Comparison of four basis sets on calculating exciton states in a suspended monolayer MoS2 using a variationally optimized diagonalization method

Abstract

Recent studies on excitons in two-dimensional (2D) materials have been widely calculated using different basis sets. Especially, the accuracy of the basis sets is in demand. Using a variationally optimized diagonalization method, I compare the results of the A exciton state calculations in a suspended monolayer MoS2 obtained using four basis sets: the basis sets of the orthogonal Laguerre, nonorthogonal Laguerre, harmonic oscillator and hydrogen atom. The best accuracies of eigenenergies are obtained by using the orthogonal and nonorthogonal basis sets, while the Hamiltonian matrix element based on the nonorthogonal Laguerre basis set has the simpler form. The eigenenergies calculated by the basis set of hydrogen atom exist the largest discrepancy, thus it is not suitable for calculating the exciton states in 2D materials. Based on these findings, the orthogonal and nonorthogonal basis sets are the best choice in calculating highly accurate exciton states in 2D materials.