Improved ab initio calculation of surface second-harmonic generation from Si(111)(1$\times$1):H

We carry out an improved ab initio calculation of surface second-harmonic generation (SSHG) from theSi(111)(1$\times$1):H surface. This calculation includes three new features in one formulation: (i) the scissorscorrection, (ii) the contribution of the nonlocal part of the pseudopotentials, and (iii) the inclusion of a cutfunction to extract the surface response, all within the independent particle approximation. We apply theseimprovements on the Si(111)(1$\times$1):H surface and compare with various experimental spectra from severaldifferent sources. We also revisit the three-layer model for the SSHG yield and demonstrate that it providesmore accurate results over several, more common, two-layer models. We demonstrate the importance of usingproperly relaxed coordinates for the theoretical calculations. We conclude that this approach to the calculation ofthe second-harmonic spectra is versatile and accurate within this level of approximation. This well-characterizedsurface offers an excellent platform for comparison with theory and allows us to offer this study as an efficientbenchmark for this type of calculation