First-principles study of boron oxygen hole centers in crystals: Electronic structures and nuclear hyperfine and quadrupole parameters

The electronic structures, nuclear hyperfine coupling constants, and nuclear quadrupole parameters of fundamental boron oxygen hole centers (BOHCs) in zircon (ZrSiO${}_{4}$, $I$4${}_{1}$/amd) and calcite (CaCO${}_{3}$, $R\overline{3}c$) have been investigated using ab initio Hartree--Fock (HF) and various density functional theory (DFT) methods based on the supercell models with all-electron localized basis sets. Both exact HF exchange and appropriate correlation functionals are important in describing the BOHCs, and the parameter-free hybrid method based on Perdew, Burke, and Ernzerhof density functionals (PBE0) turns out to be the best DFT method in reproducing the electron paramagnetic resonance (EPR) data. Our results reveal three distinct types of simple-spin ($S$ = 1/2) [BO${}_{3}$]${}^{2\ensuremath{-}}$ centers in calcite: (i) the classic [BO${}_{3}$]${}^{2\ensuremath{-}}$ radical with the ${D}_{3h}$ symmetry and the unpaired spin equally distributed on the three oxygen atoms (i.e. the O${}_{3}^{5\ensuremath{-}}$ type); (ii) the previously reported [BO${}_{2}$]${}^{0}$ center with the unpaired spin equally distributed on two of the three oxygen atoms (O${}_{2}^{3\ensuremath{-}}$); and (iii) a new variety with \ensuremath{\sim}90% of its unpaired spin localized on one (O${}^{\ensuremath{-}}$) of the three oxygen atoms with a long B-O bond (1.44 \AA{}). Calculations confirm the unusual [BO${}_{4}$]${}^{0}$ center in zircon and show it to arise from a highly distorted configuration with 90% of the unpaired spin on one oxygen atom that has a considerably longer B-O bond (1.68 \AA{}) than its three counterparts (1.45 \AA{}). The calculated magnitudes and directions of ${}^{11}$B and ${}^{17}$O hyperfine coupling constants and nuclear quadrupole constants for the [BO${}_{4}$]${}^{0}$ center in zircon are in excellent agreement with the 15 K EPR experimental data. These BOHCs are all characterized by a small negative spin density on the central B atom arising from spin polarization. Our calculations also demonstrate that the spin densities on BOHCs are affected substantially by crystalline environments, and so periodic boundary treatment, such as the supercell scheme, is a must in accounting for the electronic and spin structures of BOHCs in crystals. These atomistic and electronic models of BOHCs in the crystalline matrices provide new insights into their precursors and counterparts in glasses and other amorphous materials.

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