Semi-empirical quantum chemistry method

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-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 [ E. Hückel, Zeitschrift für Physik, 70, 204, (1931); 72, 310, (1931); 76, 628 (1932); 83, 632, (1933) ] [ Hückel Theory for Organic Chemists, C. A. Coulson, B. O'Leary and R. B. Mallion, Academic Press,1978. ] [ Andrew Streitwieser, Molecular Orbital Theory for Organic Chemists, Wiley, New York, (1961) ] For all valence electron systems, the Extended Hückel method was proposed by Roald Hoffmann. [ R. Hoffmann, Journal of Chemical Physics, 39, 1397, (1963) ]

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 Pariser-Parr-Pople method (PPP), can provide good estimates of the pi-electronic excited states, when parameterized well. [ R. Pariser and R. Parr, Journal of Chemical Physics, 21, 466, 767, (1953) ] [ J. A. Pople, Transactions of the Faraday Society, 49, 1375, (1953) ] Indeed, for many years, the PPP method outperformed ab initio excited state calculations.

or those:-

* 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. [ J. Pople and D. Beveridge, "Approximate Molecular Orbital Theory", McGraw-Hill, 1970. ] [ Ira Levine, "Quantum Chemistry", Prentice Hall, 4th edition, (1991), pg 579 - 580 ] [ C. J. Cramer, "Essentials of Computational Chemistry", Wiley, Chichester, (2002), pg 126 - 131 ] 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. [ J. J. P. Stewart, Reviews in Computational Chemistry, Volume 1, Eds. K. B. Lipkowitz and D. B. Boyd, VCH, New York, 45, (1990) ] These are MINDO, MNDO, AM1, PM3, [http://www.rm1.sparkle.pro.br/ RM1] 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 predict the geometries of coordination compounds, such as [http://www.sparkle.pro.br/ Sparkle/AM1] , available for lanthanide complexes.

:* Methods whose primary aim is to calculate excited states and hence predict electronic spectra. These include ZINDO and SINDO [ M. Zerner, Reviews in Computational Chemistry, Volume 2, Eds. K. B. Lipkowitz and D. B. Boyd, VCH, New York, 313, (1991) ] [ Nanda, D. N. and Jug, K., Theoretica Chimica Acta, 57, 95, (1980) ] .

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.

See also

* Quantum chemistry computer programs

References