Interpretation of the nonlinear optical susceptibility of borate crystals from first principles

First-principles calculations of the second-order optical susceptibility are successfully performed for practical borate crystals, namely, LiB₃O₅, CsB₃O₅ (CBO), and BaB₂O₄, using the linearized augmented plane-wave band method. Spectral and spatial decomposition are proposed to elucidate the role of different ions and different electron states. It is shown, with CBO as an example, that transitions from the high-lying part of occupied O $2p$ bands, as the initial states, to the conduction band states around the three-coordinated B site dominate in the nonlinear response.