Fig. 3.

Calculated electronic states and spin polarization. a Spin polarization obtained from DFT simulations in a Mulliken population analysis. The standard junction (all peripheral carbons bonded to H) shows spontaneous spin localization in both PC and ZZ regions, revealing the apparition of radical states. b Schema of the spontaneous spin polarization when one of the two electrons in the HO level gets promoted to the LU level to form two separated, exchange coupled spin-1/2 systems (Type 3 junction). This process is energetically favored when the reduction in Coulomb energy U_HH − U_HL plus exchange energy J exceeds the level separation δ, i.e., δ + U_HL − J < U_HH. c Single-particle TB wave functions (HO/LU) for Type 3 junction. d Same as in a but now adding a H atom to an external carbon in either the ZZ (Type 1) or PC (Type 2). The passivation with H removes the corresponding radical state and, hence, its spin-polarization. e Sketch of the spin-1/2 Kondo state generated with a single radical (Type 1 and 2 junctions). f Single-particle TB wave functions (SO) for Type 1 and Type 2 junctions. Red-green colors represent the positive-negative phase