A difference method with semi-analytical approach for achieving accuracy in optical gaps of 2D materials using exciton model in fractional space

A semi-analytical approach for the difference method using numerically calculated G0W0 band gaps and analytically calculated exciton binding energies based on the fractional Coulomb potential model is proposed to calculate optical gaps of 46 2D materials ranging from ultra-violet to infrared region. The suggested methodology is compared with difference methods of a similar hybrid approach, utilizing conventional exciton models based on Wannier-Mott theory to achieve a significant reduction in the average relative mean square error of optical gaps, up to one-third, benchmarked with a fully numerical approach, employing G0W0 band gaps and the state-of-the-art Bethe-Salpeter equation for binding energy calculation.