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Second Harmonic Generation (SHG) of single-layer monochalcogenides, such asGaSe and InSe, has been recently reported [2D Mater. 5 (2018) 025019; J. Am.Chem. Soc. 2015, 137, 79947997] to be extremely strong with respect to bulk andmultilayer forms. To clarify the origin of this strong SHG signal, we performfirst-principles real-time simulations of linear and non-linear opticalproperties of these two-dimensional semiconducting materials. The simulations,based on ab-initio many-body theory, accurately treat the electron-holecorrelation and capture excitonic effects that are deemed important tocorrectly predict the optical properties of such systems. We find indeed that,as observed for other 2D systems, the SHG intensity is redistributed atexcitonic resonances. The obtained theoretical SHG intensity is an order ofmagnitude smaller than that reported at the experimental level. This result isin substantial agreement with previously published simulations which neglectedthe electron-hole correlation, demonstrating that many-body interactions arenot at the origin of the strong SHG measured. We then show that theexperimental data can be reconciled with the theoretical prediction when asingle layer model, rather than a bulk one, is used to extract the SHGcoefficient from the experimental data.

How strong is the Second Harmonic Generation in single-layer monochalcogenides? A response from first-principles real-time simulations