC fractions in CO2–Ar collisions easier both in equilibrium and in rotational non-equilibrium conditions.

Calculation of the transport properties of carbon dioxide. III. Volume viscosity, depolarized Rayleigh scattering, and nuclear spin relaxation.

Transport properties of pure carbon dioxide have been calculated from the intermolecular potential using the classical trajectory method. Results are reported in the dilute-gas limit for volume viscosity, depolarized Rayleigh scattering, and nuclear spin relaxation for temperatures ranging from 200 to 1000 K. Three recent carbon dioxide potential energy hypersurfaces have been investigated. Calculated values for the rotational collision number for all three intermolecular surfaces are consistent with the measurements and indicate that the temperature dependence of the Brau-Jonkman correlation is not applicable for carbon dioxide. The results for the depolarized Rayleigh scattering cross section and the nuclear spin relaxation cross section show that calculated values for the generally more successful potentials differ from the observations by 9% at about 290 K, although agreement is obtained for nuclear spin relaxation at about 400 K.

Um modelo para a superfície líquida no estudo da dinâmica do espalhamento de Xe e Ne pelo esqualano

In this work we present a theoretical model to investigate the scattering of Xe and Ne by a liquid squalane surface. The liquid surface is modeled as a grid of harmonic oscillators with frequencies adjusted to experimental vibration as frequencies of the liquid squalane and the atom-surface interaction potential is modeled by a Lennard-Jones function. The three dimensional description of the dynamics of the process which occurs at the gas-liquid interface is obtained by the classical trajectory method. The general characteristics of the dynamics of the scattering process are in good agreement with experimental data.

Calculation of the transport properties of carbon dioxide. II. Thermal conductivity and thermomagnetic effects.

The transport properties of pure carbon dioxide have been calculated from the intermolecular potential using the classical trajectory method. Results are reported in the dilute-gas limit for thermal conductivity and thermomagnetic coefficients for temperatures ranging from 200 K to 1000 K. Three recent carbon dioxide potential energy hypersurfaces have been investigated. Since thermal conductivity is influenced by vibrational degrees of freedom, not included in the rigid-rotor classical trajectory calculation, a correction for vibration has also been employed. The calculations indicate that the second-order thermal conductivity corrections due to the angular momentum polarization (< 2%) and velocity polarization (< 1%) are both small. Thermal conductivity values calculated using the potential energy hypersurface by Bukowski et al. (1999) are in good agreement with the available experimental data. They underestimate the best experimental data at room temperature by 1% and in the range up to 470 K by 1%-3%, depending on the data source. Outside this range the calculated values, we believe, may be more reliable than the currently available experimental data. Our results are consistent with measurements of the thermomagnetic effect at 300 K only when the vibrational degrees of freedom are considered fully. This excellent agreement for these properties indicates that particularly the potential surface of Bukowski et al. provides a realistic description of the anisotropy of the surface.

Rotamer Dynamics of Substituted Simple Alkanes. 1. A Classical Trajectory Study of Collisional Orientation and Alignment of 1-Bromo-2-Chloroethane with Argon

The 1-bromo-2-chloroethane molecule could exist in T, G, and G‘ rotamer forms. The collisional orientation and alignment of these rotamers in colliding with the Ar atom were studied by classical trajectory method. With the initial translational collision energies and rotational energies being selected in the main energy range covered by room temperatures to around 1000 K, the collisional orientation and alignment moments of the rotamers of the title molecule were calculated as a function of the impact parameter and the rotational angular momentum along the molecular z axis. As far as the collisional orientation and alignment behaviors are concerned, the calculations show that there are similarities as well as differences between these rotamers. Following the generally accepted physical models developed for the collisional alignment of diatomic molecules, model mechanisms for the collisional orientation and alignment of the present system were proposed and discussed.

Theoretical analysis of the relation between H2 dissociation and reflection on Pd surfaces.

We study the scattering of H2 (v=0, J=0) molecules by the Pd(110) surface using classical trajectory methods. We show that the dissociative adsorption probability barely depends on incidence angle (total energy scaling) up to an impact energy of 200 meV. This is the consequence of a "loss of memory" of the initial incidence angle, mostly due to dynamic trapping, which also reflects itself in a cosinelike angular distribution of reflected molecules. Consequently, a cosinelike distribution can be the result of a subpicosecond process that involves neither energy dissipation to the surface nor transient thermal accommodation.

