Molecular orbitals symmetry properties

As a prelude to further analysis, it is useful to review one important property of molecular orbitals. As noted in Chapter 1, symmetry-correct molecular orbitals must be either symmetric or antisymmetric with respect to the full symmetry of the basis set of atomic orbitals that are used to construct the molecular orbitals. In the analysis of orbital symmetries, we will need to consider only the number of molecular S5nnmetry elements that are sufficient to distinguish between allowed and forbidden pathways. Also, it is not necessary to consider here the minor perturbation of molecular orbital symmetry that results from isotopic or alkyl substitution. In other words, to a first approximation the basis set orbitals of any conjugated diene are considered to be the same as those for 1,3-butadiene. Figtue 11.13 shows the... 

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. 

Most ah initio calculations use symmetry-adapted molecular orbitals. Under this scheme, the Hamiltonian matrix is block diagonal. This means that every molecular orbital will have the symmetry properties of one of the irreducible representations of the point group. No orbitals will be described by mixing dilferent irreducible representations. 

Extended Hiickel gives a qualitative view of the valence orbitals. The formulation of extended Hiickel is such that it is only applicable to the valence orbitals. The method reproduces the correct symmetry properties for the valence orbitals. Energetics, such as band gaps, are sometimes reasonable and other times reproduce trends better than absolute values. Extended Hiickel tends to be more useful for examining orbital symmetry and energy than for predicting molecular geometries. It is the method of choice for many band structure calculations due to the very computation-intensive nature of those calculations. 

Let us now examine the Diels-Alder cycloaddition from a molecular orbital perspective Chemical experience such as the observation that the substituents that increase the reac tivity of a dienophile tend to be those that attract electrons suggests that electrons flow from the diene to the dienophile during the reaction Thus the orbitals to be considered are the HOMO of the diene and the LUMO of the dienophile As shown m Figure 10 11 for the case of ethylene and 1 3 butadiene the symmetry properties of the HOMO of the diene and the LUMO of the dienophile permit bond formation between the ends of the diene system and the two carbons of the dienophile double bond because the necessary orbitals overlap m phase with each other Cycloaddition of a diene and an alkene is said to be a symmetry allowed reaction... 

The period 1930-1980s may be the golden age for the growth of qualitative theories and conceptual models. As is well known, the frontier molecular orbital theory [1-3], Woodward-Hoffmann rules [4, 5], and the resonance theory [6] have equipped chemists well for rationalizing and predicting pericyclic reaction mechanisms or molecular properties with fundamental concepts such as orbital symmetry and hybridization. Remarkable advances in aeative synthesis and fine characterization during recent years appeal for new conceptual models. 

All this suggests a further simplification, which has proved to be eminently successful in many cases. It is known that independent electron treatments, such as the Hiickel (HMO) treatment2 or the extended Hiickel treatment (EHT)172, which do not take the electron-electron interaction explicitly into account, yield—by and large—orbitals derived from sophisticated SCF calculations. In particular, the HMO and ETH molecular orbitals reflect faithfully the symmetry and nodal properties of their counterparts obtained from SCF treatments. 

We therefore conclude that, for a combination of model, numerical and conceptual reasons the OHAO basis is well-adapted to a theory of valence. The hybrid orbital basis (for simple molecules) has a distinctive symmetry property it carries a permutation representation of the molecular symmetry group the equivalent orbitals are always sent into each other, never into linear combinations of each other. This simple fact enables the hybrid orbital basis to be studied in a way which is physically more transparent than the conventional AO basis. 

The symmetry properties of molecular orbitals of cyclohexadiene are given in the following... 

A depiction of how molecular orbitals are formed from atomic orbitals of separated atoms and/or how these molecular orbitals correlate with atomic orbitals of the atoms united as the nuclei come together to form a molecular species. Such diagrams are especially useful in rationalizing the symmetry properties of orbitals. 

The Hartree-Fock or self-consistent-field approximation is a simplification useful in the treatment of systems containing more than one electron. It is motivated partly by the fact that the results of Hartree-Fock calculations are the most precise that still allow the notion of an orbital, or a state of a single electron. The results of a Hartree-Fock calculation are interpretable in terms of individual probability distributions for each electron, distinguished by characteristic sizes, shapes and symmetry properties. This pictorial analysis of atomic and molecular wave functions makes possible the understanding and prediction of structures, spectra and reactivities. 

SYMMETRY PROPERTIES OF MOLECULAR ORBITALS CORRELATION DIAGRAMS... 

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