Planar molecules symmetry properties, 64

The availability of 18 in one synthetic step via direct oxidative functionalization of HCTD [19-21] allows exploration of this valuable compound s chemistry for the first time. Thus, the reaction sequence shown in Scheme 9 has been utilized to prepare a novel polycyclic alkene, 30, whose symmetry properties require that its central, tetrasubstituted C=C double bond be completely planar (in the isolated molecule). The constraints imposed by the polycarbocyclic cage framework cause the CCC bond angles about the central C=C double bond in 30 to deviate significantly from the preferred value of 120°, thereby introducing additional steric strain in this molecule beyond that which is associated with its framework alone. 

Symmetry Properties of Electronic Excited States and Spin Levels to Reflection Planes in Planar Aromatic Molecules... 

The symmetry of many molecules and especially of crystals is immediately obvious. Benzene has a six-fold symmetry axis and is planar, buckminsterfullerene (or just fullerene or footballene) contains 60 carbon atoms, regularly arranged in six- and five-membered rings with the same symmetry (point group //,) as that of the Platonic bodies pentagon dodecahedron and icosahedron (Fig. 2.7-1). Most crystals exhibit macroscopically visible symmetry axes and planes. In order to utilize the symmetry of molecules and crystals for vibrational spectroscopy, the symmetry properties have to be defined conveniently. 

Multiple CT leading to three level contributions and the possibility of ordering through electrical poling is combined with dipolar 2D NLO-phores. The establishment of structure-property relationships for this type of molecule, reviewed recently (Wolff and Wortmann, 1998), is still in its infancy because application of a single analytical method is clearly inadequate to unravel the combination of different tensor elements. It is convenient to keep the number of numerically different tensor elements as low as possible and to study planar molecules of C2v symmetry. Out of the seven /3 components that are significant for this case, only hve are independent. In addition, the components in the x-direction, dehned as perpendicular to the molecular plane (y,z) are negligibly small, so only four components remain = y y, yy and A... 

If a molecule has certain symmetry properties, important predictions about the solutions of the electronic Schrodinger equation can be made without having to solve the equation itself. Consider the case of a planar molecule, i.e. of a molecule whose nuclei lie in a plane. This plane is a symmetry plane for the molecule, and it can be shown that any eigenfunction is either symmetric or antisymmetric with respect to this plane. If one chooses the plane of the nuclei as the (y, z) plane of a Cartesian coordinate system, this means that... 

Another general theorem 9>1( states that the set of NO s associated with every eigenfunction of the Schrodinger equation has definite symmetry properties. In particular, for a planar molecule the natural orbitals are either a or n orbitals. Therefore, a and n orbitals have a physical meaning independent of any model assumption or approximation. By adding the occupation numbers of each species of orbitals, one defines... 

From a quantum-theoretical point of view only the state property is observable, and this is determined by the overall symmetry of the molecule under consideration. In planar molecules the ir-a separation is physically relevant, as it is connected with state properties which are associated with projection operators for the antisymmetric (a") and symmetric (o ) representation of the symmetry group C. In nonplanar allenes only for molecules of Q symmetry, for example, monosubstituted compounds RHC=C=CH2, there exists a correspondingly physically relevant and unique iv a")-a a ) classifieation (24). 

Now we can use a similar argumentation to analyze the symmetry properties of a planar unit in the selected molecule (Fig. 3.3). 

These simple molecular orbital pictures provide useful descriptions of the structures and spectroscopic properties of planar conjugated molecules such as benzene and naphthalene, and heterocychc species such as pyridine. Heats of combustion or hydrogenation reflect the resonance stabilization of the ground states of these systems. Spectroscopic properties in the visible and near-ultraviolet depend on the nature and distribution of low-lying excited electronic states. The success of the simple molecular orbital description in rationalizing these experimental data speaks for the importance of symmetry in determining the basic characteristics of the molecular energy levels. 

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