Open-shell spherical aromaticity: The 2N2 + 2N + 1 (with S = N + 1/2) rule

4N Baird's rule represented the extension of Hückel's 4N + 2 rule to triplet state systems. In this work we extend the 2(N + 1)2 Hirsch rule for spherical aromatic species to open-shell spherical compounds and we provide evidence that those spherical species having a same-spin half-filled last energy level with the rest of the levels being fully-filled, i.e., those having 2N2 + 2N + 1 electrons and S = N +1/2 , are aromaticWe thank the Spanish MICINN (CTQ2008-03077/BQU, CTQ2008-06532/BQU, CTQ2011-23156, Ramon y Cajal contract), the Catalan DIUE (2009SGR637, 2009SGR528, ICREA Academia 2009 prize), CESCA and BS