Enhancement of intense field ionization of Rydberg atoms by nonhydrogenic cores and quantum-mechanical tunnelling

Time-dependent probabilities for ionization of Rydberg H, He, Li, Na and K in intense fields are calculated using a classical-trajectory method with allowance for quantum-mechanical tunnelling. The results depend only weakly on the nuclear charge and screening as long as the core is nonhydrogenic. However, the differences from the hydrogenic target are dramatic. The core of the nonhydrogenic atoms is treated as a 1s orbital in the case of He and as a Thomas–Fermi potential for the higher-Z atoms.

Scattering of atomic nitrogen on W(1 0 0)

We construct a 3D representation of the N/W(1 0 0) potential energy surface using the “corrugation-reducing procedure” to interpolate between ab initio data. We study the absorption and reflection dynamics on the frozen surface using classical trajectory methods. Our results show the importance of “dynamic trapping” which causes a decrease of the absorption probability with increasing impact energy. The strong corrugation of the surface induces a diffusion-like evolution of the atom degrees of freedom parallel to the surface.

Angular dependence of dissociation in steering dominated activated reaction

The angular dependence of dissociation has been explored using classical trajectory methods for model potential energy surfaces having wells into which molecules steer before dissociating. It was found that when the potential well is located at the surface site with the lowest dissociation barrier, the dissociation probability decreases with increasing angle of incidence due to shadowing effects. However when the well is moved before the site having the highest barrier, steering to that site dominates. In this case, the dissociation can increase with incidence angle due to molecular refraction onto the lowest dissociation barrier. For certain well depths we obtain almost no angular dependence to dissociation. These results are discussed with reference to experimental dissociation measurements for the O 2/Al(1 1 1) and N 2/W(1 1 0) systems, which exhibit non-monotonic and approximately zero angular dependence (so-called total energy scaling) respectively.

Angular distribution of H2 molecules scattered from the Pd(111) surface

We study the scattering of H2 (v=0,J=0) molecules by the Pd(111) surface using classical trajectory methods. We show that the variation of the reflectivity with incidence angle can be explained with the combination of two processes: “dynamic trapping” and “direct dissociation” that verify total and normal energy scaling, respectively. The presence of the dissociation channel barely affects the angular distribution of scattered molecules. In the patterns of final angular distributions, the main difference, with respect to atom scattering, is a strong momentum transfer from motion normal to the surface toward molecular rotation.

Femtosecond photoionization of RbI

The photodissociation of RbI at 267 nm was studied by femtosecond pump–probe ionization. The probe process of multiphoton ionization by 800 nm resulted in complicated electron and ion signals for dissociation on a purely repulsive curve. The Rb ion signal, produced by dissociative ionization of RbI, has a fast decay and a delayed rise. Transient zero-kinetic-energy electrons were found in the time-resolved photoelectron spectrum, as well as electrons from normal three-photon ionization. Both electron and ion signals were successfully simulated using a classical trajectory method. It is understood that resonance between excited states and their crossings play important roles during the multiphoton ionization probe process.

Nonequilibrium Molecular Dynamics Calculation of the Thermal Conductivity of Solid Materials

Tully's stochastic classical trajectory method to simulate lattice dynamics has been adapted to carry out nonequilibrium molecular dynamics calculations. The method allows for a computational experiment to be performed placing the material between two heat reservoirs at different temperatures: the resulting temperature gradient generates thermal stationary nonequilibrium states in the system. A phenomenological calculation of the thermal conductivity of the material is carried out by using Fourier's law. When applied to crystalline silicon, the method accurately describes the variation of the thermal conductivity with temperature.

Monte Carlo Evaluation of Forward−Backward Semiclassical Correlation Functions with a Quantized Coherent State Density

The derivative formulation of the forward-backward semiclassical dynamics (FBSD) representation of time correlation functions can be expressed as an integral with respect to trajectory initial conditions weighted by the coherent state transform of a corrected density operator. Expressions are derived for evaluating the relevant matrix elements for applications of particular interest, such as normal mode, bond stretching, and velocity correlation functions at zero and at finite temperature by employing the Gaussian approximation and the discretized path integral representation of the initial density operator, respectively. The obtained expressions lend themselves naturally to integration via Monte Carlo sampling techniques. The fully quantum mechanical representation of the appropriate density operator ensures a proper treatment of zero-point effects, and the use of the coherent state representation captures important imaginary components that are absent from purely classical trajectory methods. Applications to clusters of four water molecules at room temperature are presented.

