The π-electrons in benzene, the quintessential aromatic molecule, were previously shown to be distortive, i.e., they prefer localized double bonds alternating with single bonds. It is the σ-electrons that force the double bonds to delocalize, leading to a regular, D6h geometry. Herein, we computationally investigate the double-bond localizing or delocalizing propensities of σ- and π-electrons in the archetypal all-metal aromatic cluster Al4 2- and its second- and fourth-period analogs B4 2- and Ga4 2-, using Kohn-Sham molecular orbital (MO) theory at BP86/TZ2P in combination with quantitative bond energy decomposition analyses (EDA). We compare the three all-metal aromatic clusters with the structurally related organic species C4H 4 2+, C4H4, and C4H 4 2-. Our analyses reveal that the π-electrons in the group-13 M4 2- molecules have a weak preference for localizing the double bonds. Instead, the σ-electrons enforce the regular D4h equilibrium geometry with delocalized double bonds ; We thank the following organizations for financial support: the HPC-Europa2 Transnational Access program of the European Union, the Netherlands Organization for Scientific Research (NWO), the Ministerio de Ciencia e Innovacion (MICINN, project numbers CTQ2008-03077/BQU, CTQ200806532/BQU and CTQ2011-23156/BQU), the Catalan Departament d'Innovacio , Universitats i Empresa (DIUE, project number 2009SGR637) and the National Research School Combination - Catalysis (NRSC-C). J. P. thanks the MICINN for the Ramon y Cajal contract. Support for the research of M. S. was received through the ICREA Academia 2009 prize for excellence in research funded by the DIUE of the Generalitat de Catalunya