Free-electron molecular orbital method

Free Electron Molecular Orbital method colour and constitution, 1, 342 Freelingyne occurrence, 4, 706 Free radical processes in photography, 1, 387-389 Friedlander synthesis quinolines, 2, 443 thioindigo dyes, 4, 910 Fries rearrangement chroman-4-one synthesis from, 3, 850 Fructose, 1-deoxy- C NMR, 4, 575 Frusemide as diuretic, 1, 174 metabolism, 1, 245 FS-32 — see 1/f-Indazole, l-[3-... 

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. 

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... 

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. 

In the case of ethylene the a framework is formed by the carbon sp -orbitals and the rr-bond is formed by the sideways overlap of the remaining two p-orbitals. The two 7r-orbitals have the same symmetry as the ir 2p and 7T 2p orbitals of a homonuclear diatomic molecule (Fig. 1.6), and the sequence of energy levels of these two orbitals is the same (Fig. 1.7). We need to know how such information may be deduced for ethylene and larger conjugated hydrocarbons. In most cases the information required does not provide a searching test of a molecular orbital approximation. Indeed for 7r-orbitals the information can usually be provided by the simple Huckel (1931) molecular orbital method (HMO) which uses the linear combination of atomic orbitals (LCAO), or even by the free electron model (FEM). These methods and the results they give are outlined in the remainder of this chapter. 

A convenient orbital method for describing eleetron motion in moleeules is the method of molecular orbitals. Molecular orbitals are defined and calculated in the same way as atomic orbitals and they display similar wave-like properties. The main difference between molecular and atomic orbitals is that molecular orbitals are not confined to a single atom. The crests and troughs in an atomic orbital are confined to a region close to the atomic nucleus (typieally within 1-2 A). The electrons in a molecule, on the other hand, do not stick to a single atom, and are free to move all around the molecule. Consequendy, the crests and troughs in a molecular orbital are usually spread over several atoms. 

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. 

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