First-principles calculations

First-principles calculation was performed by CASTEP³⁷, a plane-wave pseudopotential total energy package based on density functional theory (DFT)^38,39. The functionals developed by Perdew, Burke, and Ernzerhof (PBE)⁴⁰ in generalized gradient approximation (GGA)⁴¹ form were adopted to model the exchange-correlation terms in Hamiltonian. The optimized ultrasoft pseudopential⁴² were used to model the effective interaction between the valence electrons and atom cores, which allow us to use a small plane basis set without compromising the accuracy required by the calculation. High kinetic energy cutoff of 300 eV and Monkhorst-pack⁴³ k-point mesh spanning <0.03 Å⁻¹ in the Brillouin zone were chosen.

The theoretical cell parameters at various pressures were calculated by geometry optimization with both cell parameters and atomic position relaxed under different hydrostatic pressures, in which the Broyden–Fletcher–Goldfarb–Shanno⁴⁴ minimization scheme was used. The convergence criteria for energy, maximum force, maximum stress and maximum displacement were set as 10⁻⁵ eV/atom, 0.03 eV/angstrom, 0.05 GPa, and 0.001 Å, respectively. The compressibilities based on the theoretical cell parameters were also fitted by the PASCal software³³. The constituent atoms in LiBO₂ are very light and their atomic scattering factor is very low, especially for lithium. The structural modification induced by pressure cannot be accurately determined by experiments only (see the experimentally refined CIF files in SI). The variation of atomic positions was determined by first-principles geometry optimization with the cell parameters fixed at the experimental values. For the electronic band structure calculation of LiBO₂ the hybridized PBE0 functionals⁴⁵ were adopted. Our previous studies have demonstrated that this type of functionals can accurately predict the band gaps of UV and deep-UV borates^46,47. Raman and infared spectra were calculated by linear response method⁴⁸. In band gap prediction and Raman/infrared spectrum calculation, norm-conserving pseudopotential⁴⁹ and kinetic energy cutoff of 900 eV were used.