This is referred to as the Neglect of Diatomic Differential overlap or NDDO approximation, and reduces the number of electron-electron interaction terms from OCN) in the Roothaan-Hall equations too0N where N is the total number of basis functions.
Additional approximations are introduced in order to further simplify the overall calculation, and more importantly to provide a framework for the introduction of empirical parameters. Except for models for transition metals, semi-empirical parameterizations are based on reproducing a wide variety of experimental data, including equilibrium geometries, heats of formation, dipole moments and ionization potentials. Parameters for PM3 for transition metals are