Non-centrosymmetric structures designed rationally <i>via</i> a “dimensionality addition” strategy toward the promising nonlinear optical family [A–X][In–Se] (A = K/Ba and Rb/Ba; X = Cl and Br)

Formulating a well-defined strategy for designing non-centrosymmetric (NCS) structures is an urgent requirement but a formidable challenge. Herein, we conducted a comprehensive statistical analysis of tetrahedra-based chalcogenide systems, revealing a significantly high probability for obtaining NCS structures in rigid three-dimensional (3D) systems, where the arrangement of tetrahedral units is minimally influenced by the non-directional spherical coordination of electropositive cations. Based on this premise, a "dimensionality addition" strategy implemented by regulating the A/M ratio (A = electropositive cations and M = tetrahedrally coordinated cations) is established for the first time. Consequently, six 3D NCS salt-inclusion selenides were successfully synthesized, namely, A[A₄Cl][In₁₄Se₂₃] (A = K and Rb), A₂[A₃BaCl][In₁₈Se₃₀] (A = K and Rb), and [K₄Cl][AK_9-10Cl₄][In₂₂Se₃₈] (A = Li and Ba). All these compounds collectively employed separated polycations as "dimension regulators" to facilitate the assembly of [InSe₄] tetrahedra into 3D NCS diamond-like frameworks, enabling promising second-harmonic generation (SHG) responses (0.69-2.10 × AgGaS₂). This study may serve as an instructive guidance for exploring symmetry-dependent materials.