{'fraction_non_alphanumeric': 0.017391304347826087, 'fraction_numerical': 0.0006688963210702341, 'mean_word_length': 5.590308370044053, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
First-principles electronic structure calculations for incommensurately modulated calaverite

Fully relativistic first-principles electronic structure calculations of both the average structure and a supercell approximation of silver-free incommensurately modulated calaverite (AuTe2) are presented. The differences between the results of both calculations are relatively small for the occupation numbers and the density of states, but quite dramatic for the shape of the Fermi surface. From the occupation numbers it is concluded that a previously proposed idea for explaining the modulation, based on mixed valencies for the gold atoms, is probably not applicable. The calculated Fermi surface of the average structure shows that the modulation cannot be understood in terms of Fermi-surface nesting either. The density of states in the supercell approximation compares very favourably with recently obtained X-ray photoelectron spectroscopy data. A rigid-potential calculation shows that the integral of the one-electron valence energies for the supercell is substantially more negative than the corresponding energy for the average structure, while the electrostatic energy difference has the opposite sign but is much smaller. This provides a qualitative indication of the electronic instability of the average structure with respect to the modulation of the supercell. Finally the authors conclude that Te s-like states a (Te p-Au d)-like complex dominate the energetics of the modulation.