Free, electron molecular orbital theory electrons

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. 

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)... 

The electron-sea model is a simple depiction of a metal as an array of positive ions surrounded by delocalized valence electrons. Molecular orbital theory gives a more detailed picture of the bonding in metals. Because the energy levels in a metal crowd together into bands, this picture of metal bonding is often referred to as band theory. According to band theory, the electrons in a crystal become free to move when they are excited to the unoccupied orbitals of a band. In a metal, this re-... 

The first indication of the existence of a captodative substituent effect by Dewar (1952) was based on 7t-molecular orbital theory. The combined action of the n-electrons of a donor and a captor substituent on the total Jt-electron energy of a free radical was derived by perturbation theory. Besides the formulation of this special stabilizing situation and the quotation of a literature example [5] (Goldschmidt, 1920, 1929) as experimental evidence, the elaboration of the phenomenon was not pursued further, neither theoretically nor experimentally. 

Chapter 2 introduces the band theory of solids. The main approach is via the tight binding model, seen as an extension of the molecular orbital theory familiar to chemists. Physicists more often develop the band model via the free electron theory, which is included here for completeness. This chapter also discusses electronic condnctivity in solids and in particular properties and applications of semiconductors. 

When the unpaired electron is delocalized over a number of atoms, molecular orbital theory must be applied to obtain a molecular description of the resulting magnetic species. In this situation there is less opportunity for substantial contributions from L, and in general the more delocalized the electron the more like a free electron it appears. In some cases, the electron is delocalized over only a few atoms, and in these cases modest contributions from L are expected, especially if one of the atoms is a transition metal. If more extensive delocalization is present, or if all the atoms involved are light, only small contributions (e.g., from 2fi orbitals) may be observed. 

Like benzenoid hydrocarbons, pyridine-like heterocycles give well-developed two-electron waves on reduction at the dropping mercury electrode. The latter are polarographically much more reducible than the former. This can be explained easily in terms of the HMO theory It is assumed (cf. ref. 3) that the value of the half-wave potential is determined essentially by the energy of the lowest free 7r-molecular orbital (LFMO) of the compound to be reduced, and for models of hetero analogues this quantity is always lower than that for the parent hydrocarbons. Introduction of an additional heteroatom into the molecule leads to a further enhancement of the ease of polarographic reducibility.95 On the other hand, anodic oxidation of the heterocyclic compounds is so much more difficult in comparison with benzenoid hydrocarbons that they are not oxidizable under the usual polarographic conditions. An explanation in terms of the HMO theory is obvious. 

Molecular orbital theory predicts that if the total energy of the electrons in a molecule is lower (more negative) than the total electron energy of its constituent atoms, then that molecule will be stable with respect to the free atoms. 

Figure 3.12 shows how the -electrons of the double bond of an allylic cation can move towards the carbon atom bearing the positive charge. This generates an isomeric allylic cation, with the positive charge on the opposite end of the 3-atom system. In free allylic cations, this exchange is so rapid that the two isomers are indistinguishable. In fact, in molecular orbital theory, we consider the system to consist of a single set of orbitals which stretches across all three atoms. Since there is single bond character in each of the bonds, rotation is possible and the three cations, viz. geranyl (3.22), neryl (3.21) and linalyl (3.23), become equivalent. This is often represented as a smear of electrons as shown in structure (3.24) at the foot of Figure 3.12. Therefore in reactions such as those of...

Clearly, we need to be able to construct Gaussian approximations to the atomic orbitals of atoms other than hydrogen. For applications in molecular orbital theory, we need, in addition, to make allowance for the evident fact that an atom in a molecule is in a different environment to the isolated atom in free space, since any other atoms in a molecule give rise to extra potentials disturbing the free space electron distribution for that atom. 

In the previous chapters, we discussed various models of bonding for covalent and polar covalent molecules (the VSEPR and LCP models, valence bond theory, and molecular orbital theory). We shall now turn our focus to a discussion of models describing metallic bonding. We begin with the free electron model, which assumes that the ionized electrons in a metallic solid have been completely removed from the influence of the atoms in the crystal and exist essentially as an electron gas. Freshman chemistry books typically describe this simplified version of metallic bonding as a sea of electrons that is delocalized over all the metal atoms in the crystalline solid. We shall then progress to the band theory of solids, which results from introducing the periodic potential of the crystalline lattice. 

The BDE theory does not explain all observed experimental results. Addition reactions are not adequately handled at all, mostly owing to steric and electronic effects in the transition state. Thus it is important to consider both the reactivities of the radical and the intended coreactant or environment in any attempt to predict the course of a radical reaction (31). Application of frontier molecular orbital theory may be more appropriate to explain certain reactions (32,33). Radical reactivities have been studied by esr spectroscopy (34-36) and modeling based on general reactivity and radical polarity (37). Recent radical trapping studies have provided considerable insight into the course of free-radical reactions, particularly addition polymerizations, using radical traps such as 2,4-diphenyl-4-methyl-l-pentene (a-methylstyrene dimer, MSD) (38-44) and 1,1,3,3-tetramethyl-2,3-dihydro-liT-isoindol-2-yloxyl (45-49). 

---