Daniel Neuhauser

Bound state eigenfunctions from wave packets: Time→energy resolution

We present a method to obtain bound‐state eigenfunctions in any arbitrary range of energies, by a Fourier resolution (from time to energy) of a real‐time wave packet. The resolution is done simultaneously at a number of energies within the sought range, and the resulting vectors yield, after diagonalization, all bound‐state eigenvalues and eigenfunctions within that range. The method is exemplified on a Morse potential: eigenfunctions for 18 high‐lying states (n∼200) are obtained from resolution at 25 energies.

The application of time-dependent wavepacket methods to reactive scattering

In this article, we review several methods for performing numerically-exact reactive scattering calculations using time-dependent wavepackets. The basic idea we imply is to take the multi-arrangement reactive problem and reformulate it as one or more inelastic ones. In the simplest method, we extract total reaction probabilities by calculating the flux of the wavepacket as it leaves the interaction region in the direction of the reactive arrangement. To make this practical, we use complex potentials that absorb the wavepacket before it reaches the numerical grid boundary. We describe methods that generate observables ranging from total, energy-averaged reaction probabilities up to energy- and state-resolved S-matrix elements. We also review techniques for efficiently performing the necessary inelastic wavepacket propagation.

TIme-dependent reactive scattering in the presence of narrow resonances : avoiding long propagation times

Time‐dependent scattering is extended to systems possessing narrow resonances. At short times the wave function is integrated directly, and at late times the wave function is expanded in terms of the slowly decaying (complex) resonance eigenfunctions of the Hamiltonian, Ψ(X,t)≂Σn ane−ient−Γ nt/2Φn(X). The slowly decaying eigenfunctions are easily found via a short‐time filterization approach adapted from bound‐state studies, in which a random wave packet is filtered at various energies and the resulting vectors are then diagonalized. The method is exemplified for collinear reactions of H+H2, where it halves the propagation time.

Optimal control of curve‐crossing systems

Controlling curve‐crossing dynamics of a model diatomic system between two dissociative electronic states through radiative coupling with a third bound state is examined. Starting with an initial wave packet on one of the crossing surfaces, optimal control theory is used to design the radiative field to either enhance or eliminate (at our choice) selectivity of one product channel over another. A new optimization procedure is introduced which filters out dc and low frequency components from the optimal field, but still allows for resonant transitions to a third bound state. This procedure forces the fields to employ interesting physical mechanisms involving the bound state in order to control the electronic branching ratios rather than directly negating or enhancing the diabatic coupling term in the Hamiltonian. A new propagation scheme for a multisurface Hamiltonian using Pauli matrices is also presented.

Teaching lasers to control molecules in the presence of laboratory field uncertainty and measurement imprecision

An iterative optimization algorithm for designing laser fields to control molecular motion which utilizes laboratory input (test fields) and output (resulting product yields) information is proposed. Laboratory uncertainties such as laser field noise and limited precision in the product yield measurements are included in the simulations of the experiments. Two simulated examples of implementation of the algorithm are presented: selective electronic excitation in a model four‐state system and maximizing dissociation yield of the hydrogen fluoride molecule. Both examples demonstrate that, even with the inclusion of laboratory uncertainties, the experimental learning‐based algorithm is a potentially feasible method of controlling molecular motion and possibly manipulating chemical reactions.

Total integral reactive cross sections for F + H2 → HF + H: comparison of converged quantum, quasiclassical trajectory and experimental results

Abstract We report converged quantum total integral reactive cross sections for the reaction F + H 2 → HF + H, for initial rotational states j i = 0 and 1, using a time-dependent method. Our results are compared to classical results and to the experimental results of Neumark . Strong quantum effects are found in the threshold region for both initial states; i.e. in the dependence of the reaction on initial state for low energies. The classical results agree better with experiment than do the quantum results; this appears to be due to errors in the potential used.

Time-dependent (wavepacket) quantum approach to reactive scattering: Vibrationally resolved reaction probabilities for F+H2→HF+H

Abstract We present total and vibrationally resolved reactive scattering probabilities for the F+H2→HF(νf)+H reaction in three dimensions, for J=0, obtained using a fully quantal wavepacket method. The wavepacket propagation is done with an inelastic scattering method, using the Jacobi coordinates of the initial arrangement and a complex absorbing potential in the product (HF+H) arrangement. The complex absorbing potential alleviates having to propagate the packet a large distance out into the product arrangement, but precludes obtaining rotationally resolved probabilities. However, one does not have to propagate so far to obtain vibrationally resolved reaction probabilities. Results for a range of total energies are obtained in a single wavepacket propagation. Results are compared with those of Bacic, Kress, Parker and Pack using a time-independent method.

The application of optical potentials for reactive scattering: A case study

Recently we introduced a new kind of optical potential [D. Neuhauser and M. Baer, J. Chem. Phys. 90, 4351 (1989)], which allows us to treat an exchange collision as if it were an inelastic one. In this article we present, for the first time, a systematic study with respect to the optical potential parameters, and we discuss how the actual parameters to be used are related to those determined a priori, employing analytical arguments. We also show that the resulting extended inelastic arrangement channel can be treated using the common propagation technique, although the potential is complex.

Optimal control of unimolecular reactions in the collisional regime

The possibility of controlling unimolecular–dissociation processes with multiple laser fields in the collisional regime is examined. Employing the Bloch equations to describe optical excitation and decay processes, optimal control theory is used to design amplitude modulated fields which produce the desired excited‐state products. The selectivity of the product distribution of a simple four‐state photodissociation system is shown to have a square‐root dependence on the relative value of the mean dephasing time T 2 to the pulse length τ, i.e, (T 2/τ)1/2. The equivalence between T 2 decay and phase disruptions occurring in a random‐walk fashion is also examined. In the Appendix it is shown that the essential effect of the system temperature is to introduce a Boltzmann population factor on the product selectivity without affecting the nature of the optimal field.

State‐to‐state reactive scattering amplitudes from single‐arrangement propagation with absorbing potentials

A new paradigm is presented for calculation of reactive state‐to‐state transition amplitudes. The wave function is propagated in one arrangement (either reagents or the sought products, the choice being at one’s convenience); other arrangements are blocked with an absorbing potential. Reactive information is then obtained from the integral expression for the T matrix (〈ψ‖H−H0‖Ψ〉). The approach is exemplified on a collinear system, yielding accurate transition probabilities that are insensitive to the parameters of the absorbing potential. Expressions for the complete T matrix in the new reactive IOS are then derived, based solely on an IOS assumption in one of the arrangements, without a need to invoke matching procedures between different arrangements.