G. J. Kroes

An analytical six‐dimensional potential energy surface for dissociation of molecular hydrogen on Cu(100)

A six‐dimensional (6D) potential energy surface (PES) describing the molecule–surface interaction in the dissociative chemisorption system H2+Cu(100) is presented. The PES is based on slab calculations performed using the generalized gradient approximation (GGA) of density functional theory (DFT). To allow the use of the PES in dynamics calculations which can test the validity of the DFT/slab approach by comparing with available experiments on dissociative chemisorption, the PES was fit to an analytical form. The fit used describes the orientational dependence of the molecule–surface interaction above the high symmetry sites upto second order in spherical harmonics. The barriers to dissociation calculated for H2 approaching with its molecular axis parallel to the surface are all located in the exit channel. Also, for different impact sites and orientations, the height and the distance to the surface associated with the barrier correlate well with the chemisorption energy of the H‐atoms in the sites to whi...

Performance of a time‐independent scattering wave packet technique using real operators and wave functions

We investigate the performance of a scattering algorithm which uses purely real algebra for the major part of the wave function calculation, while incorporating automatically the appropriate boundary conditions. The algorithm falls in the category of time‐independent wave packet methods ([R. Kosloff, J. Phys. Chem. 92, 2087 (1988)], and, more specifically for scattering [Y. Huang, W. Zhu, D. J. Kouri, and D. K. Hoffman, Chem. Phys. Lett. 206, 96 (1993)]), and combines two previous approaches: A method [V. A. Mandelshtam and H. S. Taylor, J. Chem. Phys. 103, 2903 (1995)] in which the action of the absorbing potentials is implicitly inserted in a polynomial expansion of the Green’s function, and a real initial wave function approach, in which zero initial momenta are avoided. Compared to the conventional, multiple time‐step Chebyshev method, the new algorithm required three times less Hamiltonian evaluations for a model problem involving direct scattering. The new method also showed faster convergence for a...

Dissociation of H2 on Cu(100): Dynamics on a new two‐dimensional potential energy surface

A two‐dimensional (2‐D) potential energy surface (PES) has been calculated for H2 interacting with the (100) face of copper. The PES is for H2 approaching with its internuclear axis parallel to the surface and dissociating over a bridge site into neighboring hollow sites. The density functional calculations were performed both within the local density approximation (LDA) and within a generalized gradient approximation (GGA). The LDA surface shows no barrier to chemisorption, but the GGA surface has a barrier of height 0.4 eV. A fit of the GGA surface has been used to calculate reaction probabilities for H2 in its v=0 and v=1 vibrational states, employing a wave packet method. The 2‐D wave packet results for the v=0 and v=1 thresholds are consistent with experiment, indicating that the barrier height calculated within the GGA used is accurate. The GGA results for the value of the barrier height are also consistent with the GGA value (0.5 eV) recently obtained for H2+Cu(111) by Hammer et al. [Phys. Rev. Let...

Dissociative chemisorption of H2 on Cu(100): A four‐dimensional study of the effect of parallel translational motion on the reaction dynamics

Results are reported of a four‐dimensional dynamics study on the dissociation of H2 on Cu(100). The potential‐energy surface was taken from density functional calculations, which employed the generalized gradient approximation and a slab representation for the surface. Reaction occurs preferentially in impacts near the bridge and hollow sites. Collisions near top sites promote vibrational excitation. The conclusion that vibrationally inelastic scattering and reaction occur preferentially on different sites can be generalized to other low index Cu surfaces. Resonances affect the reaction in the 4D model through a mechanism in which the molecule, trapped by excitation of the molecular bond which is weakened at the surface near top sites, is allowed more time to tunnel through the barrier to reaction. The calculated dependence of the diffraction probabilities on incidence energy suggests that a measurement of low‐order diffraction would be able to determine whether the minimum barrier to reaction occurs for ...

Application of an efficient asymptotic analysis method to molecule-surface scattering.

