Relativistic effects on the energetic stability of $$\hbox {Pb}_5$$ clusters

Abstract

In this work, we study isomers of small lead clusters with five atoms, $$\hbox {Pb}_5$$ , at different levels of approximation namely Scalar-Relativistic (SR), Scalar-Relativistic plus Spin–Orbit coupling interaction (SR + SO) and four-component Dirac–Hartree–Fock (4c-DHF), in order to analyze the effects of relativity in these heavy molecular systems. The exploration of potential energy surface (PES) with a genetic algorithm produces four possible equilibrium structures, and we find that when Relativity is included at a major level in calculations, the global minimum energy structure changes from S4 isomer with $$\hbox {D}_{3\mathrm{h}}$$ symmetry at SR level to S1 isomer with $$\hbox {C}_2$$ symmetry at 4c-DHF level; this change is related to modifications in the electronic structure and geometric parameters. We explain this significant result using two methodologies in order to analyze the electronic structure and strength of chemical bonds, like energy decomposition analysis (EDA) and Quantum Theory Atoms In Molecules (QTAIM). On the one hand, in the framework of EDA, results at SR + SO level show significant differences on the steric and orbital interactions compared with SR ones, with which the S1 isomer is more stable than S4; this means that SO effects stabilize the interactions on S1 isomer more than S4. The HOMO–LUMO gap also shows a drastic reduction due to the SO effects on S4 isomer, while for the other systems remains unchanged. This result can be associated with the lower stability of S4 isomer with respect to the others when Relativity is included at a major level. On the other hand, in the framework of QTAIM, calculations with SR + SO scheme show the formation of two new critical points compared with SR for S1 isomer, which is reflected in a greater stability of this system.