A recently-developed ab initio theory of second harmonic generation (SHG) spectroscopy of semiconductor surfaces is used to develop a new 'modified' semi-empirical tight binding model (SETBM) of SHG spectroscopy. Some key quantitative features of experimental SHG spectra for H- and Ge-covered Si(001) are not well explained by a simple two-parameter SETBM, despite its success in explaining linear semiconductor surface spectra. The ab initio theory identifies the source of this short-coming as the stronger contribution of optical transitions involving surface atom/adatom states to the SHG response, and is then used to quantify additional SETBM parameters describing these transitions, resulting in a complete, accurate, and convenient description of surface orbital hybridization and experimental results.