Semiclassical modeling of Rydberg wave-packet dynamics in diatomic molecules: Average decoupling theory

The semiclassical dynamics of Rydberg electronic wave packets in diatomic molecules is investigated using a sum over classical trajectories method, which is based on the semiclassical form of Feynman's path integral. Our approach allows us to calculate intramolecular energy redistribution rates based on averaging of coupling parameters over classical trajectories associated with time-dependent parts of the overall system that exhibit different periodicities. The accuracy of our method is tested against perturbation theory and good agreement is obtained. A resonance structure in the computed autocorrelation function has also been observed in the case of rotating nuclei, when the periods of the classical trajectories of the electron match an integer multiple of the rotational period. This has previously been called the stroboscopic effect.

Classical dynamics of dissociative adsorption for a nonactivated system: The role of zero point energy

We present dissociative adsorption probabilities of H2 on Pd(111) computed with the classical trajectory method. We perform both classical (C) and quasiclassical (QC) calculations, the latter including, by contrast with the former, the initial zero point energy (ZPE) of H2. We analyze in detail the role played by the ZPE and demonstrate the strong and weak points of both C and QC calculations. We show that ZPE is crucial in accelerating the molecules toward the surface through vibrational softening. However, at low energies, dynamic trapping is quenched in QC calculations by processes of vibration to rotation energy transfer that would be associated with closed channels in a quantum approach. In this study we use a new representation of the H2/Pd(111) potential energy surface (obtained by interpolation of ab initio data) with a significantly better accuracy in the entrance channel region which plays a decisive role in the dissociation dynamics.

Classical theories of the ion/linear quadrupole capture

The dependence of the ion/linear quadrupole capture rate constant on the resultant orbital-rotational momentum and individual energetic and molecular parameters that characterize a given system are calculated using a microcanonical version of the transition state theory and classical trajectory method. Both methods indicate that the dependencies are similar to those obtained for the ion/linear dipole system. It is shown that, contrary to the ion/polar molecule systems, the capture rate constant for the quadrupoles frequently does not fall on the plateau which corresponds to the assumption that the resultant momentum can be approximated to the orbital momentum. Therefore, the theories that use this approximation are not adequate for description of the ion/quadrupole capture. Both TST and classical trajectory calculations agree very well with experiment and give identical or slightly different results for | b 3|≤10 which covers the whole range of temperatures down to extremely low. At so low temperatures the discrepancies are larger which seems to be of little consequence since both methods do not account for the quantum effects.

Phases and amplitudes of recurrences in autocorrelation function by a simple classical trajectory method

The interference between time-dependent recurrences in the quantum autocorrelation function is eliminated by carrying out orthogonal transformations in the time-energy domain. The time-dependent phases and amplitudes of the individual recurrences are compared with the results obtained from simple classical trajectory calculations. Using classical trajectories we calculate a two-dimensional survival probability which is defined in the time and energy domain. The two-dimensional survival probability provides the phase and enables to distinguish between overlapping recurrences. Remarkable agreement between the quantum and classical results is obtained for the initial Gaussian wave packet which is preferentially located either in the regular or in the chaotic regimes in the classical phase space of the Pullen–Edmonds Hamiltonian (nonlinearly coupled two harmonic oscillators). A novel method which enables to determine the molecular potential energy surfaces from a measured absorption or emission spectra is proposed. The method employs the matching of Wigner transforms of individual quantum recurrences with the two-dimensional classical survival probability.

Quantum Dressed Classical Mechanics: Application to the HO + CO → H + CO2 Reaction

Reaction dynamics of a four atom system (HO + CO) is investigated using the classical trajectory method and two quantum-classical theories. At 298 K, the new quantum-classical method predicts a rate of 1.49 x 10 - 1 3 cm 3 /s, compared to an experimental value of 1.5 x 10 - 1 3 cm 3 /s. It also reproduces the unusual temperature dependence.

Bremsstrahlung emission from interactions between two dressed dust grains in dusty plasmas

Bremsstrahlung emission from interactions between two dressed grains charged with the same sign in dusty plasmas are investigated using the classical trajectory method. An interaction potential model taking into account the cross terms of shield effects is applied to describe the interaction potential between dressed dust grains in dusty plasmas. The classical straight-line trajectory method is applied to represent the bremsstrahlung cross section as a function of the scaled impact parameter, collision energy, and photon energy. The result shows that the potential well in the interaction potential plays an important role in the bremsstrahlung spectrum. It is also found that there exists a nonradiation position in the bremsstrahlung radiation due to the balance between the repulsive and attractive interactions.