The strong mutual coupling of and even the opposite change in the key parameters, such as the band gap (E g ) and second-order harmonic generation (SHG), leads to the extreme scarcity in high-performance IR nonlinear optical (NLO) chalcogenides. Herein, we report 8 new sulfides, Na 2 Ba[(Ag x Na 1À x ) 2 Sn 2 S 7 ] (1, x = 0; 1 series, x = 0.1-0.6; Na 2 Ba[(Li 0.58 Na 0.42 ) 2 Sn 2 S 7 ], 1-0.6Li); Na 2 Sr[Cu 2 Sn 2 S 7 ] (2); and Na 2 Ba[Cu 2 Sn 2 S 7 ] (3). We use the structural tolerance factor (t exp I ) to connect the chemical composition, crystal structure, and NLO properties. Guided by these correlations, a better balance between E g and SHG is realized in 1, which exhibits a large E g of 3.42 eV and excellent NLO properties (SHG: 1.5 × AGS; laser-induced damage threshold: 12 × AGS), representing the best performance among the known Hg-or As-free sulfides to date.