Relativistic Time-Dependent Density Functional Theory and Excited States Calculations for the Zinc Dimer

I present a time-dependent density functional study of the 20 low-lying excited states as well the ground states of the zinc dimer Z n 2 , analyze its spectrum obtained from all electrons calculations performed using time-depended density functional with a relativistic 4-component and relativistic spin-free Hamiltonian as implemented in Dirac-Package, and show a comparison of the results obtained from different well-known and newly developed density functional approximations, a comparison with the literature and experimental values as far as available. The results are very encouraging, especially for the lowest excited states of this dimer. However, the results show that long-range corrected functionals such as CAMB3LYP gives the correct asymptotic behavior for the higher states, and for which the best result is obtained. A comparable result is obtained from PBE0 functional. Spin-free Hamiltonian is shown to be very efficient for relativistic systems such as Zn2. 1. Introduction Zinc dimer Z n 2 is the first member of the group 12 (IIB) ( Z n 2 , C d 2 , H g 2 , and C n 2 ) and has a representative character of these dimers. The interest in the dimers of the group IIB ( 1 2 ) is in part due to the possibility of laser applications in analogy with the rare gas dimers. A second point is the importance of the metallic complexes similar to the transition metal complexes [1–4] and some important application like the solar cell and renewable energy [5, 6] as well as electric battery for new cars technology [7, 8]. Z n 2 , C d 2 , and H g 2 are exciter with a shallow, predominantly Van der Waals ground state and low-lying covalent bound excited states. They are also interesting from a theoretical point of view due to the different character of the ground and excited states and consequently the different methodological demands for an accurate theoretical description of the spectrum. The dimer of group 12 has been studied both experimentally and theoretically. Relevant reviews have been provided by Morse [9] and more recently by Koperski [10, 11]. The covalent contributions to the ground state bonding in the group 12 dimers have been investigated in [12], it was concluded that the bond is a mixture of 3/4 Van der Waals and 1/4 covalent interactions. Bucinisky et al. [13] provides spectroscopic constants using the coupled cluster method (CCSD(T)) and different level of the theory 4-component relativistic Hamiltonian, using Dirac-Coulomb Hamiltonian, relativistic spin-free Hamiltonian and nonrelativistic (NR) Hamiltonian. Furthermore, they investigated the