Density　functional　theory　(DFT)　calculations　have　been　performed　on　electronic　structures　of　11　middle-infrared　(mid-IR)　nonlinear　optical　quaternary　sulfides:　Ln4GaSbS9　(Ln=Ce-Nd,　Sm,　Gd-Tm,　Lu).　Our　results　show　that　Ln4GaSbS9　are　indirect　gap　semiconductors　with　a　slight　band　gap　increase　from　Ce　to　Lu.　Their　linear　optical　properties,　including　refractive　index,　absorption　coefficient　and　energy　loss　function,　as　well　as　the　nonlinear　optical　coefficients　including　static　d31,　d32,　d33　and　dynamic　d　32,　are　calculated.　More　importantly,　the　strong　SHG　response　of　Ln4GaSbS9　can　be　attributed　to　the　electronic　transitions　from　S　3p　states　in　valence　bands　(VB)　to　Sb-S　and　Ln-S　antibonding　states　(CB).　©　2012　Elsevier　Inc.