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Within the framework of Hartree-Fock calculations, some pieces of information (such as two-elecron integrals) are sometimes approximated or completely omitted. In order to correct for this loss, semi-empirical methods are parametrized, that is their results are fitted by a set of parameters, normally in such a way as to produce results that best agree with experimental data, but sometimes to agree with ''ab initio'' results.

Semi-empirical methods follow what are often called empirical methods where the two-electron part of the Hamiltonian is not explicitly included. For π-electron systems, this was the Hückel Method proposed by Erich Hückel , and for all valence electron systems, the Extended Hückel Method proposed by Roald Hoffmann .

Semi-empirical calculations are much faster than their ''ab initio'' counterparts. Their results, however, can be very wrong if the molecule being computed is not similar enough to the molecules in the database used to parametrize the method.

Semi-empirical calculations have been most successful in the description of organic chemistry, where only a few elements are used extensively and molecules are of moderate size.

As with empirical methods, we can distinguish methods that are:-

  • restricted to pi-electrons. These method exist for the calculation of electronically excited states of polyenes, both cyclic and linear. These methods, such as the ), the pi-electron theories have a very strong Ab Initio basis. The PPP formulation is actually an approximate pi-electron effective operator, and the empirical parameters, in fact, include effective Electron Correlation effects. A rigorous, ab initio theory of the PPP method is provided by diagrammatic, multi-reference, high order perturbation theory (Freed, Brandow, etc). Large scale ab initio calculations (Martin and Freed, Sheppard and Freed) have confirmed many of the approximations of the PPP model and explain why the PPP-like models work so well with such a simple formulation.


or those:-

  • restricted to valence electrons. These methods can be grouped into several groups:-


  • Methods such as CNDO/2 , INDO and NDDO that were introduced by John Pople . The implementations aimed to fit, not experiment, but ab initio minimum basis set results. These methods are now rarely used but the methodology is often the basis of later methods.


  • Methods that are in the MOPAC and/or AMPAC computer programs originally from the group of Michael Dewar . These are MINDO , MNDO , AM1 , PM3 and SAM1 . Here the objective is use parameters to fit experimental heats of formation.


  • Methods whose primary aim is to calculate excited states and hence predict electronic spectra. These include ZINDO and SINDO .


the latter being by far the largest group of methods.

The table below shows some software packages that carry out semi-empirical methods, indicating the other methods that they include where applicable.