Drew A. McCormack

Rovibrationally inelastic scattering of (v=1, j=1) H-2 from Cu(100) experiment and theory

A comparison between experiment and theory is performed for the scattering of (v=1, j=1) H2 from Cu(100) at normal incidence. Experimentally, this system was studied using molecular beam techniques, with stimulated Raman pumping employed to overpopulate (v=1, j=1) in the incident beam, and resonance enhanced multi-photon ionization used to detect the H2 scattered in two (v=1, j) states, and two (v=0, j) states. Theoretically, six-dimensional wave packet calculations were performed, employing a new, extended potential energy surface that was computed with density functional theory, using the generalized gradient approximation and a slab representation of the metal surface. Theory and experiment are in good agreement for the survival probability, i.e., the probability for rovibrationally elastic scattering. However, the theory overestimates the probabilities for rotationally inelastic scattering (to v=1, j=3) and for rovibrationally inelastic scattering (to v=0, j=5 and 7) for channels that could be determi...

Rotational Effects in Six-Dimensional Quantum Dynamics for Reaction of H2 on Cu (100).

We present results of six-dimensional (6D) quantum wave-packet calculations for the dissociative adsorption of (ν=0,j=4,mj) H2 on Cu(100). The potential-energy surface is a fit to points calculated using density-functional theory (DFT), with the generalized gradient approximation (GGA), and a slab representation for the surface. New aspects of the methodology we use to adapt the wave function to the symmetry of the surface, which relate to calculations for initial rotational states with odd mj (the magnetic quantum number), are explained. Invoking detailed balance, we calculate the quadrupole alignment for H2 as it would be measured in an associative desorption experiment. The reaction of the helicopter (ν=0,j=4,mj=4) state is preferred over that of the (ν=0,j=4,mj=0) cartwheel state for all but the lowest collision energies considered here. The energy dependence of the quadrupole alignment that we predict for (ν=0,j=4) H2 desorbing from Cu(100) is in good qualitative agreement with velocity-resolved asso...

Mechanisms of H2 dissociative adsorption on the Pt(211) stepped surface.

We utilize classical trajectory calculations to study the reaction dynamics of the dissociative adsorption of H2 on the stepped Pt(211) surface. The potential-energy surface has been obtained through an accurate interpolation of density-functional theory data at the generalized gradient approximation level, using the corrugation reduction procedure. New techniques for visualizing the collective dynamics of trajectories are introduced to elucidate the reaction mechanisms involved. Reaction exhibits a nonmonotonic dependence on collision energy, first decreasing with energy, and then increasing. A strong component of direct nonactivated reaction exists at the top edge of the step over the entire range of energies. The inverse relationship between reaction and collision energy at low energies is attributed to trapping in weak chemisorption wells. These wells also influence the direct reaction at the step, leading to a strong asymmetric dependence on incidence angle. Reaction on the terrace is activated, and only contributes significantly at high energies. Agreement with experiments on Pt(533) [A. T. Gee, B. E. Hayden, C. Mormiche, and T. S. Nunney, J. Chem. Phys. 112, 7660 (2000); Surf. Sci. 512, 165 (2002)] is good, and we are able to suggest new interpretations of the experimental data.

The conservation of quantum zero-point energies in classical trajectory simulations

We propose a computational technique to constrain the vibrational modes of a classical molecule to have energy greater than the quantum zero‐point energy (ZPE). The trajectory of any mode with energy less than ZPE is projected to a neighboring point in phase space where the energy is equal to the ZPE and the phase angle of the mode is unchanged. All other modes are then perturbed in such a way as to conserve the total energy of the system. This technique is similar in principle to the method of holonomic constraints. We apply this ‘‘semiholonomic’’ TRAPZ (trajectory projection onto ZPE orbit) scheme to the two mode Henon–Heiles system and find that it results in a decrease of ergodicity. Periodic limit cycle internal vibrational energy redistribution is observed. Implications of this method for the conservation of ZPE in quasiclassical trajectory simulations are discussed.

Signatures of site-specific reaction of H2 on Cu(100)

Six-dimensional quantum dynamical calculations are presented for the reaction of (v,j) H2 on Cu(100), at normal incidence, for v=0–1 and j=0–5. The dynamical calculations employed a potential energy surface computed with density functional theory, using the generalized gradient approximation and a slab representation for the adsorbate-substrate system. The aim of the calculations was to establish signatures from which experiments could determine the dominant reaction site of H2 on the surface and the dependence of the reaction site on the initial rovibrational state of H2. Two types of signatures were found. First, we predict that, at energies near threshold, the reaction of (v=1) H2 is rotationally enhanced, because it takes place at the top site, which has an especially late barrier and a reaction path with a high curvature. On the other hand, we predict the reaction to be almost independent of j for (v=0) H2, which reacts at the bridge site. Second, we predict that, at collision energies slightly above...

