The current state of understanding of the VDOF complexity in solid-state qubits is further compounded by the recent realization that the energy gaps in the relevant excitation spectra (with the potential to be involved in the operation of the qubit) depend crucially on Wigner-molecule (WM) formation and the strong electron-electron interactions that naturally arise * Constantine.Yannouleas@physics.gatech.edu † Uzi.Landman@physics.gatech.edu in these silicon nanodevices (also found in GaAs 3e hybrid qubits ), due to an interplay between materials parameters and size that yields large values for the Wigner parameter R W > 1; see Sec. III A.