Semi-empirical quantum chemistry methods

Semi-empirical quantum chemistry methods are based on the Hartree–Fock formalism, but make many approximations and obtain some parameters from empirical data. They are very important in computational chemistry for treating large molecules where the full Hartree–Fock method without the approximations is too expensive. The use of empirical parameters appears to allow some inclusion of electron correlation effects into the methods.

Within the framework of Hartree–Fock calculations, some pieces of information (such as two-electron 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.

Type of simplifications used

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. For all valence electron systems, the extended Hückel method was proposed by Roald Hoffmann.

Semi-empirical calculations are much faster than their ''ab initio'' counterparts, mostly due to the use of the zero differential overlap approximation. 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.

Preferred application domains

Empirical research is a way of gaining knowledge by means of direct and indirect observation or experience.

Methods restricted to π-electrons

These methods exist for the calculation of electronically excited states of polyenes, both cyclic and linear. These methods, such as the Pariser–Parr–Pople method (PPP), can provide good estimates of the π-electronic excited states, when parameterized well. For many years, the PPP method outperformed ab initio excited state calculations.

Methods restricted to all 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.
:* Semiempirical quantum mechanical methods GFNn-xTB

:* Methods that are in the MOPAC, AMPAC, SPARTAN and/or CP2K computer programs originally from the group of Michael Dewar. These are MINDO, MNDO, AM1, PM3, and SAM1. Here the objective is to use parameters to fit experimental heats of formation, dipole moments, ionization potentials, and geometries.

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

The latter is the largest group of methods.

See also

* List of quantum chemistry and solid-state physics software

References

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