Definition of Larger Fragments

Without going into the mathematical details we shall qualitatively overview and compare the possibilities for defining polyatomic fragments in quantum chemical calculations. Since the present-day techniques always use finite basis expansions for the development of the molecular wave function, the crucial question is how to partition this basis set in the most effective way. 

From a purely formal point of view the molecules are assemblies of atoms and bonds, consequently the definition of fragments may be done in terms of these constituents. We can imagine fragments as ensembles of (a) atoms, (b) bonds. Evidently in the first case the bonds linking the fragments should be broken, while in the second case the atomic centres at the borderline of two fragments should be artificially partitioned. 

It may seem that the more physical choice is to define a fragment as the set of atoms with the associated atomic basis functions. This works quite well, if there are no covalent bonds to be broken, i.e. the fragments are separate molecules. However such a treatment is not very practical if the fragments are linked by strong covalent interaction (cf. Fig. 1). 

One cannot mention the a priori use of localized orbitals, without emphasising the importance of the hybrid orbitals. It is well-known that hybridization is an extremely fruitful concept in chemistry and in the rationalization of molecular structure and bonding [7]. As it was shown by Maksic, hybridization often takes into account the most essential modifications of the atomic properties, and it can be a very good starting point for a MAM (modified atoms in molecules) model [50]. The SLMOs 

In the context of using localized orbitals as the building blocks of the fragments, we are faced with another problem what to do with the nuclei. It is a common procedure to consider a certain portion of the nuclear charge to belong to the bond, thus forming electrically neutral subunits [46]. It is useless to say that such a prescription is quite arbitrary, therefore the problem needs further study. 

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