Structural and electronic properties of rhodium surfaces: an ab initio approach

Structural and electronic properties of the low-index surfaces of rhodium have been investigated via fully self-consistent ab initio local density functional (LDF) calculations. Our technique is based on ultrasoft pseudopotentials, a preconditioned conjugate-gradient technique for the calculation of the electronic ground-state and of the Hellmann-Feynman forces and stresses, and on a conjugate-gradient technique for the optimization of the atomic structure. The calcualtions were performed for five- to ten-layer slabs in symmetric and asymmetric geometries, allowing for the relaxation of up to seven surface layers. For the (111), (100), and (110) surfaces an inward relaxation of the top layer by −1.7±0.2, −3.8±0.2, and −9.8±0.6% is predicted, the surface energies increase parallel to the inward relaxation. The analysis of the electronic structure shows that the inward relaxation is caused by the de-population at the surface of anti-bonding states at the top of the d-band. We also present a detailed analysis of electronic surface states.