Full-dimensional quantal initial state-selected reaction probabilities (J=0) for the reaction OH(v=0,j=0)+CO(v=0,j=0)→CO2+H

Abstract We present six-dimensional (6D) quantum dynamics calculations of initial state-selected reaction probabilities for the reaction of OH( v =0, j =0) with CO( v =0, j =0), for total angular momentum J =0. The results are compared to five-dimensional (5D) calculations in which the potential was averaged over the vibrational ground state wavefunction of CO. The 6D reaction probabilities are in good overall agreement with the 5D results up to a collision energy E i of 0.47 eV, but they exceed the 5D values at larger energies, by up to 40% at E i =0.8 eV. Significant vibrational excitation of the CO fragment occurs for E i ⩾0.4 eV.

Zero-point energy constraints in RRKM and non-RRKM molecules

The TRAPZ method for zero-point energy (ZPE) preservation (Lim and McCormack, J. Chem. Phys., 1995, 102, 1705) is generalised to molecular systems of non-zero angular momentum. The method is shown to conserve linear momentum, angular momentum and total energy. It is also found to preserve the intrinsic Rice–Ramsperger–Kassel–Marcus (RRKM) behaviour of a dissociating Al3 cluster. The TRAPZ rate coefficients are lower than those calculated for classical ensembles, since regions of phase space with less than ZPE can no longer react. As required, the RRKM rate coefficients are upper bounds to the TRAPZ rate coefficients. The TRAPZ reaction threshold is higher than the classical (asymptotic-limit) product ZPE due to fluctuations in instantaneous normal mode ZPEs. Rotationally hot Al2 is produced as Al3 ZPE bending motion is converted to Al2 angular momentum. The TRAPZ method does not preserve the non-RRKM behaviour of HNC isomerisation.

Resonance affected scattering: Comparison of two hybrid methods involving filter diagonalization and the Lanczos method

We apply two hybrid methods for solving scattering problems affected by resonances, to a four-dimensional reactive surface scattering system. In each method the solution of the problem is divided into two parts: a wave packet propagation, and a resonance calculation; results of the resonance calculation are used to extrapolate the long-time behavior of the system. In the first hybrid method, the propagation is by the multistep Chebyshev method, with calculation of resonances performed by the Lanczos method. In the second, the propagation is done using an implementation of the absorbing boundary condition (ABC) evolution operator, and the resonance calculation by filter diagonalization (FDG). Each method produces accurate scattering results in much less computation time than standard long-time wave packet propagation. The Chebyshev–Lanczos approach proves most capable for the calculation of resonances, but is computationally expensive. The ABC–FDG method is much cheaper to implement, but could not be made to extract accurate data for certain broad, overlapping resonances. This was overcome by propagating longer (still much shorter than for long-time propagation) to allow the elusive resonances time to decay.

Converged five-dimensional quantum calculations for OH+CO→H+CO2

We perform five-dimensional quantum wave packet calculations of initial-state-resolved reaction probabilities for the reaction OH+CO→H+CO2, with OH and CO initially in the rovibrational ground state, and total angular momentum J=0. In essence, the dynamics are treated exactly for all molecular degrees of freedom except the CO reactant bond, for which a vibrational-averaging approximation is adopted. Comparison of reaction probabilities to those obtained in an earlier, similar study [D. H. Zhang and J. Z. H. Zhang, J. Chem. Phys. 103, 6512 (1995)] show that the previously obtained results were not well converged, primarily because too few rotational basis functions were used in the calculations. The resonances found in the current study are also more abundant and narrower than in the earlier study. Reaction probabilities from calculations on an updated potential energy surface (PES) [K. S. Bradley and G. C. Schatz, J. Chem. Phys. 106, 8464 (1997)] do not differ significantly from those for the PES used in ...

THE ZERO-POINT ENERGY PROBLEM IN CLASSICAL TRAJECTORY SIMULATIONS AT DISSOCIATION THRESHOLD

Quasiclassical trajectory calculations offer a cost-effective means of investigating the dynamics of chemical reactions. However, they suffer from the zero-point energy (ZPE) problem, whereby the (quantum) ZPE motion can contribute to an overestimation of the rate coefficient. This paper reports on some dynamics of the Henon–Heiles system. Dynamics of the water molecule at energies just below the (quantum) dissociation threshold, are also reported. The TRAPZ method [Lim and McCormack, J. Chem. Phys. 102, 1705 (1995)] leads to a definite improvement over unconstrained classical mechanics.