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By Giuseppe Del Re

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Extra resources for Electronic States of Molecules and Atom Clusters: Foundations and Prospects of Semiempirical Methods

Sample text

Nevertheless, here too we have an essentially qualitative aspect, namely the way in which the presence of a given bond is felt by the rest of the molecule. In other words, although the parametrization is rather heavy, it does not really concern the description of inductive effects; it is just needed to represent the building blocks of the molecule, much as in certain semiempirical and ab initio methods the atoms are represented by ad hoc sets of orbital exponents and quantum numbers. The above consideration, of course, does not answer the question whether or not a bond should be represented in a simpler way, vis.

And that is the only way in which the presence of other bonds affects any given bond AB. 4) is valid both in an orthogonal and in a non-orthogonal basis (let aside the fact that in the latter case 6 is no longer the number operator). The original method assumed orthogonal orbitals on the nuclei. It must be shown that such an assumption does not imply an internal contradiction (Del Re 1960. 1976) j it is found that some care in the expression for orbital energies may be necessary. but there is no problem with charges.

8) and are the well-known elements of the "one-particle density matrix" i. e. of the "charge and bond-order" matrix (the signs < > denote the expectation value over the given M. E. S. ) • In the specific case of a single M. E. S. 6). 2. Intermediate models. - The independent particle model, in its strictest version, has a Hamiltonian that is obtained from the general one by formally neglecting the two-electron terms. There are other models intermediate between the IPM mo- 29 del and the full treatment.

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