Efficient Calculation of the Rotational <b>g</b> Tensor from Auxiliary Density Functional Theory

The computation of the rotational <b>g</b> tensor with the recently developed auxiliary density functional theory (ADFT) gauge including atomic orbital (GIAO) methodology is presented. For the rotational <b>g</b> tensor, the calculation of the magnetizability tensor represents the most demanding computational task. With the ADFT-GIAO methodology, the CPU time for the magnetizability tensor calculation can be dramatically reduced. Therefore, it seems most desirable to employ the ADFT-GIAO methodology also for the computation of the rotational <b>g</b> tensor. In this work, the quality of rotational <b>g</b> tensors obtained with the ADFT-GIAO methodology is compared with available experimental data as well as with other theoretical results at the Hartree–Fock and coupled-cluster level of theory. It is found that the agreement between the ADFT-GIAO results and the experiment is good. Furthermore, we also show that the ADFT-GIAO <b>g</b> tensor calculation is applicable to large systems like carbon nanotube models containing hundreds of atom and thousands of basis functions

Nature of Valence Transition and Spin Moment in Ag_<i>n</i>V⁺ Clusters

Evolution in the atomic structure, bonding characteristics, stability, and the spin magnetic moment of neutral and cationic Ag_<i>n</i>V clusters has been investigated using first-principles density functional approach with gradient corrected functional. It is shown that at small sizes, the V 4s states hybridize with Ag states to form 1S and 1P like superatomic orbitals, whereas the 3d states are localized on V giving the V atom an effective valence of 1 or 2. Starting from Ag₈V⁺, the V 3d states begin to participate in the bonding by hybridizing with the nearly free electron gas to form 1D superatomic orbitals increasing the V atom effective valence toward 5. For the cationic clusters, this changing valence results in three shell closures that lead to stable species. These occur for cationic clusters containing 5, 7, and 14 Ag atoms. The first two stable species correspond to filled 1S and 1P shells in two and three dimensions with a valence of 2 for V, whereas the closure at 14 Ag atoms correspond to filled 1S, 1P, and 1D shells with V site exhibiting a valence of 5. The transition from filled 1S and 1P shells to filled 1S, 1P, and 1D shells is confirmed by a quenching of the spin magnetic moment. The theoretical findings are consistent with the observed drops in intensity in the mass spectrum of Ag_<i>n</i>V⁺ clusters after 5, 7, and 14 Ag atoms