Monoelectronic molecular wave functions

This theory endeavors to describe the molecule by a method intrinsically similar to that used for obtaining atomic orbitals but considering multicenter wave functions. Thus this approach consists of finding the best functions for describing the state of one electron in a field formed by the totality of the nuclei placed in their equilibrium positions. These monoelectronic molecular wave functions may be obtained according to the MO-theory by a linear combination of atomic orbitals (LCAO). 

It is often useful to be able to determine the symmetry of a function that is a product of two (or more) functions whose symmetry is already known. This need arises, for example, when we consider a polyelectronic wave function that is written as a product of monoelectronic flmctions (atomic or molecular orbitals), or when we are interested in the overlap between two orbitals (see 6.5.1). 

The electronic criteria of aromaticity/antiaromaticity are based on the electronic structure of the molecules. Molecular orbitals (MOs) that are highly delocalized over the entire cyclic nuclear framework support cyclic electron delocalization which characterizes aromaticity. Based on the symmetry of the highly delocalized MOs we can distinguish between the orbital-types of aromaticity, e.g., a-, it-, 8-, and (p-aromaticity. Many planar cyclic clusters formulated as c-E and c-E L (E = element, L = H, C, O, NH, n = 3-6) exhibit the so-called multifold aromaticity, which arises from various combinations of the aforementioned orbital types. Molecular orbitals are multicenter monoelectronic wave functions constructed from the overlap of atomic orbitals (AOs) belonging to the nuclear centers. The o-aromaticity is supported by delocalized ct-MOs, which can result from the linear combination of S-, p-, d-, or f-AOs. Similarly jr-aromaticity is supported by delocalized tt-MOs... 

In the theoretical description of regular polymers, the monoelectronic levels (orbital energies in the molecular description) are represented as a multivalued function of a reciprocal wave number defined in the inverse space dimension. The set of all those branches (energy bands) plotted versus the reciprocal wave number (k-point) in a well defined region of the reciprocal space (first Brillouin zone) is the band structure of the polymers. In the usual terminology, we note the analogy between the occupied levels and the valence bands, the unoccupied levels and the conduction band. 

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