Intraatomic interactions

This is a good discussion of the importance of intraatomic interactions in determining molecular geometry. 

Direct exchange between spins in orthogonal orbitals is a potential exchange as it does not involve electron transfer like the intraatomic interactions, it is ferromagnetic. 

The transition from localized to itinerant electronic behavior occurs where the interatomic interactions become greater than the intraatomic interactions. A measure of the strength of the interatomic interactions is the bandwidth W and of the strength of the intraatomic interactions is the energy C/eff that separates successive redox energies. The transition from localized to itinerant electronic behavior occurs where... 

The intraatomic interactions, on the other hand, are stronger the weaker the covalent mixing, which makes the on-site coulomb energies... 

The main handicap of MD is the knowledge of the function [/( ). There are some systems where reliable approximations to the true (7( r, ) are available. This is, for example, the case of ionic oxides. (7( rJ) is in such a case made of coulombic (pairwise) interactions and short-range terms. A second example is a closed-shell molecular system. In this case the interaction potentials are separated into intraatomic and interatomic parts. A third type of physical system for which suitable approaches to [/( r, ) exist are the transition metals and their alloys. To this class of models belong the glue model and the embedded atom method. Systems where chemical bonds of molecules are broken or created are much more difficult to describe, since the only way to get a proper description of a reaction all the way between reactant and products would be to solve the quantum-mechanical problem at each step of the reaction. 

The intraatomic d-d electron-electron interaction includes Coulomb and exchange interactions, and it is responsible for orbital and spin polarization. To account for orbital polarization, the idea of the LDA + U method was followed.70 A generalized Hartree-Fock approximation including all possible pairings was then used to write... 

The most important information (by Baer and Schoenes ) obtained when using the combined XPS/BIS method is the Coulomb interaction energy Uh that we have discussed in Part II. For UO2, Uh = 4.6 0.8 eV has been obtained. This large separation between the two final states (2(5f ) —> 5f + 5f ) is in itself a hint to the localized character of the 5 f states in UO2. Baer and Schoenes compared the value for Uh with theoretical values they found an agreement with Uh = 4 eV as calculated by Herbst et al. for a U" " metal core. As discussed in Chap. A, intraatomic calculations of Uh in metals possibly underestimate screening by conduction electrons nevertheless, they should be valid in the case of an insulating solid as UO2. 

The localized-electron model or the ligand-field approach is essentially the same as the Heitler-London theory for the hydrogen molecule. The model assumes that a crystal is composed of an assembly of independent ions fixed at their lattice sites and that overlap of atomic orbitals is small. When interatomic interactions are weak, intraatomic exchange (Hund s rule splitting) and electron-phonon interactions favour the localized behaviour of electrons. This increases the relaxation time of a charge carrier from about 10 s in an ordinary metal to 10 s, which is the order of time required for a lattice vibration in a polar crystal. 

Localized electrons in a partially filled shell carry a net spin (provided Hund s rule is obeyed), and interactions between these localized electrons and the collective electrons gives rise to a large effective field Hex acting on the collective electrons. Since the intraatomic exchange correlations minimize the electrostatic interactions between electrons of parallel spin, Hcx is directed parallel to the atomic moment due to localized electrons. Below a magnetic-ordering temperature, this internal field induces a contribution to the atomic moment from the collective electrons whether the localized electrons are ordered parallel or antiparallel. From equation 58, this contribution is... 

Finally, one should not overlook the possible role of correlation effects in atom-metal differences. In atoms the dominant contributions to the correlation energy arise from interaction between electrons of the same principal quantum number n, since these have the greatest overlap. As far as purely intraatomic electrons are concerned, the correlation terms differ very little between atom and metal correlation does, of course, affect interatomic screening of the final state vacancy in metals. 

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