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　3,4-dithiohydroxy-3-cyclobutene-1,2-　ditellurone　(TeSSQ).　The　correlation　effect　was　investigated　at　the　second-order　Møller-Plesset　(MP2)　perturbation　and　density　functional　theory　(DFT)　levels.　The　frequency　dispersion　and　solvent　effect　were　considered　to　compare　the　theoretical　values　with　the　experimental　observations.　Based　on　all　of　these　studies,　it　is　worthy　to　point　out　that　the　heavy　atom　effect　discovered　for　furan　homologues　is　an　influence　on　the　first　hyperpolarizabilities　of　squaric　acid　homologues.