Systematic Approach To Calculate the Band Gap Energy of a Disordered Compound with a Low Symmetry and Large Cell Size via Density Functional Theory

An ab initio calculation based on density functional theory (DFT) was used to verify the disordered structure of a novel oxynitride phosphor host, La4-xCaxSi12O3+xN18-x, with a large unit cell (74 atoms), low level of symmetry (C2), and large band gap (4.45 eV). Several Wyckoff sites in the La4-xCaxSi12O3+xN18-x structure were randomly shared by La/Ca and O/N ions. This type of structure is referred to as either partially occupied or disordered. The adoption of a supercell that is sufficiently large along with an infinite variety of ensemble configurations to simulate such a random distribution in a partially occupied structure would be an option that could achieve a reliable DFT calculation, but this would increase the calculation expenses significantly. We chose 5184 independent unit cell configurations to be used as input model structures for DFT calculations, which is a reduction from a possible total of 20 736 unit cell configurations for C2 symmetry. Instead of calculating the total energy as well as the band gap energy for all 5184 configurations, we pinpointed configurations that would exhibit a band gap that approximated the actual value by employing an elitist nondominated sorting genetic algorithm (NSGA-II) wherein the 5184 configurations were represented mathematically as genomes and the calculated total and band gap energies were represented as objective (fitness) functions. This preliminary screening based on NSGA-II was completed using a generalized gradient approximation (GGA), and thereafter, we executed a hybrid functional calculation (HSE06) for only the most plausible GGA-relaxed configurations with higher band gap energies and lower total energies. Finally, we averaged the HSE06 band gap energy over these selected configurations using the Boltzmann energy distribution and achieved a realistic band gap energy that more closely approximated the experimental measurement.