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Hund's First and Second Rules in Spherical Quantum Dots (I) in the Zero-Magnetic Field

We theoretically studied the validity of Hund's first and second rules in the three-dimensionally spherically parabolic quantum dot (3D-SPQD). We extended the unrestricted Hartree–Fock (exUHF) approach in order to determine the ground state while conserving the expectation values of the total orbital angular momentum <\hatL2> and its z component <\hatLz> during the scf procedure. We applied this exUHF method to a GaAs 3D-SPQD and obtained the ground-state energy spectra. Our calculation reveals that, among those states having the largest spin multiplicities, the state giving the largest value of <\hatL2> is energetically more stable than the others having a smaller value of <\hatL2>; that is the spin filling in the 3D-SPQD obeys Hund's first and second rules.