Mobius molecular orbitals

If you compare the orbital energies of the Hiickel and Mobius cyclic 7r systems (Figures 21-13 and 21-16), you will see that the Hiickel systems have only one lowest-energy MO, whereas the Mobius systems have two. Hiickel systems have an odd number of bonding orbitals (which, when full, accommodate 2, 6, 10, 14, or An + 2 electrons) and the Mobius systems have an even number of bonding orbitals (which, when full, accommodate 4, 8, 12, or An electrons). The Hiickel molecular orbitals have zero or an even number of nodes (see, for example, the benzene MOs, Figure 21-5) the Mobius molecular orbitals are not shown, but they have one or an odd number of nodes. 

How can we account for the stereoselectivity of thermal electrocyclic reactions Our problem is to understand why it is that concerted 4n electro-cyclic rearrangements are conrotatory, whereas the corresponding 4n + 2 processes are disrotatory. From what has been said previously, we can expect that the conrotatory processes are related to the Mobius molecular orbitals and the disrotatory processes are related to Hiickel molecular orbitals. Let us see why this is so. Consider the electrocyclic interconversion of a 1,3-diene and a cyclobutene. In this case, the Hiickel transition state one having an... 

M. Plato, E. Trankle, W. Lubitz, F. Lendzian, and K. Mobius, Molecular orbital investigation of dimer formations of bacteriochlorophyll a. Model configurations for the primary donor of photosynthesis, Chem. Phys. 107 185 (1986). 

M. Plato, F. Lendzian, W. Lubitz, and K. Mobius, Molecular orbital study of electronic asymmetry... 

Figure 21-16 Calculated 77-molecular-orbital energies for N overlapping p orbitals in Mobius cyclic n systems...

H. E. Zimmerman, /. Am. Chem. Soc., 88, 1566 (1966). Molecular Orbital Correlation Diagrams, Mobius Systems, and Factors Controlling Ground- and Excited-State Reactions. II. 

We start with some biographical notes on Erich Huckel, in the context of which we also mention the merits of Otto Schmidt, the inventor of the free-electron model. The basic assumptions behind the HMO (Huckel Molecular Orbital) model are discussed, and those aspects of this model are reviewed that make it still a powerful tool in Theoretical Chemistry. We ask whether HMO should be regarded as semiempirical or parameter-free. We present closed solutions for special classes of molecules, review the important concept of alternant hydrocarbons and point out how useful perturbation theory within the HMO model is. We then come to bond alternation and the question whether the pi or the sigma bonds are responsible for bond delocalization in benzene and related molecules. Mobius hydrocarbons and diamagnetic ring currents are other topics. We come to optimistic conclusions as to the further role of the HMO model, not as an approximation for the solution of the Schrodinger equation, but as a way towards the understanding of some aspects of the Chemical Bond. 

On molecular orbital correlation diagrams, the occurrence of Mobius systems in cyclization reactions, and factors controlling ground- and excited- state reactions. I. J. Amer. chem. Soc. 88, 1564 (1966),... 

E. Heilbronner, Tetrahedron Lett. 5, 1923 (1964). Hiickel Molecular Orbitals of Mobius-Type Conformations of Annulenes. 

Heilbronner, E. Hiickel molecular orbitals of Mobius-type conformations of annulenes, Tetrahedron Lett. 1964, 5,1923-1928. 

Figure 7.12 Molecular orbitals for the (hypothetical) Mobius cyclobutadiene...

Plato M, Steinhoff HJ, Wegener C, Torring JT, Savitsky A, Mobius K (2002) Molecular orbital study of polarity and hydrogen bonding effects on the g and hyperfine tensors of site directed NO spin labelled hacteriorhodopsin. Mol Phys 100(23) 3711-3721... 

Again, the value of fi is assumed to be the same for the Hiickel and Mobius systems. Zimmerman advocated this approach as a general tool in organic chemistry and called it MO following, noting that it is the molecular orbital theory counterpart to electron pushing in valence bond theory. For a discussion, see reference 172c. 

Another explanation has been proposed by K. Fukuii on the basis of frontier molecular orbitals (HOMO—LUMO) of the substrates this method is known as the frontier molecular orbitals (FMO) method. Alternatively, the PMO theory based on the Woodward—Hoffmann rule and Hiickel-Mobius method is also used to explain the results of pericyclic reactions. 

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