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We have calculated the first hyperpolarizabilities of four squaric acid homologue molecules: 3,4-dithiohydroxy-3-cyclobutene-1,2-dione (OSSQ), 3,4-dithiohydroxy-3-cyclobutene-1, 2-dithione (SSSQ), 3,4-dithiohydroxy-3-cyclobutene-1,2-diselenone (SeSSQ) and