One-electron theory

As mentioned above, HMO theory is not used much any more except to illustrate the principles involved in MO theory. However, a variation of HMO theory, extended Huckel theory (EHT), was introduced by Roald Hof nann in 1963 [10]. EHT is a one-electron theory just Hke HMO theory. It is, however, three-dimensional. The AOs used now correspond to a minimal basis set (the minimum number of AOs necessary to accommodate the electrons of the neutral atom and retain spherical symmetry) for the valence shell of the element. This means, for instance, for carbon a 2s-, and three 2p-orbitals (2p, 2p, 2p ). Because EHT deals with three-dimensional structures, we need better approximations for the Huckel matrix than... 

One-electron pictures of molecular electronic structure continue to inform interpretations of structure and spectra. These models are the successors of qualitative valence theories that attempt to impose patterns on chemical data and to stimulate experimental tests of predictions. Therefore, in formulating a one-electron theory of chemical bonding, it is desirable to retain the following conceptual advantages. 

Quantum Theory of the DNA Molecule (Lowdin). New Developments in the One-Electron Theory of v- 8 163... 

One-Dimensional Plasma (Prager). One-Electron Theory of w-Electron Systems, New Develop- 4 201... 

The remaining difficulties in solving the L.C.A.O. problem were left by rather trivial assumptions such as the neglect of electron repulsion (one-electron theory), of overlap and of long-range (non-bonding) interactions. 

Karplus and Pople 55>, using one-electron theory, have shown that, to a first approximation, the 13C chemical shift at a carbon atom A may be calculated by the following expression ... 

All conclusions, drawn before the importance of Planck s quantum of action was appreciated, were strictly qualitative. Introduction of the quantum condition was Bohr s innovation, and it could have been more effectively combined with Nagaoka s stable orbits, rather than with electrodynamically unstable orbits. Whereas Bohr s was a one-electron theory, Nagaoka proposed a model for all atoms, with electrons spread across a set of concentric rings. Developing this into a quantum model remains an intriguing possibility. 

The One-Electron Mechanism. Both the electric and magnetic dipole transitions reside in the same chromophore. The rest of the dissymmetric molecule acts as a perturbing field which partially breaks down the symmetry of the chromophore, and therefore mixes the two transitions. The one-electron theory is also known as the Condon, Altar, and Eyring theory. 

One-electron theory is typically applied to molecules in which the chromophore is only part of the whole molecule. This chromophoric part is locally symmetric, but the entire molecule is dissymmetric. It is the dissymmetric perturbation of the locally symmetric chromophore by the rest of the molecule that induces the optically active absorption bands. An example of such a molecule is (+)-3-methylcyclohexanone, in which the lowest energy transition is the n-it transition which is centered on the carbonyl group [31]. Locally, this carbonyl group is symmetric, and without the perturbing effects of the rest of the molecule, it would be optically inactive like formaldehyde. However, the coulombic field of the methyl group statically perturbs the carbonyl group and the subsequent mixing causes the transition to become... 

Absorption of the X-ray makes two particles in the solid the hole in the core level and the extra electron in the conduction band. After they are created, the hole and the electron can interact with each other, which is an exciton process. Many-body corrections to the one-electron picture, including relaxation of the valence electrons in response to the core-hole and excited-electron-core-hole interaction, alter the one-electron picture and play a role in some parts of the absorption spectrum. Mahan (179-181) has predicted enhanced absorption to occur over and above that of the one-electron theory near an edge on the basis of core-hole-electron interaction. Contributions of many-body effects are usually invoked in case unambiguous discrepancies between experiment and the one-electron model theory cannot be explained otherwise. Final-state effects may considerably alter the position and strength of features associated with the band structure. 

Calculations for the oxide XANES are clearly less developed than for metals, where the one-electron theory is adequate. 

Interaction is a two-orbital, four-electron one. It is destabilizing, repulsive, as 55a shows. In one-electron theories, this is where steric effects, lone pair repulsions, and the like are to be found.11 41 These interactions may be important. They may prevent bonding interactions and from being realized. There is a special variant of this interaction that may occur in the solid but is unlikely to occur in discrete molecules. This is sketched in 55b—the antibonding component of a four-electron, two-... 

We shall not specify further the screened Coulomb interaction Uirn) which is taken to be some average of the true configuration dependent operator, as discussed in Sect. 5 instead it will be more illuminating to develop a one-electron theory of Vl p that parallels... 

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