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We report results from a fast, efficient, and first-principles full-potentialN$^{th}$-order muffin-tin orbital (FP-NMTO) method combined with vanLeeuwen-Baerends correction to local density exchange-correlation potential. Weshow that more complete and compact basis set is critical in improving theelectronic and structural properties. We exemplify the self-consistent FP-NMTOcalculations on group IV and III-V semiconductors. Notably, predicted bandgaps,lattice constants, and bulk moduli are in good agreement with experiments(e.g., we find for Ge $0.86~e$V, $5.57$~\AA, $75$~GPa vs. measured $0.74~e$V,$5.66$~\AA, $77.2$~GPa). We also showcase its application to the electronicproperties of 2-dimensional $h-$BN and $h-$SiC, again finding good agreementwith experiments.

Simple correction to bandgap in IV and III-V semiconductors: an improved first-principles local density functional theory