Semiempirical Selfconsistent Field Methods

In the SCF methods, the matrix elements F depend on the coefficients in Eqs. (2.4), therefore the solutions are sought iteratively. Various semiempirical SCF methods differ from one another in parametrization procedures as well as in the character and number of the integrals in Eq. (2.5) whose calculation is neglected. The set of parameters for each method is dependent upon what property (or properties) of a given molecular system has been chosen for a parameter calibration. For this reason, the semiempirical methods yield the most reliable results in, as a rule, rather narrow areas of application. 

The complete neglect of differential overlap (CNDO) method [1] rests on the zero differential overlap (ZDO) approximation, which means that all the products of 

The CNDO method admits of several variants of parametrization of which the CNDO/2 scheme is the one which is used more frequently than others. The ZDO approximation drastically reduces the number of two electron integrals since all the three-center, four-center, and exchange integrals are set to zero  

When Eqs. (2.31) and (2.32) are taken into account, the matrix elements of the Fock operator take in the CNDO/2 method the form  

The chief calibration parameter is the resonance integral which depends only on the type of the atom A. It is chosen in such a way as to ensure that the relative order of the energy levels of the occupied MO s and the expansion coefficients of the MO s in the LCAO of Eq. (2.3) optimally coincide with the ab initio calculations using the minimal basis set of the AO. 

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