Alternate molecular orbitals

Having just seen a resonance description of benzene, let s now look at the alternative molecular orbital description. We can construct -tt molecular orbitals for benzene just as we did for 1,3-butadiene in Section 14.1. If six p atomic orbitals combine in a cyclic manner, six benzene molecular orbitals result, as shown in Figure 15.3. The three low-energy molecular orbitals, denoted bonding combinations, and the three high-energy orbitals are antibonding. 

In conclusion we note that the method of alternant molecular orbitals leads to a correct behavior of the energy curve for separated atoms, which is of essential importance in considering correlation effects (see Section II.D(4c)) and in studying magnetic phenomena. 

Lowdin, P.-O., Symposium on Molecular Physics atNikko, Japan, Maruzen, Tokyo, 1953, p. 13. A method of alternant molecular orbitals."... 

Yoshizumi, H., and Itoh, T., J. Chem. Phys. 23, 412, "Applications of the alternant molecular orbital method to six and four electron systems."... 

J.-L. Calais, Abstracts of Uppsala Dissertations in Science 52 ( 1965 ), R. Pauncz, Alternant Molecular Orbital Method ( W. B. Saunders, Philadelphia 1967 )... 

Ruben Pauncz, Studies in Physics and Chemistry, No. 4. Alternant Molecular Orbital Method, Saunders, Philadelphia, 1967. 

But an alternative Molecular-Orbital (MO) approach eclipsed the VB approach, in so far as quantum-chemical research was concerned (say from the 1940s onward for a few decades). There were a variety of reasons for this, including perceived theoretical conceptual difficulties and supposed predictive failures - and perhaps most seriously the MO approach seemed much more computationally amenable. 

Having just seen a resonance description of benzene, let s now look at the alternative molecular orbital description. An orbital view of benzene makes clear the cyclic conjugation of the benzene molecule and the equivalence of the. six carbon-carbon bonds. Benzene is a planar molecule with the shape of a regular hexagon. All C-C-C bond angles are 120 , all six carbon atoms are sp -hybridized, and each carbon has a p orbital perpendicular to the plane of the six-membered ring. 

Pauncz, R. Alternant Molecular Orbital Method, Philadelphia Saunders 1967. 3°) Empedocles, D. D., Linnett, J. W. Theoret. Chim. Acta 4, 377 (1966) Proc. 

Another possible solution included in (34) is the alternant molecular orbital (AMO) function in which the six n orbitals are divided into two sets of three. The orbitals in each set have the symmetry a and e" of the subgroup D31, of the molecular point group, and the two sets are interchanged by the operation Cg. However for this case, only one spin function may occur that where the spins of each set are coupled to the maximum S =, and the two subsystems coupled to give the final resultant S = 0 (i.e. the Hund s rule coupling for A = 6, S = 0). 

There is, however, a method which has not been fully exploited yet, in particular for extended systems, namely the single-determinant method without any restrictions on the spin orbitals. Thanks to very important work by Fukutome and collaborators we now have a clear picture of the various possible forms of such spin orbitals, which includes, in addition to the well-known doubly filled restricted Hartree-Fock (RHF) orbitals, alternant molecular orbitals and other forms of different orbitals for different spins, Overhauser s spin density waves, as well as others. It has been known for a long time that a sufficiently general single determinant can... 

Although the available experimental and theoretical evidence in favour of bond alternation for the higher An + 2) systems is fairly compelling, a dissonant note is sounded in the alternant molecular orbital calculations of Hultgren, who predicts the total absence of bond alternation 10>. 

Several calculations have been performed, particularly in the case of alkaline and alkaline-earth metals, using various methods i.e., molecular orbital method alternant molecular orbitals... 

A comparative study between the classical molecular orbital method and the more improved method of alternant molecular orbitals performed for lithium, shows that both procedures are in fact equivalent for interatomic distances close to the equilibrium distances in the crystal. Nevertheless, the cohesive energy obtained is equal to zero 1 This result is very depressing. The cohesive energy is in fact less than 1/100 of the total energy. Therefore, it is very difficult to obtain a good value, even using sophisticated methods. 

Alternant Molecular Orbitals, P.-O. Lowdin, Synip. Mol Phys., Nikko (Tokyo Mantzen), (1954), p. 13 also R. Pauncz, Alternant Molecular Orbitals. Saunders. Philadelphia (19671. 

AMO Alternant Molecular Orbitals A version of the unrestricted Hartree-Fock... 

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