QUALITATIVE PICTURE OF BONDING IN METAL COMPLEXES

In the previous section we developed the DMM methodology and derived formulae for the energy (force fields) for interactions of donor atoms with acceptors. A simplified representation of the acceptor with a single s -orbital was used there. Here we consider the metal-ligand interactions from a different point of view - that of the metal. The metal ion in a CC acquires some density not from one but from many lone pairs of the ligating donor atoms. Constructing a mechanistic or at least an economic QM description for such a case would possibly help to rationalize terms of interligand interaction force fields, which are sometimes included in the standard MM picture to assure proper description of the metal CC. 

Polarization of the surrounding by the metal ion (either formal or effective) charge can be fit into the electronegativity equilibration scheme by ascribing new electronegativities to the atoms in the external field induced by the ion. However, it must be realized that neither of the characteristic quantum features of polarizability, such as the alternating polarity law [27] can be reproduced by classical methods. 

A possible approximation to be used for the cls function can be chosen considering two ideas. In contrast to the directionality and saturability characteristic for organic covalent bonds, those formed by metal ions do not possess these properties. Thus there is no need to invoke the HO formation on the metal ion. At the infinite separation limit, the cls wave function must flow to the antisymmetrized product of the lone pair geminals of eq. (2.61). The latter is in fact a single determinant function with all lone pair HOs doubly filled. With these arguments, we arrive at the conclusion that the single determinant (HFR) wave function is an appropriate form 

As in eq. (2.95) here x7 X-7 are directed along the 7 axis (7 = x, y, z) of the Cartesian coordinate system centered at the metal atom in the positive and negative direction respectively. Coefficients xp and yr = — x describe the mixing 

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