Density　functional　theory　(DFT)　calculations　have　been　performed　on　electronic　structures　of　11　middle-infrared　(mid-IR)　nonlinear　optical　quaternary　sulfides:　Ln　4GaSbS　9　(Ln=Ce-Nd,　Sm,　Gd-Tm,　Lu).　Our　results　show　that　Ln　4GaSbS　9　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　d　31,　d　32,　d　33　and　dynamic　d　32,　are　calculated.　More　importantly,　the　strong　SHG　response　of　Ln　4GaSbS　9　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.