A Calculation of Atomic Forces and Structural Relaxation
for the Pd(001) and Rh(001) Surfaces

I. G. Batyrev*, Ya. A. Leiro**, K. Kh. Li***, V. R. Li***, and T. Oguchi****

* Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, Leninskii pr. 29, Moscow, 117912 Russia
** Faculty of Applied Physics, University of Turku, Turku, Finland
*** Faculty of Chemistry, Wonquang University, Iksan, Korea
**** Faculty of Materials Science, Hiroshima University, Hiroshima, Japan

Received April 12, 1996

Abstract—The method of a linear combination of augmented plane waves (APW), which is based on ab initio
molecular dynamics ideas put forth by Car and Parinello, was used to calculate the electronic structure and
atomic forces for three- and five-layer Rh(001) and Pd(001) films. The Hellmann–Feynman atomic forces cal-
culated with Pulay corrections were used to optimize the structure of the surface of the films. The interatomic
distance in the direction normal to film surfaces was shortened in the surface layer in comparison with the bulk.
The shortening values in percent of the equilibrium bulk lattice parameters were 1.23 and 1.11% (Rh) and 1.35
and 1.18% (Pd) for three- and five-layer (001) films, respectively. The surface atomic core levels, which were
calculated in the APW approximation taking into account the s, p, and d electrons of rhodium and palladium,
were close to those determined from the X-ray photoelectron spectra. The calculations show that the Rh(001)
and Pd(001) surfaces are nonmagnetic, which is at variance with the earlier suggestions of Rh surface ferro-
magnetism.

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