We present a new implementation of the cluster expansion formalism. The new code, UNiversal CLuster Expansion (UNCLE), consolidates recent advances in the methodology and leverages one new development in the formalism itself. As a core goal, the package reduces the need for user intervention, automating the method to reduce human error and judgment. The package extends standard cluster expansion formalism to the more complicated cases of ternary compounds, as well as surfaces, including adsorption and inequivalent sites.

The detailed knowledge of a system's ground state is the most important prerequisite to understand its physical properties. We have extended the cluster-expansion formalism to apply it to adsorbate systems with an in-principle arbitrary number of adsorbate sites. The formalism will be applied to a system where a number of different adsorbate sites are occupied already at T = 0 K, H on the Ir͑100͒-͑5 ϫ 1͒-H surface. It will be shown that our predictions are in quantitative agreement with the experiment.

The adsorption of hydrogen on the metastable, unreconstructed Ir͑100͒-͑1 ϫ 1͒ surface is investigated by density functional theory ͑DFT͒, quantitative low-energy diffraction ͑LEED͒, and thermal desorption spectrometry ͑TDS͒ complemented by scanning tunneling microscopy ͑STM͒. The bridge site is unequivocally identified as the adsorption site, rather unusual for metallic fcc͑100͒ surfaces. There is excellent quantitative agreement between calculated and experimentally determined structural parameters both for the clean surface and the adsorbate covered surface. Given the uncertainty of DFT to reproduce absolute energies there is also good agreement with the measured adsorption energy ͑460 meV/atom͒. Additionally, theoretical vibrational and electronic properties are provided without, however, related experiments being available.

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The adsorption of hydrogen on the stable state of the Ir͑100͒ surface, the quasihexagonally reconstructed phase Ir͑100͒-͑5 ϫ 1͒-hex, was investigated by density functional theory ͑DFT͒ for different coverages and zero temperature. It appears that the adsorbate induces significant structural substrate modifications which are typical for the adsorption site͑s͒ and are due to a complex interaction between adsorbate and substrate. The system's energetics, as well as the structure of the adsorbate and substrate, are provided for different coverages at which the mirror symmetry of the clean surface is either broken or saved. The total energy per H atom decreases with coverage. So, there is no island formation but always a homogeneous phase accessible by experiment. The structure of the substrate-which can be determined with high precision by experimental methods as low-energy electron diffraction-can be used by DFT as an identifier for the actual adsorbate coverage, and the corresponding adsorption sites can be determined by the usual energy minimization procedure.