Franck Condon shift assessment in 2D MoS 2 .

Optical spectroscopy (OS) techniques are often coupled with first-principles density functional theoretical (DFT) calculations for determining the precise influence of defects on the electronic and structural properties of two-dimensional (2D) transition metal dichalcogenides. Such calculations are carried out presuming there is little or no effect of vibrational transitions on the observed electronic spectrum. However, if the effect of change in vibrational energy (Franck Condon (FC) shift) associated with such a transition is large, it could possibly lead to a different origin for the observed peak. One such instance is the attribution of the 0.75 eV cathodoluminescence peak by Fabbri et al (2016 Nat. Commun. 7 13044) to an optical transition from an S vacancy level in the band gap, under the assumption that the FC shift is negligible. Here, by first principles constrained DFT calculations using hybrid HSE06 functional we show that this combined prediction of OS and DFT calculations is valid for 2D MoS2 since the FC shift associated with electronic transitions from a sulfur vacancy is indeed small ~28 meV. Based on our calculations we conclude that it is reasonable to make a direct connection between DFT calculations and optical spectroscopy techniques in this material, hence, establishing a one to one relation between defect related emission bands and electronic transitions from the defect levels.