Semi-empirical quantum chemistry methods
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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, 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 Pariser-Parr-Pople method (PPP), can provide good estimates of the pi-electronic excited states, when parameterized well. Indeed, for many years, the PPP method outperformed ab initio excited state calculations. In contrast to their Hartree-Fock-based Semiempirical methods counterparts (i.e: MOPAC), 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, Lindgren, etc). (The exact formulation is non-trivial, and requires some field theory) Large scale ab initio calculations (Martin and Birge, Martin and Freed, Sheppard and Freed, etc.) 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 all valence electrons. These methods can be grouped into several groups:-
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- 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.
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- Methods whose primary aim is to predict the geometries of coordination compounds, such as Sparkle/AM1, available for lanthanide complexes.
the latter being by far the largest group of methods.
A major complaint against ZINDO in particular is that while it could reproduce the low lying spectra of larger polyenes and some organo-metallic compounds, it lacked a consistent parameterization. To obtain good results, it had been frequently necessary to fit the parameters to a given molecule, thereby reducing its the generality and predictive capacity. In contrast, ab initio packages, such as GAUSSIAN, gained popularity because they would always produce the same results for a given input, even if the results were sometimes inaccurate.
The table below shows some software packages that carry out semi-empirical methods, indicating the other methods that they include where applicable.
| Package | Molecular Mechanics | Hartree-Fock | Post-Hartree-Fock methods | Density Functional Theory | |
| AMPAC | N | N | N | N | |
| GAUSSIAN | Y | Y | Y | Y | |
| GAMESS (UK) | N | Y | Y | Y | |
| GAMESS (US) | N | Y | Y | Y | |
| MOLCAS | Y | Y | Y | Y | |
| MOPAC | N | N | N | N | |
| PQS | Y | Y | Y | Y | Y |
| VASP | N | Y | N | Y |
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