Qualitative models, electronic structure

Although a separation of electronic and nuclear motion provides an important simplification and appealing qualitative model for chemistry, the electronic Sclirodinger equation is still fomiidable. Efforts to solve it approximately and apply these solutions to the study of spectroscopy, stmcture and chemical reactions fonn the subject of what is usually called electronic structure theory or quantum chemistry. The starting point for most calculations and the foundation of molecular orbital theory is the independent-particle approximation. 

In this section, the conceptual framework of molecular orbital theory is developed. Applications are presented and problems are given and solved within qualitative and semi-empirical models of electronic structure. Ab Initio approaches to these same matters, whose solutions require the use of digital computers, are treated later in Section 6. Semi-empirical methods, most of which also require access to a computer, are treated in this section and in Appendix F. 

Two qualitative models have been successful in accounting for many of the structural changes in sulfoxides and sulfones5. One is the Faience Shell Electron Pair Repulsion (VSEPR) theory8, while the other approach involves considerations of nonbonded ligand/ligand interactions9. 

Model A cannot be eliminated definitely by the photographs there are, however, some points which make this model improbable. From the curve for this model the first minimum would be expected to be at least as well pronounced as the second minimum, whereas on the photographs the first minimum is not very well defined. That the qualitative appearance of the photographs supports model C rather than model A is further shown by the fact that the photographs resemble those of methyl nitrate more closely than those of carbon tetrafluoride. Some evidence is also provided by the radial distribution curve (Fig. 1), the first peak being displaced by 0.15 A. from the position expected for it for model A. For these reasons and the additional reason that it is difficult to correlate the tetrahedral configuration with an electronic structure involving only completed octets, we consider model A not to be satisfactory.7... 

One-electron pictures of molecular electronic structure continue to inform interpretations of structure and spectra. These models are the successors of qualitative valence theories that attempt to impose patterns on chemical data and to stimulate experimental tests of predictions. Therefore, in formulating a one-electron theory of chemical bonding, it is desirable to retain the following conceptual advantages. 

In the previous Sections (2.1-2.3) we summarized the experimental and computational results concerning on the size-dependent electronic structure of nanoparticles supported by more or less inert (carbon or oxide) and strongly interacting (metallic) substrates. In the following sections the (usually qualitative) models will be discussed in detail, which were developed to interpret the observed data. The emphasis will be placed on systems prepared on inert supports, since - as it was described in Section 2.3 - the behavior of metal adatoms or adlayers on metallic substrates can be understood in terms of charge transfer processes. 

For many years, investigations on the electronic structure of organic radical cations in general, and of polyenes in particular, were dominated by PE spectroscopy which represented by far the most copious source of data on this subject. Consequently, attention was focussed mainly on those excited states of radical ions which can be formed by direct photoionization. However, promotion of electrons into virtual MOs of radical cations is also possible, but as the corresponding excited states cannot be attained by a one-photon process from the neutral molecule they do not manifest themselves in PE spectra. On the other hand, they can be reached by electronic excitation of the radical cations, provided that the corresponding transitions are allowed by electric-dipole selection rules. As will be shown in Section III.C, the description of such states requires an extension of the simple models used in Section n, but before going into this, we would like to discuss them in a qualitative way and give a brief account of experimental techniques used to study them. 

It must be emphasized that the duodectet rule (4.6) initially has no structural connotation, but is based on composition only. Indeed, the compositional regularity expressed by (4.6) encompasses both molecular species (such as the metal alkyls) and extended lattices (such as the oxides and halides) and therefore appears to transcend important structural classifications. Nevertheless, we expect (following Lewis) that such a rule of 12 may be associated with specific electronic configurations, bond connectivities, and geometrical propensities (perhaps quite different from those of octet-rule-conforming main-group atoms) that provide a useful qualitative model of the chemical and structural properties of transition metals. 

Eq. (22) have been derived from the variation principle alone (given the structure of H) they contain only the single model approximation of Eq. (9) the typically chemical idea that the electronic structure of a complex many-electron system can be (quantitatively as well as qualitatively) understood in terms of the interactions among conceptually identifiable separate electron groups. In the discussion of the exact solutions of the Schrodinger equation for simple systems the operators which commute with the relevant H ( symmetries ) play a central role. We therefore devote the next section to an examination of the effect of symmetry constraints on the solutions of (22). 

The simple orbital basis expansion method which is used in the implementation of most models of molecular electronic structure consists of expanding each R as a linear combination of determinants of a set of (usually) atom-centred functions of one or two standard forms. In particular most qualitative and semi-quantitative theories restrict the terms in this expansion to consist of the (approximate) occupied atomic orbitals of the constituent atoms of the molecule. There are two types of symmetry constraint implicit in this technique. 

The most widely used qualitative model for the explanation of the shapes of molecules is the Valence Shell Electron Pair Repulsion (VSEPR) model of Gillespie and Nyholm (25). The orbital correlation diagrams of Walsh (26) are also used for simple systems for which the qualitative form of the MOs may be deduced from symmetry considerations. Attempts have been made to prove that these two approaches are equivalent (27). But this is impossible since Walsh s Rules refer explicitly to (and only have meaning within) the MO model while the VSEPR method does not refer to (is not confined by) any explicitly-stated model of molecular electronic structure. Thus, any proof that the two approaches are equivalent can only prove, at best, that the two are equivalent at the MO level i.e. that Walsh s Rules are contained in the VSEPR model. Of course, the transformation to localised orbitals of an MO determinant provides a convenient picture of VSEPR rules but the VSEPR method itself depends not on the independent-particle model but on the possibility of separating the total electronic structure of a molecule into more or less autonomous electron pairs which interact as separate entities (28). The localised MO description is merely the simplest such separation the general case is our Eq. (6)... 

The electron diffraction molecular structure research is in a fruitful and mutually beneficiary relationship with nonempirical quantum chemical investigations as well as with the development of qualitative models on bonding and molecular geometry. 

The aromatic stabilization of the planar bond configuration may qualitatively be interpreted in terms of a model of the electronic structure of pseudo-olefines (87JA5303), in which the planar structure (249) is viewed as resulting from the interaction between two analogs of carbene XH2 in the triplet state, whereas the frans-pyramidalized structure (250) results from that between two carbene-type units XH2 in the singlet state. 

There are (at least) two major opportunities for research by those interested in this topic. On the computational side, there is definite room for improvement in simulation methods. Right now none of the simulation approaches has the user friendliness that has brought electronic-structure calculation into the realm of routine applicability by nonspecialists. Nor has the field seen the development of the qualitative or semiquantitative models that did so much to make the results of molecular orbital calculations useful to organic chemists. On the experimental side, it will be obvious to the reader that the techniques for detecting the effects of nonstatistical dynamics are still very rudimentary and indirect. There is clearly room for creative scientists to come up with techniques whose results can give us more direct insight into these issues. 

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