Symmetry of molecular orbitals

The 71 molecular orbitals of ethene have opposite symmetries with respect to the vertical plane that bisects the 7t bond. The bonding orbital is symmetric with respect to the vertical plane. However, the antibonding orbital is antisymmetric with respect to this plane. Thus, for the antibonding orbital, the vertical plane is also a nodal plane. 

The number of n molecular orbitals is the same as the number of 2p orbitals used to form them. So, if we begin with n 2p orbitals we obtain n n molecular orbitals. 

The energies of the n molecular orbitals are symmetrically distributed above and below the energy of the isolated, atomic 2p orbitals. 

The energies of bonding molecular orbitals are lower than the energies of antibonding molecular orbitals. 

Each molecular orbital has a horizontal nodal plane that contains the carbon nuclei. 

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The Woodward-Hoffmann method [52], which assumes conservation of orbital symmetry, is another variant of the same idea. In it, the emphasis is put on the symmetries of molecular orbitals. Longuet-Higgins and Abramson [53] noted the necessity of state-to-state correlation, rather than the orbital correlation, which is not rigorously justified (see also, [30,44]). However, the orbital symmetry conservation rules appear to be very useful for most themial reactions. 

Fig, 4,18 The stereochemistry of many reactions is easily predicted from the symmetry of molecular orbitals, usually the highest occupied n MO (n HOMO). In the ring closure of 1,3-butadiene to cyclobutene the phase (+ or —) of the HOMO (i//2) at the end carbons (the atoms that bond) is such that closure must occur in a conrotatory sense, giving a definite stereochemical outcome. In the example above there is only one product. The reverse process is actually thermodynamically favored, and the cis dimethyl cyclobutene opens to the cis, trans diene. No attempt is made here to show quantitatively the positions of the energy levels or to size the AOs according to their contributions to the MOs... 

Roald Hoffmann, bom Zloczow, Poland, 1937. Ph.D. Harvard, 1962, Professor, Cornell. Nobel Prize 1981(shared with Kenichi Fukui Section 7.3.5) for work with organic chemist Robert B. Woodward, showing how the symmetry of molecular orbitals influences the course of chemical reactions (the Woodward-Hoffmann rules or the conservation of orbital symmetry). Main exponent of the extended Hiickel method. He has written poetry, and several popular books on chemistry. 

Extraction of information from p may not be as elegant as from P. For example, the Woodward-Hoffmann rules follow fairly transparently from the symmetries of molecular orbitals (wavefunctions), but deriving them from p requires using a dual descriptor function [1]. 

For example, the rules involved in the pairing of electrons and the symmetry of molecular orbitals lead to patterns of what were initially recognized as unusually... 

Table 7-1. The Symmetry of Molecular Orbitals in the Face-to-Face Dimerization of Ethylene3...

The principle of maintaining the symmetry of molecular orbitals within stereoselectivity requirements during the phosphacarba valence isomerization is supported by comparison of the stereochemically important atomic centers of the educts (1,6-diphosphahexa-l,5-dienes) and products (1,2-diphosphacycloalkandiene) ... 

Fig. 5.11 Symmetry of molecular orbitals formed from atomic orbitals illustrating

This alternation of chemical behavior, 67t-system versus 47t-system, thermal versus photochemical, has at its core the quantum effeas that dictate the symmetries of molecular orbitals. In 1964, Roald Hoffmann (1937- ) was 27, had completed his Ph.D. at Harvard two years earlier, and was in the second year of an appointment as a Harvard junior fellow. The renowned Woodward (who would win the Nobel Prize in chemistry in 1965) discussed his observations on electrocyclic reactions with Hoffmann. Although Kenichi Fukui had developed frontier molecular orbital theory more than a decade earlier and many related theoretical ideas were percolating in the chemical community, it was Woodward and Hoffmann who published, in 1965, their intellectual synthesis as a book titled The Conservation of Orbital Symmetry. Their theory explained a broad spectrum of concerted reactions and made bold predictions that were later verified. 

Atoms in the row of the periodic table running from Li to F have electrons in 2s and 2p orbitals, and as all molecules of interest to organic chemists contain at least one such atom we now need to think about how 2s and 2p orbitals interact. We also need to introduce you to a useful piece of terminology that is used to describe the symmetry of molecular orbitals. 

Consider the set of perpendicular -orbitals in the poly aromatic planar molecule coronene shown below. This set gives rise to a symmetry of molecular orbitals of a u and b g. Can you draw both these orbitals (Use the standard orientation of the central benzene frame, as shown in Fig. 3.10)... 

First method takes into account S3mametry properties of reactants and products second is based upon FMOs but in third forecasts can be made without considering symmetries of molecular orbitals. 

This approach was developed by M.J.S. Dewar and too leads to similar conclusion about pericyclic reactions as above two methods without taking into account symmetry of molecular orbitals. 

The highest occupied molecular orbital of a tetraene is 714 because the eight electrons are distributed starting at Tti, and two electrons are added to each molecular orbital until 714 is filled. The symmetry of molecular orbitals in an array of molecular orbitals alternates between adjacent orbitals. The tij molecular orbital of any hnear polyene is symmetric. Thus, 714 is antisymmetric. 

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