Quasiparticle self-consistent GW calculations of the band structures and related effective mass parameters are carried out for bulk, monolayer and bilayer MoS2. Including excitonic effects within the Mott-Wannier theory, quantitative agreement is obtained between the A, B excitons, measured by absorption (Phys. Rev. Lett. 105,136805 (2010)), and the calculated exciton gap energies at K. The A-B splitting arises from the valence band splitting which in the monolayer is entirely due to spin-orbit coupling and leads to spin-split states, while in the bilayer it is a combined effect of interlayer and spin-orbit coupling.

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The development of a method for calculating the frequency dependent second harmonic generation coefficient of insulators and semiconductors based on the self-consistent linearized muffin-tin orbitals (LMTO) band structure method is reported. The calculations are at the independent particle level and are based on the formulation introduced by Aversa and Sipe (1995). The terms are re-arranged in such a way as to exhibit explicitly all required symmetries including the Kleinman symmetry in the static limit. Computational details and convergence tests are presented. The calculated frequency dependent χ (2) (−2ω, ω, ω) for the zinc-blende materials GaAs, GaP and wurtzite GaN and AlN are found to be in excellent agreement with that obtained by other first-principles calculations when corrections to the local density approximation (LDA) are implemented in the same manner, namely, using the "scissors" approach. Similar agreement is found for the static values of χ (2) for zincblende GaN, AlN, BN and SiC. The strict validity of the usual "scissors" operator implementation is, however, questioned. We show that better agreement with experiment is obtained when the corrections to the low lying conduction bands are applied at the level of the Hamiltonian, which guarantees that eigenvectors are consistent with the eigenvalues. New results are presented for the frequency dependent χ (2) (−2ω, ω, ω) for 3C-SiC. The approach is found to be very efficient and flexible which indicates that it will be useful for a wide variety of material systems including those with many atoms in the unit cell.