Insight into stabilities and magnetism of EuGen (n = 1–20) nanoclusters: an assessment of electronic aromaticity

Abstract

The present study reports insight into electronic structure and stability of EuGen (n = 1–20) nanoclusters under the framework of density functional theory within the generalized gradient approximation. To understand the stabilities and the magnetic behavior of endohedral nanoclusters with the structural growth, different parameters, such as, average binding energies, fragmentation energies, energy difference between highest occupied and lowest unoccupied molecular orbitals, vertical ionization potential and adiabatic ionization potential are studied. It is found that EuGe16 in octet spin state is the most stable both thermodynamically and chemically. Furthermore, the study of natural bond orbital and electron localization function indicates that the charge transfer in global ground state EuGe16 is from Gen cage to Eu atom. Calculated density of states and projected density of states show the hybridization between 5d, 6 s, and 6p orbitals are mainly responsible for the stability, and 4f7 is responsible for the high magnetic moment of the EuGe16 cluster. Single-electron orbital analysis of the upper 34 electrons of EuGe16 with the sequence 2S21G162P42D22P22D8 can be split as 18σ and 16π electrons. These 18σ electrons follow Hirsch’s 2(n + 1)2 rule for n = 2. The remaining 16π electrons do not directly follow Hückel (4n + 2) π rule. After splitting 16 electrons as 6π + 10π for n = 1 and 2, respectively, can follow Hückel’s rule. So, by applying the mixed π-σ mixed electron counting rule, the stability of the cluster can be explained. Further, calculated nucleus-independent chemical shift also supports the existence of the Hückel (4n + 2) π-electron rule. Further, infrared and Raman spectra confirm that EuGe16 is a symmetric spherical shape with fewer vibrational modes than the other ground-state structures.