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In order to shed light on the second harmonic generation (SHG) of new 2-Dsystems, first principles methods are used to calculate the second ordersusceptibility \chi(2) for different types of layered alloys such as monolayersof transition metal dichalcogenide (TMD) alloys, TMD Haeckelite alloys,nanotubes of TMD alloys, hexagonal boron nitride (h-BN) systems which includeBxNyCz alloys, BN and BNC2 nanotubes, BxNxCy Haeckelites and BN Schwarzites(porous BN). It is found that the tungsten based alloys possess higher \chi(2)than Mo based at high photon energies, but at low energies, one type of MoSSedominates. The hypothetical TMD Haeckelites NbSSe and Nb0.5Ta0.5S2 reveal thehighest \chi(2) of all the calculated structures. Zigzag TMD alloy nanotubesshow higher \chi(2) as the diameter is reduced and approximate to the monolayerfor big diameters. BNC alloys exhibit a higher \chi(2) than the h-BN monolayerand are comparable to TMD alloys, except for one case which doubles itsintensity. The BN tubes show an increase of \chi(2) as the diameter decreases,similarly to the TMD nanotubes. BxNxCy Haeckelites possess a very high \chi(2)and may shed light on the role of extended defects in nonlinear opticalproperties. One of the BN Schwarzites exhibits a higher \chi(2) than alreadyknown 3-D materials.

First principles second harmonic generation of transition metal  dichalcogenides and boron nitride alloys: from monolayers and nanotubes to  Haeckelites and Schwarzites