  Semiempirical molecular orbital (SEMO) models based on the neglect of
diatomic differential overlap (NDDO) approximation efficiently solve the
self-consistent field equations by rather drastic approximations. The
computational efficiency comes at the cost of an error in the electron-electron
repulsion integrals. The error may be compensated by the introduction of
parametric expressions to evaluate the electron-electron repulsion integrals,
the one-electron integrals, and the core-core repulsion. We review the
resulting formalisms of popular NDDO-SEMO models (such as the MNDO(/d), AM1,
PMx, and OMx models) in a concise and self-contained manner. We discuss the
approaches to implicitly and explicitly describe electron correlation effects
within NDDO-SEMO models and we dissect strengths and weaknesses of the
different approaches in a detailed analysis. For this purpose, we consider the
results of recent benchmark studies. Furthermore, we apply bootstrapping to
perform a sensitivity analysis for a selection of parameters in the MNDO model.
We also identify systematic limitations of NDDO-SEMO models by drawing on an
analogy to Kohn--Sham density functional theory.
