Crystal structure of the lead bromo-borate Pb₂[B ₅O₉]Br from precision single-crystal X-ray diffraction data and the problem of optical nonlinearity of hilgardites

The structural features responsible for the high nonlinear optical activity of crystals of the hilgardite-like anhydrous bromo-borate Pb₂[B ₅O₉]Br (space group Pnn2) are analyzed with the use of data obtained from two (precision and conventional) single-crystal X-ray diffraction experiments. The electron-density peaks associated with the stereochemically active lone electron pair are located in free space at two equally probable positions in the vicinity of the Pb(2) atom on the side of the two most distant atoms, Br(1) and Br(2). The stereochemical activity of two nonequivalent lead atoms in the crystal structure increases upon changing over from the Pb(1) atom to the Pb(2) atom. This is in agreement with the behavior of the lone electron pairs in the hilgardite-like hydrated borate Na _0.5Pb₂[B₅O₉](OH)_1.5 • 0.5H₂O and another nonlinear optical borate, namely, Pb ₂[B₄O₅(OH)₄](OH)₂ • H₂O, which is related to the compound BiB₃O₆. The most pronounced nonlinear optical properties of the lead bromo-borate Pb₂[B₅O₉]Br as compared to other orthorhombic hilgardites and lead borates are associated with the presence of highly polarized Pb-Br bonds. In this case, the electron density of the lone electron pair of the Pb(2) atom enhances the polarization effect.