Contributions of Correlated Acentric Atomic Displacements to the Nonlinear Second Harmonic Generation and Response

Group theory and ab initio electronic structure calculations are combined to formulate a general protocol called "SAFOR" to understand and predict how to improve the second harmonic generation (SHG) response in acentric nonlinear optical crystals. Using the prototypical SHG borate β-BaB₂O₄, we show how the SHG d-tensor can be formulated from mode effective d_ij coefficients obtained as a linear combination of symmetry-adapted displacement patterns that transform as irreducible representations of a centrosymmetric parent structure. Since this protocol does not require any constraints on the crystal topology or anionic moieties in the structure, we suggest it constitutes a powerful tool to understand and design new SHG compounds through atomic-structure governing principles. (Figure Presented).