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It is shown that in large symmetrical nanoparticles additional quantumnumbers are required to label unambiguously symmetry adapted linearcombinations of the wave functions. It is obtained that the labels ofirreducible representations (IRs) of intermediate subgroups (between the wholesymmetry group and local subgroup) can be used for complete classification ofstates in the case of repeating IRs. The examples of Oh and Ih groups areconsidered and the connection of additional quantum numbers with localinteractions is discussed

Additional Quantum Numbers for Electron Orbitals of Nanoparticles