Free-electron molecular-orbital

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-... 

Investigations of vinyl derivatives, however, show a stronger interaction between the oleflnic bond system and the Si—Si bond87-181>4"). This interaction was also theoretically substantiated by an antisymmetrized free-electron molecular-orbital method1 s 5 and HUckel molecular orbital (HMO) calculations confirm these results457. ... 

V-UV Application First Excited State of Linear Polyenes. The first electronic absorption band of perfect linear aromatic polyenes (CH)X, or perfect polyacetylene shifts to the red (to lower energies) as the molecule becomes longer, and the bond length alternation (BLA) would be zero. This was discussed as the free-electron molecular orbital theory (FEMO) in Section 3.3. If this particle-in-a-box analysis were correct, then as x > oo, the energy-level difference between ground and first excited state would go to zero. This does not happen, however first, because BLA V 0, next, because these linear polyenes do not remain linear, but are distorted from planarity and linearity for x > 6. 

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. 

Space does not unfortunately permit more than a mention of the free-electron molecular orbital theory and its application to the spectra of unsaturated hydrocarbons and heteromolecules. The very recent calculations of Ham and Ruedenberg on unsaturated hydrocarbons cover a more extensive range than the LCAO calculations of Pariser, with which they agree very well. It seems fair, however, to say that in spite of brilliant exploratory work in this field the free-electron theory in its present form still lacks foundations as secure as those which have now been provided for the LCAO theory. A particular difficulty in the free-electron molecular orbital theory is the proper inclusion of electron repulsion various ways have been devised of introducing it into the theory but the validity of these expedients still rests on goodwill rather than on rigor. Nevertheless the free-electron theory, in the hands of Platt and Kuhn, has already pointed the way to a sound theory of the spectra of linear and branched systems, and there seems little doubt that the next few years will witness advances in the theory of d)re spectra - as important as those which have already occurred in the theory of simpler molecules. 

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)... 

FEMO Free Electron Molecular Orbitals rr - electrons in a molecule treated as iree... 

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

FEMO free electron molecular orbital Hacac acetylacetone... 

In the free-electron molecular orbital model, the electrons actually move in three dimensions. For 1,3-butadiene represent the electrons as particles in a three-dimensional box with a length in the x direction equal to 694 pm, width in the y direction equal to 268 pm, and height in the z direction equal to the width. Find the wavelength of the photons absorbed in the longest-wavelength absorption due to changes in the quantum numbers Uy and n. Explain why the representation as a one-dimensional box can successfully be used to understand the near-ultraviolet spectrum. 

---