Semi-empirical quantum method

the semi-empirical methods are techniques of resolution of the equation of Schrödinger of systems to several electron S. Contrairement to the methods Ab.initio , the semi-empirical methods use data adjusted on experimental results in order to simplify calculations. The length and the difficulty of calculations are mainly due to the bielectronic integrals which appear with the courses of the process of resolution. Those have as a form:

$\ int \ int \ chi_p (r_1) \ chi_q (r_1) ~ \ frac {1} {r_ {12}} ~ \ chi_r (r_2) \ chi_s (r_2) ~ D \ tau_1 D \ tau_2$

They are generally written in a simplified form

$\ big (pq|rs)$

These integrals evolve/move in $\ frac {n^4} {8}$ with N the number of basic function.

Characteristics

The various semi-empirical methods will be differentiated according to the type of approximation used. There exist however several common points between all these methods.

Seuls the electrons of valence are treated in an explicit way in calculations (this approximation is based on the fact that in fact the electrons of valence intervene in the chemical bonds and thus define the properties of the system.
a great number of integrals bielectronic are neglected (those to 3 and 4 centers to which the value is often close to zero)
the remaining integrals are replaced by empirical parameters

Concerning this last point, it is to be announced that this parameterization is done on 2 levels:

the bielectronic integrals with 1 centers are extracted from experimental atomic spectra
the others are paramétrisées so as to as well as possible reproduce experimental data obtained on a great number of system

Semi-empirical methods

The principal semi-empirical methods are the following ones:

Supplements Neglect Differential Overlap off: Intermediate CNDO
Neglect off Differential Overlap : INDO/MINDO
Neglect off Diatomic Differential Overlap : NDDO / MNDO , AM1 , PM3

See too

Theory VSEPR

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