Rotationally inelastic molecule–surface scattering in the sudden approximation

Abstract

Rotational and reorientational transitions in molecular collisions with solid surfaces are investigated by a model based on a sudden approximation with respect to both the rotational and the diffraction states that play a role in the scattering. The approximation developed leads to computationally simple expressions and provides detailed insight into the physical properties of the processes involved. A detailed quantitative study is made of the rotational state distribution produced by the collision, the variation of rotational excitation probabilities with the scattering angle, and related questions. A number of factorizations, sum-rule, and scaling properties are predicted for ‖ Sjmj,00;j′m′j′,mn ‖2, the transition probability between the initial (jmj) and the final (j′m′j′) rotational states for scattering into the (mn) diffraction channel. The strongest sum rules and scaling laws are obtained using additional approximations beyond the sudden decoupling. Among the latter results: (1) The j,j′ dependence of ‖ Sj0,00;j’m’0,mn ‖2 is determined entirely by the difference variable Δj=j′−j. (2) The diffractive intensity distribution summed over all final rotational states is the same as that obtained for a mass-equivalent atom (with an interaction that is the orientation-averaged molecule–surface potential). (3) The rotational state distribution, summed over all diffraction states, equals that calculated from a corresponding flat surface. (4) All rotational transition probabilities for the (m,n) diffraction spot can be obtained from the diffraction–rotational transition probabilities in the (m,0) and (n,0) diffraction spots. The above and other properties are tested numerically in the framework of the full sudden approximation for a model of H2/LiF(001) in the energy range 0.5–0.9 eV. They are found to hold to excellent accuracy. Systematics of the results with regard to variation of the surface corrugation parameter are noted.

The effect of dissociative chemisorption on the diffraction of D2 from Ni(110)

“…The determination of the D 2 diffraction reflectivities requires some additional considerations. It is generally accepted 17,18,22,40 that for inert surfaces the interaction of the molecule with the surface can be separated into the product of a term describing the surface corrugation and another term which accounts for the rotational excitation V͑r,⌰ ͒ϭ͓V 0 ͑ z ͒ϩhV 1 ͑z͒Q͑x,y ͔͓͒1ϩP 2 ͑cos ⌰ ͔͒. ͑5͒…”

“…RID has in the past been quite extensively investigated both theoretically and experimentally on the surfaces of ionic solids. [17][18][19][20][21] Only a few studies have been reported for H 2 and its isotopes on the low index metal surfaces. For example, RID peaks have been clearly resolved for the anisotropic strongly rotationally coupled HD molecules scattered from the reactive Pt͑111͒ 22 and Ni͑001͒ 23 surfaces.…”

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

“…6,7 This attribution is in contrast with early theoretical work, which suggested that collisions of H 2 with the surface would be mostly m j conserving. [9][10][11][12][13] In fact, most scattering calculations [11][12][13][14][15][16] performed on this system made use of the potential form introduced by Wolken, 11-13 which contains no dependence on the H 2 azimuthal angle of orientation ͑thereby forbidding ⌬m j transitions͒. On a historical note, it is of interest that Wolken 11 justified the approximate form of his potential by arguing that the LiF surfaces studied at the time 4,5,17 should be covered by H 2 O, which was later shown to be untrue by Estel et al 18 Other calculations 8,9 made use of a hard corrugated wall potential which did contain a dependence on ͑thus allowing ⌬m j transitions͒, but the electrostatic interaction between the quadrupole moment of H 2 and the ionic lattice was not considered in these calculations.…”

Molecular self-diffraction on a surface: Inversion symmetry changes in scattering of state-selectedND3on graphite (0001)

“…To connect the molecule-surface interaction potential to the inversion symmetry change, the infinite-order sudden approximation, introduced for the scattering of a rigid rotor on a surface by Gerber et ai [19], is used. The scattering operators are written 5/, r =exp[2/77/, r (0,^,0)] ,…”