Spin-orbit effects in the photoabsorption of WAu12 and MoAu12: A relativistic time dependent density functional study

The electronic structure of both WAu12 and MoAu12 has been calculated at the density functional theory (DFT) level, employing the zero order regular approximation at the scalar relativistic level and including a spin-orbit coupling. The effect of the inclusion of the spin-orbit coupling is discussed, and the differences assigned to the nature of the encaged atom (W or Mo) are identified. Then, the excitation spectra of both clusters are calculated at the time-dependent DFT level, also in this case at both scalar relativistic and spin-orbit levels. The inclusion of spin-orbit coupling is mandatory for an accurate description in the low energy region. At higher energy, where the density of states is higher, the convoluted intensity can be properly described already at the scalar relativistic level. The consequences of the spin-orbit coupling on the excitation spectrum of the clusters indicate that while in WAu12 the lowest excitations are essentially shifted in energy with respect to the scalar relativistic results, in MoAu12, a dramatic splitting in many lines is actually predicted, revealing a quite different behavior of the two clusters.