Robert E. Wyatt

Dynamics of the Collinear H+H2 Reaction. I. Probability Density and Flux

The time evolution of the collinear H+H2 reaction as given by classical mechanics and by time‐dependent quantum mechanics has been studied. The calculations employed the Porter–Karplus potential surface. The relevant equations of motion were solved to high accuracy by direct numerical integration. The evolution of the quantal probability density in the interaction region of the potential surface is shown in a series of perspective plots. Classical mechanics gives an amazingly good description of the probability density and flux patterns during most of the reaction; however, the classical and quantal descriptions begin to diverge near the end of the reaction. Essentially, the classical reaction terminates before the quantal reaction. The dynamic behavior of the reaction is hydrodynamically turbulent, as shown by transient whirlpool formation on the inside of the reaction path. All results reported in this paper are for one average system energy, namely, 0.65 eV (initial average translational energy = 0.38 eV).

Optical potential for laser induced dissociation

A new computational approach to molecular multiphoton dissociation is presented. Use of an optical potential allows the continuum channels to be represented as a set of pseudobound states coupled to the actual bound states of the molecule. The evolution of the system is thus amenable to the standard problem of laser induced transitions between bounds states. The long time behavior is then efficiently computed by using Floquet analysis. Results for a nonrotating diatomic are discussed.

Quantum mechanical reaction cross sections for the three‐dimensional hydrogen exchange reaction

The results of extensive multi−channel quantum mechanical studies of the three dimensional hydrogen exchange reaction are reported. Reaction cross sections were obtained for both the Porter−Karplus potential surface (collinear barrier height 0.396 eV) and the Yates−Lester−Liu surface (collinear barrier 0.424 eV).

Quantum scattering via the log derivative version of the Kohn variational principle

Abstract The log derivative version of Kohns variational principle is used as a setting for a new numerical approach to quantum scattering problems. In particular, a new radial basis set is devised which is both (a) ideally suited to the log derivative boundary value problem, and (b) directly amenable to a discrete representation based on Gauss-Lobatto quadrature. This discrete representation greatly facilitates the evaluation of the exchange integrals which arise in Millers formulation of chemical reactive scattering, and therefore significantly simplifies calculations which exploit this formulation. Applications to the 3-D H+H 2 reaction clearly demonstrate the practical utility of the method.

Quantum resonance structure in the three-dimensional F + H2 reaction

Abstract Evidence for a quantum resonance in the three-dimensional F + H 2 ( v = 0, i = 0) → FH( v = 2, all i ) + H reaction is presented. Relative to the collinear reaction, this resonance is much broader and is shifted by about 0.1 eV to higher energies. This resonance has not been predicted in previous quasiclassical trajectory computations, or in approximate quantum calculations.

Three‐dimensional natural coordinate asymmetric top theory of reactions: Application to H + H2

A particular partitioning of the Hamiltonian in natural collision coordinates is shown to lead to the use of hindered asymmetric top basis functions to represent all rotational motion (triangle tumbling plus internal bending) during reaction. These functions (along with perturbed Morse oscillator functions) are used as an adiabatic basis for expansion of the scattering wavefunction. The theory is discussed for both one and two reaction path potentials. The close coupled equations for the translational wavefunctions are then solved for the H + H2 reaction at total angular momentum J = 0. Wavefunction bifurcation and matching at the reactant–product boundary surface is considered in detail. Finally, numerical results (reaction probabilities, probability conservation, detailed balance, energy dependence of reactive S‐matrix elements, probability density, wavefunction real part, and flux) are presented and comparisons are made with other quantum mechanical, semiclassical, and statistical reaction studies.

Quantum wave packet dynamics with trajectories: Application to reactive scattering

The quantum trajectory method (QTM) for time-dependent wave packet dynamics involves integration of the de Broglie–Bohm hydrodynamic equations for the evolving probability fluid [C. Lopreore and R. E. Wyatt, Phys. Rev. Lett. 82, 5190 (1999)]. The equations of motion for discretized elements of the probability fluid (particles) are integrated in the Lagrangian, moving with the fluid, picture. These fluid elements move under the influence of both the usual potential energy function and the quantum potential, which involves the curvature of the quantum amplitude. The quantum potential and the quantum force are evaluated using a moving weighted least squares algorithm. As a demonstration of applicability, the QTM is applied to a model collinear reaction with an activation barrier. The reaction probabilities are in good agreement with exact quantum results, even for a relatively small number of particles in the ensemble. The QTM accurately describes tunneling using only real valued trajectories. In addition to...

Quantum wavepacket dynamics with trajectories: wavefunction synthesis along quantum paths

Abstract The quantum trajectory method (QTM) for wavepacket dynamics involves integration of the quantum hydrodynamic equations for fluid elements (particles) [C. Lopreore and R.E. Wyatt, Phys. Rev. Lett. 82 (1999) 5190]. In this study, it is shown how the wavefunction modulus and phase (action function) may be computed from information carried by the particles as they move along quantum trajectories. The action function is computed by integrating the quantum Lagrangian along the particle trajectories. For a model collinear reaction, plots are presented for the time evolving probability density, Lagrangian, and action function.

Quantum wave packet dynamics with trajectories: Implementation with adaptive Lagrangian grids

The quantum trajectory method was recently developed to solve the hydrodynamic equations of motion in the Lagrangian, moving-with-the-fluid, picture. In this approach, trajectories are integrated for fluid elements (“particles”) moving under the influence of the combined force from the potential surface and the quantum potential. To accurately compute the quantum potential and the quantum force, it is necessary to obtain the derivatives of a function given only the values on the unstructured mesh defined by the particle locations. However, in some regions of space–time, the particle mesh shows compression and inflation associated with regions of large and small density, respectively. Inflation is especially severe near nodes in the wave function. In order to circumvent problems associated with highly nonuniform grids defined by the particle locations, adaptation of moving grids is introduced in this study. By changing the representation of the wave function in these local regions (which can be identified ...

Quantum molecular dynamics in intense laser fields: Theory and applications to diatomic molecules

The quantum dynamics of vibration–rotation excitation in diatomic molecules in intense laser fields is investigated. The Floquet method is used in solving the equations‐of‐motion for a Hamiltonian explicitly time‐dependent. This method requires computation of the time‐displacement propagator only over the first optical cycle of the laser field, and is accomplished both numerically and with Magnus approximations. A number of features of single and multiphoton absorption in the LiH, CO, IBr, and HF molecules are studied as functions of the laser intensity and frequency. Average photon absorption spectra are studied with respect to power broadening, dynamic Stark shifts and line shapes. In some cases effective two‐state perturbative results accurately agree with the numerical results. In addition, rotational distributions in IBr following two‐photon absorption are found to have both thermal components for nonresonant states and structured nonthermal components for states nearly in resonance with the field. F...