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An ab initio calculation based on density functional theory (DFT) was used to verify the disordered structure of a novel oxynitride phosphor host, La 4- x  Ca  x  Si 12 O 3+ x  N 18- x  , with a large unit cell (74 atoms), low level of symmetry ( C 2), and large band gap (4.45 eV). Several Wyckoff sites in the La 4- x  Ca  x  Si 12 O 3+ x  N 18- 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 C 2 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.

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