We present an efficient algorithm for one- and two-component relativistic exact-decoupling calculations. Spin-orbit coupling is thus taken into account for the evaluation of relativistically transformed (one-electron) Hamiltonian. As the relativistic decoupling transformation has to be evaluated with primitive functions, the construction of the relativistic one-electron Hamiltonian becomes the bottleneck of the whole calculation for large molecules. For the established exact-decoupling protocols, a minimal matrix operation count is established and discussed in detail. Furthermore, we apply our recently developed local DLU scheme [D. Peng and M. Reiher, J. Chem. Phys. 136, 244108 (2012)] to accelerate this step. With our new implementation two-component relativistic density functional calculations can be performed invoking the resolution-of-identity density-fitting approximation and (Abelian as well as non-Abelian) point group symmetry to accelerate both the exact-decoupling and the two-electron part. The capability of our implementation is illustrated at the example of silver clusters with up to 309 atoms, for which the cohesive energy is calculated and extrapolated to the bulk.

We present an efficient algorithm for one- and two-component analytical energy gradients with respect to nuclear displacements in the exact two-component decoupling approach to the one-electron Dirac equation (X2C). Our approach is a generalization of the spin-free ansatz by Cheng and Gauss [J. Chem. Phys. 135, 084114 (2011)], where the perturbed one-electron Hamiltonian is calculated by solving a first-order response equation. Computational costs are drastically reduced by applying the diagonal local approximation to the unitary decoupling transformation (DLU) [D. Peng and M. Reiher, J. Chem. Phys. 136, 244108 (2012)] to the X2C Hamiltonian. The introduced error is found to be almost negligible as the mean absolute error of the optimized structures amounts to only 0.01 pm. Our implementation in TURBOMOLE is also available within the finite nucleus model based on a Gaussian charge distribution. For a X2C/DLU gradient calculation, computational effort scales cubically with the molecular size, while storage increases quadratically. The efficiency is demonstrated in calculations of large silver clusters and organometallic iridium complexes.

Show some metal: the first bimetallic adamantane-like cluster, [{Fe(CO)(3)}(4){SnI}(6)I(4)](2-), was prepared by an ionic-liquid-based synthesis. The valence states of iron and tin were verified based on bond-length considerations, FT-IR and (119)Sn Mössbauer spectroscopy, as well as with DFT calculations.

By reacting Fe(CO)(5) and SnI(4) in the ionic liquids [XIm][NTf(2)] (XIm: 1-ethyl-3-methylimidazolium/EMIm, 1-ethyl-imidazolium/EHIm, 1-propyl-3-methylimidazolium/PMIm; NTf(2): bistrifluoridomethansulfonimide), the compounds [XIm][FeI(CO)(3)(SnI(3))(2)] are obtained as transparent, dark red crystals. According to single-crystal structure analysis, the title compounds crystallize monoclinically and contain the anionic carbonyl complex [FeI(CO)(3)(SnI(3))(2)](-) as well as [EMIm](+), [EHIm](+) or [PMIm](+) cations. The anionic carbonyl is composed of a Sn-Fe-Sn barbell-shaped building unit with Fe-Sn distances of 252.0(1) pm. Herein, tin is coordinated distorted tetrahedrally by iodine; iron is coordinated pseudo-octahedrally by three carbonyl ligands, one iodine atom and two tin atoms. Bonding situation and valence state are investigated in detail for [EMIm][FeI(CO)(3)(SnI(3))(2)] based on bond-lengths considerations, infrared spectroscopy, Mössbauer spectroscopy, density functional theory and DFT-based Mulliken population analysis. Hence, the formal oxidation state of the metal atoms can be concluded to Fe(±0) and Sn(3+).

Despite the relatively small size of molecular bromine and iodine, the physicochemical behavior in different solvents is not yet fully understood, in particular when excited-state properties are sought. In this work, we investigate isolated halogen molecules trapped in clathrate hydrate cages. Relativistic supermolecular calculations reveal that the environment shift to the excitation energies of the (nondegenerate) states 3Πu and 1Πu lie within a spread of 0.05 eV, respectively, suggesting that environment shifts can be estimated with scalar-relativistic treatments. As even scalar-relativistic calculations are problematic for excited-state calculations for clathrates with growing size and basis sets, we have applied the subsystem-based scheme frozen-density embedding, which avoids a supermolecular treatment. This allows for the calculation of excited states for extended clusters with coupled-cluster methods and basis sets of triple-zeta quality with additional diffuse functions mandatory for excited-state properties, as well as a facile treatment at scalar-relativistic exact two-component level of theory for the heavy atoms bromine and iodine. This simple approach yields scalar-relativistic estimates for solvatochromic shifts introduced by the clathrate cages.