The structures of ruthenium cluster anions have been investigated using a combination of trapped ion electron diffraction and density functional theory computations in the size range from eight to twenty atoms. In this size range, three different structural motifs are found: Ru8(-)-Ru12(-) have simple cubic structures, Ru13(-)-Ru16(-) form double layered hexagonal structures, and larger clusters form close packed motifs. For Ru17(-), we find hexagonal close packed stacking, whereas octahedral structures occur for Ru18(-)-Ru20(-). Our calculations also predict simple cubic structures for the smaller clusters Ru4(-)-Ru7(-), which were not accessible to electron diffraction measurements.

The effect of hydrogenation on the structure of Ru19 – has been studied using a combination of trapped ion electron diffraction and density functional computations. While the bare Ru19 – cluster has a closed-shell octahedral geometry, hydrogenation of the cluster changes the structure type of the ruthenium core toward an icosahedral motif. The experiments show a gradual structural transition depending on the number of adsorbed hydrogen atoms. Density functional theory computations reveal the driving force behind this process to be the larger hydrogen adsorption energies for the bi-icosahedral structure and predict a corresponding structural rearrangement at around 20 adsorbed hydrogen atoms, which is consistent with the experimental findings. Additionally, the computations provide insight into the hydrogen-binding situation. They show that hydrogen is preferentially atomically bound only to surface Ru atoms. H2 binding is predicted only at high hydrogen loadings.

Time-dependent density functional theory has become state-of-the-art for describing photophysical and photochemical processes in extended materials due to its aordable cost. The inclusion of exact exchange was shown to be essential for the correct description of the long-range asymptotics of electronic interactions and thus a well-balanced description of valence, Rydberg and charge-transfer excitations. Several approaches for an ecient treatment of exact exchange have been established for the ground state, while implementations for excited-state properties are rare. Furthermore, the high computational costs required for excited-state properties in comparison to ground-state computations often hinder large-scale applications on periodic systems with hybrid functional accuracy. We therefore propose two approximate schemes for improving computational eciency for the treatment of exact exchange. Within the auxiliary density matrix method (ADMM), exact exchange is estimated using a relatively small auxiliary basis and the introduced basis-set incompleteness error is compensated by an exchange density functional correction term. Benchmark results for a test set of 35 molecules demonstrate that the mean absolute error introduced by ADMM is smaller than 0.30.2 pm for excited-state bond lengths and in the range of 0.02 -0.070.06 eV for vertical excitation, adiabatic excitation and uorescence energies. Computational timings for

The connection between the random-phase approximation and the ring-coupled-cluster-doubles method bridges the gap between density-functional and wave-function theories and the importance of the random-phase approximation lies in both its broad applicability and this linking role in electronic-structure theory. In this contribution, we present an explicitly correlated approach to the random-phase approximation, based on the direct ring-coupled-cluster-doubles ansatz, which overcomes the problem of slow basis-set convergence, inherent to the random-phase approximation. Benchmark results for a test set of 106 molecules and a selection of 10 organic complexes from the S22 test set demonstrate that convergence to within 99% of the basis-set limit is reached for triple-zeta basis sets for atomisation energies, while quadruple-zeta basis sets are required for interaction energies. Corrections due to single excitations into the complementary auxiliary space reduce the basis-set incompleteness error by one order of magnitude, while contributions due to the coupling of conventional and geminal amplitudes are in general negligible. We find that a non-iterative explicitly correlated correction to first order in perturbation theory exhibits the best ratio of accuracy to computational cost.

Within the framework of density-functional theory, the basis-set convergence of energies obtained from the random-phase approximation to the correlation energy is equally slow as in wavefunction theory, as for example in coupled-cluster or many-body perturbation theory. Fortunately, the slow basis-set convergence of correlation energies obtained in the random-phase approximation can be accelerated in exactly the same manner as in wavefunction theory, namely by using explicitly correlated two-electron basis functions that are functions of the interelectronic distances. This is demonstrated in the present work.