The Free-Electron Molecular Orbital Method

Using the FEMO method, calculate the wavelength of the light absorbed when 1,3-butadiene makes the transition from the ground-state to the first excited state. 

This is in fairly poor agreement with the experimental value of 217 nm, but it is remarkable that the agreement is not worse than this. Better results could be attained by adding more or less than a full bond length at each end of the carbon-carbon chain. 

Modify the length of the hox to recover the experimental wavelength of 217 nm for 1,3-butadiene. What liaction of a hond added at the ends of the box does this correspond to Could this fraction be negative  

36 Using the same value of p as obtained for benzene in Exanple 21.10, find the wavelength of the lowest-energy electronic transition in 1,3-butadiene according to the Hiickel method. Compare with the expalmental value of 217 nm. 

37 Using the same bond lengths as with 1,3-butadiene, find the reciprocal wavelength of the longest-wavelength electronic transition of 1,3,5-hexatriene according to the FEMO method. Compare with the experimental value, 24,000 cm- . 

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The generalized free electron molecular orbital method (G-FEMO) gives a good description of the ground state properties of imidazole and yields equivalent results299 to Hiickel molecular orbital calculations. 

The simplest semiempirical w-electron theory is the free-electron molecular-orbital (FE MO) method, developed about 1950. Here the interelectronic repulsions l/r,y are ignored, and the effect of the cr electrons is represented by a particle-in-a-box potential-energy function V" = 0 in a certain region, while V = oo outside this region. With the interelectronic repulsions omitted, in (16.1) becomes the sum of Hamiltonians for each electron hence (Section 6.2)... 

The idea we are describing is called the Free Electron Molecular Orbitals (FEMO) method. 

The simplest molecular orbital method to use, and the one involving the most drastic approximations and assumptions, is the Huckel method. One str ength of the Huckel method is that it provides a semiquantitative theoretical treatment of ground-state energies, bond orders, electron densities, and free valences that appeals to the pictorial sense of molecular structure and reactive affinity that most chemists use in their everyday work. Although one rarely sees Huckel calculations in the resear ch literature anymore, they introduce the reader to many of the concepts and much of the nomenclature used in more rigorous molecular orbital calculations. 

There are other methods. For a discussion of the free-electron method, see Streitwieser Jr., A. Molecular Orbital Theory for Organic Chemists Wiley NY, 1961, p. 27. For the nonpairing method, in which benzene is represented as having three electrons between adjacent carbons, see Hirst, D.M. Linnett, J.W. J. Chem. Soc., 1962,1035 Firestone, R.A. J. Org. Chem., 1969, 34, 2621. 

Compound 41 can be expected to be the strongest 77-acid of the compounds 40, 41, and 43. It has been found84 that 41 is considerably more easily reduced polarographically than 40, and it is worth noting that the energy of the LFMO (lowest free 77-molecular orbital) of the model of compound 41 is substantially lower than that of 40 (Fig. 5). Much attention has been paid61 to the electronic structure of 44, and models of 49 and 50 have been studied by the HMO method. In structural formulas 49 and 50, X represents (CH3)2N, CH3, CF8, and CN. 

A mathematical analysis of all four isomeric thiadiazoles by the simple molecular orbital method has provided molecular diagrams of the free base and conjugate acid of each thiadiazole, with electron densities, bond orders, and free valencies. On this basis, predictions have been made concerning the reactivities of the six non-equivalent carbon atoms, the basicities of the nitrogen atoms, and the delocalization energies in these molecules. The 5-position in free 1,2,4-thiadiazole should possess maximum reactivity in nucleophilic substitution reactions. The treatment also accounts for the order of the polarographic half-wave potentials and the position of the absorption maxima in the ultraviolet region of the spectra of 1,2,4- and 1,3,4-thiadiazoles.4... 

Both singlet and triplet states are generated by the orbital promotion of an electron, n- -it transitions are totally allowed. These energy values can also be calculated from HQckel molecular orbital (HMO) method. For benzene, the free electron perimeter model has been found to be useful. The energy levels and nodal properties of benzene molecule are given in Figure 2.19. 

A basis set may be employed that is of the same form throughout the space of the system, or one in which the orbitals are expanded in different types of basis functions in different parts of space. Such partitioned bases are often used in solid-state calculations in which one must describe an overall wave function that is rapidly varying near the nuclei and slowly varying and free-electron-like when far from the nuclei. Such partitioned bases will be considered further in our discussion of band-theoretical calculations and the multiple-scattering Xa molecular-orbital method. 

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