An improved method for performing asymptotic analysis developed by Balint‐Kurti et al. [J. Chem. Soc. Faraday Trans. 86, 1741 (1990)] was used with the close‐coupling wave packet (CCWP) method. S‐matrix elements are computed from the time dependence of the wave packet amplitude at a dividing surface in the asymptotic region. The analysis technique can be combined in a natural way with the use of an optical potential to absorb the scattered wave function beyond the dividing surface and with a technique in which the initial wave function is brought in on a separate, one‐dimensional grid, thereby allowing the use of a smaller grid. The use of the method in conjunction with the Chebyshev and short‐iterative Lanczos propagation techniques is demonstrated for a model problem in which H2 is scattered from LiF(001). Computed S‐matrix elements are in good agreement with those obtained using a time‐independent close‐coupling method.

Performance of close-coupled wave packet methods for molecule-corrugated surface scattering

The H2+LiF(001) system was used to investigate the performance of the hybrid close‐coupling wave packet (CCWP) method and of a symmetry adapted, fully close‐coupled wave packet (SAWP) method for a molecule–surface problem characterized by fairly high corrugation. In the calculations, a realistic, φ‐dependent model potential was used. The calculations were performed for a collision energy of 0.2 eV, with H2 initially in its j=0 rotational state at normal incidence to the surface. Large increases in the computational efficiencies of both wave packet methods were achieved by taking advantage of the potential coupling matrices associated with both methods becoming sparser with increasing molecule–surface distance. For the present model problem and employing this increased sparseness at longer range, the SAWP method is faster than the CCWP method by a factor of 2. The potential usefulness of the SAWP method for dissociative chemisorption problems is discussed.

Performance of a fully close‐coupled wave packet method for the H2+LiF(001) model problem

We have investigated the performance of a fully close‐coupled wave packet method and its symmetry‐adapted version for a model problem of H2 scattering from LiF(001). The computational cost of the fully close‐coupled methods scales linearly with the number of rotation‐diffraction states present in the basis set, provided that the sparseness of the potential coupling matrix is taken into account. For normal incidence, the symmetry adapted version is faster than the conventional close‐coupling wave packet method by almost an order of magnitude. An extension of the method to more realistic molecule‐surface problems is considered.

Scattering of H₂ by LiF(001) studies using a new model potential. I. Prediction of large differences in diffractin of cold beams of para H₂ and normal H₂.

The close‐coupling wave packet (CCWP) method has been used for performing calculations on rotationally and diffractionally inelastic scattering of H2 from LiF(001), using a model potential. The scattering from the initial j=0, 1, and 2 states was investigated at normal incidence for a collision energy of 0.1 eV. If the quadrupole‐ionic lattice interaction is included in the potential model, large probabilities (up to 0.3) are obtained for reorientational (mj changing) transitions in the scattering from the initial j=1 and j=2 states. This is in contrast with results of previous theoretical work which used model potentials not including the electrostatic interaction and found much smaller probabilities for Δmj transitions. Inclusion of the quadrupole‐ionic lattice interaction in the model also leads to the prediction of large differences between the diffraction of H2 in its j=0 rotational state and diffraction of j=1 H2. It should be possible to check this result by diffraction experiments employing cold b...

Calculations on rotationally and diffractionally inelastic molecule‐surface scattering for arbitrary angles of incidence: A new wave packet technique

The close‐coupling wave packet (CCWP) method has been adapted for performing calculations on molecule‐surface scattering with arbitrary angles of incidence. The method used involves a slight modification of the fast Fourier transform (FFT) technique for evaluating the action of the translational kinetic energy operator on the wave function, employing the shifting theorem of Fourier analysis. We present and compare results of CCWP and close‐coupling (CC) calculations on the He+LiF and H2+LiF systems using simple model potentials. The results presented establish the validity of the proposed technique and may be useful as benchmarks.

Avoiding long propagation times in wave packet calculations on scattering with resonances: A hybrid approach involving the Lanczos method

We investigate the usefulness of a hybrid method for scattering with resonances. Wave packet propagation is used to obtain the time‐dependent wave function Ψ(t) up to some time T at which direct scattering is over. Next, Ψ(t) is extrapolated beyond T employing resonance eigenvalues and eigenfunctions obtained in a Lanczos procedure, using Ψ(T) as starting vector to achieve faster convergence. The method is tested on one two‐dimensional (2D) and one four‐dimensional (4D) reactive scattering problem, affected by resonances of widths 0.1–5 meV. Compared to long time wave packet propagation, the hybrid method allows large reductions in the number of Hamiltonian operations NH required for obtaining converged reaction probabilities: A reduction factor of 24 was achieved for the 2D problem, and a factor of 6 for the 4D problem.