GaN bandgap bias caused by semi-core treatment in pseudopotentials analyzed by the diffusion Monte Carlo method

This study investigates how the prediction of the gallium nitride (GaN) bandgap is affected by treating semi-core d-electrons as either valence or core states in the pseudopotentials, which correspond to small-core and large-core approximations, respectively. To distinguish the effect of semi-core treatment from another bandgap problem recognized in density functional theory (DFT), that is, the underestimation related to the self-interaction problem, we perform diffusion Monte Carlo (DMC) evaluations under the fixed-node approximation and the optical gap scheme (where the evaluation uses N-electron many-body wavefunctions). A comparison to experimental measurements of bandgap energies indicates that DMC predictions are overestimated, whereas DFT simulations, which are used as a guiding function (DFT → DMC), are typically underestimated. This agrees with the trend reported in previous DMC studies on bandgap estimates. The large-core approximation results in a greater overestimation than the small-core treatment in both DFT and DMC. The bias in the overestimation is ∼30% for the DFT → DMC operation. Several possible causes of this bias are considered, such as pd-hybridization, core-polarization, and electronic screening effects. However, although these factors could qualitatively account for the overestimation caused by the large-core treatment, the estimated magnitude of the bias is too small to explain the evaluated difference between small-core and large-core approximations of the bandgap.