Identifying Molecular Orbital Symmetries

consider staggered ethane, which we have earlier assigned to the Dm point group. Orbital energy levels and sketches of the MOs appear in Fig. 13-14. The character table for the Dm group is given in Table 13-24. 

As before, we observe that certain of the orbitals have the same energies, so we assign such doubly-degenerate MOs the main symbol e. These MOs are either symmetric or 

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The most important observation in the smdy of pericyclic reactions is the existence of conservation of molecular orbital symmetry throughout the transformation, meaning thereby that the symmetric orbitals are converted into symmetric orbitals whereas antisymmetric orbitals are converted into antisymmetric orbitals. In this approach, symmetry properties of various molecular orbitals of the bonds that are involved in the bond breaking and formation process during the reaction are considered and identified with respect to C2 and m elements of symmetry. These properties remain preserved throughout the course of reaction. Then a correlation diagram is drawn in which the molecular orbital levels of like symmetry of the reactant are related to that of the product by drawing lines. 

The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) may be identified by finding the point where the occupied/virtual code letter in the symmetry designation changes from O to V. 

The symmetry of each excited state must be used when matching up predicted and observed states. You cannot simply assume that the theoretical excited state ordering corresponds to the experimental. In most cases, Gaussian will identify the symmetry for each excited state. In those relatively rare instances when it cannot —as will be true for benzene—you will need to determine it by examining the transition wavefiinction coefficients and molecular orbitals. 

The triangular planar (D3h symmetry) CO/ molecular ion with 24 electrons (AB324-type) in CaC03 is easily ionized by radiation to electron and hole centres self-trapped in the lattice or an oxygen vacancy type C02 molecular ion at the anon site. Molecular orbital schemes based on the general scheme of AB3 molecules with 25,24 and 23 electrons for atoms A (B, C, Si, N, P, As and S) and B (O) characterize their specific -factor. Hence, the anisotropic -factor of these radicals estimated from the powder spectrum has been to identify the radical species.1... 

In a quantum chemical calculation on a molecule we may wish to classify the symmetries spanned by our atomic orbitals, and perhaps to symmetry-adapt them. Since simple arguments can usually give us a qualitative MO description of the molecule, we will also be interested to classify the symmetries of the possible MOs. The formal methods required to accomplish these tasks were given in Chapters 1 and 2. That is, by determining the (generally reducible) representation spanned by the atomic basis functions and reducing it, we can identify which atomic basis functions contribute to which symmetries. A similar procedure can be followed for localized molecular orbitals, for example. Finally, if we wish to obtain explicit symmetry-adapted functions, we can apply projection and shift operators. 

With a total of fourteen valence electrons to accommodate in molecular orbitals, ethane presents a more complicated picture, and we now meet a C—C bond. We will not go into the full picture—finding the symmetry elements and identifying which atomic orbitals mix to set up the molecular orbitals. It is easy enough to see the various combinations of the Is orbitals on the hydrogen atoms and the 2s, 2px, 2py and 2pz orbitals on the two carbon atoms giving the set of seven bonding molecular orbitals in Fig. 1.19. 

Three levels of explanation have been advanced to account for the patterns of reactivity encompassed by the Woodward-Hoffmann rules. The first draws attention to the frequency with which pericyclic reactions have a transition structure with (An + 2) electrons in a cyclic conjugated system, which can be seen as being aromatic. The second makes the point that the interaction of the appropriate frontier orbitals matches the observed stereochemistry. The third is to use orbital and state correlation diagrams in a compellingly satisfying treatment for those cases with identifiable elements of symmetry. Molecular orbital theory is the basis for all these related explanations. 

In the course of their synthesis of Vitamin B12, R. B. Woodward and co-workers were puzzled by the failure of certain cyclic products to form from apparently appropriate starting materials—in particular, the stereochemistry of interconversions of cyclohexadienes with conjugated trienes in thermal and photochemical reactions. Woodward, in collaboration with Roald Hoffmann (ca. 1965), discovered that the course of such reactions depended on identifiable symmetries of the participating molecular orbitals. The principle of conservation of orbital symmetry can be stated thus ... 

Some of the possible combinations of atomic orbitals are shown in Fig. 5.11. Those orbitals which are cylindrically symmetrical about the internuclear axis are called cr orbitals, analogous to an s orbital, the atomic orbital of highest symmetry. If the internuclear axis lies in a nodal plane, a n bond results. In S bonds (Chapter 16) the internuclear axis lies in two mutually perpendicular nodal planes. All antibonding orbitals (identified with an ) possess an additional nodal plane perpendicular to the internuclear axis and lying between the nuclei. In addition, the molecular orbitals may or may not have a center of symmetry. Of particular interest in this regard are orbitals, which are ungerade, and tt orbitals, which are gerade. 

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