Self-trapped holes (small polarons) in ferroelectric KH₂PO₄ crystals

Density functional theory is used to establish the ground-state structure of the self-trapped hole (STH) in KH₂PO₄ crystals. The STHs in this nonlinear optical material are free small polarons, a fundamental intrinsic point defect. They are produced with ionizing radiation in the low-temperature orthorhombic structure of KH₂PO₄ and are only stable (i.e. long-lived) below approximately 70 K. A large 129-atom cluster, K₁₉H₄₀P₁₄O₅₆, is constructed to model the STH. The ωB97XD functional with the 6-31+G^* basis set is used and geometry optimization is performed. Our results show that two of the oxygen ions in a PO₄ unit relax toward each other and equally share the hole. These two oxygen ions do not initially have close hydrogen neighbors. This equal sharing of the hole is related to the presence of isolated, slightly distorted, PO₄ units and is significantly different from the small-polaron behavior often observed in other oxide crystals where the hole is localized on only one oxygen ion. The computational results provide a detailed description of the lattice relaxation occurring during formation of the STH. Characteristic spectral features of this defect are a larger hyperfine interaction with one ³¹P nucleus and equal, but smaller, hyperfine interactions with two ¹H nuclei. The computed values for these isotropic and anisotropic hyperfine coupling constants are in excellent agreement with results obtained from electron paramagnetic resonance experiments.