Comparison between the special displacement method and quasi-degenerate perturbation theory for calculating phonon-assisted optical properties

The ability to model phonon-assisted optical processes is important to correctly capture the optical properties of indirect- and quasidirect-gap semiconductors and insulators. One significant limitation of the standard textbook theory of phonon-assisted absorption is that it exhibits a nonphysical divergence at the onset of direct transitions. Recently, two first-principles methods have been put forth to overcome this limitation and compute phonon-assisted optical absorption from first principles. The first approach, called the special displacement method, constructs a supercell with a special set of atomic displacements that represent an optimal single-point sampling of the quantum nuclear wavefunctions for computing observables. The second approach, called quasi-degenerate perturbation theory, generalizes the standard textbook theory to the case of quasi-degenerate optical transitions. While both methods have been shown to provide reliable optical spectra, they have not been compared directly with each other. Here we perform such a comparison for a set of semiconductors, and discuss the relative strengths and limitations of each method.