The Molecular Orbital Theory

In principle the molecular-orbital method could be applied to any molecule whether simple or complex and whether finite (as in benzene) or infinite (as in diamond). In practice the mathematical difficulties are insuperable and we must adopt a compromise solution. For all but the simplest diatomic molecules, therefore, we first form the atomic orbitals of the individual atoms in the usual way and then, by a linear combination of the relevant bonding orbitals, we deduce the molecular orbitals of the molecule or crystal. We may illustrate this point by considering the molecules of ethylene, H2C=CH2, acetylene, HC=CH, and benzene, C6H6. 

There is, however, another type of hybridization possible in the carbon atom in which the zs orbital is hybridized with only two of the 2p orbitals (say the px and py). The three sp2 hybrid bonds will then lie in a plane symmetrically inclined at 1200, leaving the unaltered pz orbital perpendicular to this plane, as shown in fig. 4.08 a. The three hybrid bonds of each carbon atom will then be responsible for the two bonds between it and the hydrogen atoms with which it is associated and also for one bond between it and the other carbon atom. This picture explains the observed interbond angles of 120° but does not 

We see that this picture explains the planar character of the molecule, for if the carbon atoms were twisted about their common axis overlap of the pz orbitals would be reduced and the tt bond would be broken. 

Similar arguments apply to the acetylene molecule. Here we must assume that in each carbon atom hybridization takes place between the zs orbital and only one of the 2p orbitals (say px), giving rise to two collinear sp or cr bonds. The unaltered py and pz orbitals stand perpendicular to these bonds and to each other. In the molecule the cr bonds will be responsible for the bonding H-C-C-H, but again there 

5 THE METALLIC BOND AND THE STRUCTURES OF SOME METALLIC ELEMENTS 

For an octahedral complex MLg, let us consider that the ligands have only six sigma orbitals, viz, ay a y, a, a ) directed toward the metal 

Metal Orbitals Complex MO s Ligand group orbitals 

While the coordination chemistry was earHer the chemistry of compounds with coordinate covalent bonds, eventually it became the chemistry of 

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M. J. S. Dewar, The Molecular Orbited Theory of Organic Chemistry, McGraw-Hill, New York, 1969,... 

Salem, L., 1966. The Molecular Orbital Theory of Conjugated Systems. Benjamin, New York. Saunders, M., 1987. 7. Amer. Chem. Soc. 109, 3150. 

Lennard-Jones, J., Proc. Roy. Soc. London) A198, 1, The molecular orbital theory of chemical valency. I. The determination of molecular orbitals."... 

The molecular orbital theory of polyatomic molecules follows the same principles as those outlined for diatomic molecules, but the molecular orbitals spread over all the atoms in the molecule. An electron pair in a bonding orbital helps to bind together the whole molecule, not just an individual pair of atoms. The energies of molecular orbitals in polyatomic molecules can be studied experimentally by using ultraviolet and visible spectroscopy (see Major Technique 2, following this chapter). 

PMO Theory of Organic Chemistry Plenum NY, 1975 Zimmerman, H.E. Quantum Mechanics for Organic Chemists Academic Press NY, 1975 Borden, W.T. Modem Molecular Orbital Theory for Organic Chemists Prentice-Hall Englewood Cliffs, NJ, 1975 Dewar, M.J.S. The Molecular Orbital Theory of Organic Chemistry McGraw-Hill NY, 1969 Liberies, A. Introduction to Molecular Orbital Theory Holt, Rinehart, and Winston NY, 1966. 

Salem, L. The molecular orbital theory of conjugated systems. New York Benjamin 1966. 

Parallel to this use of relatively simple approximations of the molecular orbital theory to the study of complex molecules Berthier has investigated the possible utilization of more refined molecular orbital procedures in the study of necessarily smaller molecules. We owe him the first application of the SCF method to the study of fulvene and azulene and also a pioneering extension, presented in 1953, of the SCF method to the study of molecules with incomplete electronic shells. 

The Molecular Orbital Theory of Organic Chemistry, p. 331. New York McGraw-Hill 1969. 

With the absorption of a quantum with an energy of more than 3.05 eV resp. 3.29 eV, an electron is lifted out of the valence band and into the conduction band, thereby forming an exciton (Fig. 5). This interpretation is also supported by the molecular orbital theory and the crystal field theory regarding the bonding conditions in the TiC lattice. 

Dewar, M. J. S. The molecular orbital theory of organic chemistry, Chapt. 6 and 8. New York McGraw-Hill Bank Co. 1969. 

L. Salem, The Molecular Orbital Theory of Conjugated Systems, W. A. Benjamin, New York, 1966 B. M. Gimarc, Molecular Structure and Bonding The Qualitative Molecular Orbital Approach, Academic Press, New York, 1979 T. A. Albright, J. K. Burdet and M. H. Whangbo, Orbital Interactions in Chemistry, Wiley, New York, 1985. 

Salem, L. (1966), The Molecular Orbital Theory of Conjugated Systems, Benjamin, New York. 

Dewar, M. J. S. Angew. Chem., in press Tetrahedron Suppl. 8 (1), 75 (1966) The Molecular Orbital Theory of Organic Chemistry , McGraw-Hill Book Co. Inc., New York, N.Y. (1969). 

The development of localized-orbital aspects of molecular orbital theory can be regarded as a successful attempt to deal with the two kinds of comparisons from a unified theoretical standpoint. It is based on a characteristic flexibility of the molecular orbital wavefunction as regards the choice of the molecular orbitals themselves the same many-electron Slater determinant can be expressed in terms of various sets of molecular orbitals. In the classical spectroscopic approach one particular set, the canonical set, is used. On the other hand, for the same wavefunction an alternative set can be found which is especially suited for comparing corresponding states of structurally related molecules. This is the set of localized molecular orbitals. Thus, it is possible to cast one many-electron molecular-orbital wavefunction into several forms, which are adapted for use in different comparisons fora comparison of the ground state of a molecule with its excited states the canonical representation is most effective for a comparison of a particular state of a molecule with corresponding states in related molecules, the localized representation is most effective. In this way the molecular orbital theory provides a unified approach to both types of problems. 

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