Localized electrons, atomic description

From the early advances in the quantum-chemical description of molecular electron densities [1-9] to modem approaches to the fundamental connections between experimental electron density analysis, such as crystallography [10-13] and density functional theories of electron densities [14-43], patterns of electron densities based on the theory of catastrophes and related methods [44-52], and to advances in combining theoretical and experimental conditions on electron densities [53-68], local approximations have played an important role. Considering either the formal charges in atomic regions or the representation of local electron densities in the structure refinement process, some degree of approximate transferability of at least some of the local structural features has been assumed. 

In this paper we examined quantum aspects of special classical configurations of two-electron atoms. In the doubly excited regime, we found quantum states of helium that are localized along ID periodic orbits of the classical system. A comparison of the decay rates of such states obtained in one, two and three dimensional ab initio calculations allows us to conclude that the dimension of the accessible configuration space does matter for the quantitative description of the autoionization process of doubly excited Rydberg states of helium. Whilst ID models can lead to dramatically false predictions for the decay rates, the planar model allows for a quantitatively reliable reproduction of the exact life times. 

While the embedded atom method has been formally derived by Daw and Baskes the functions used in computer simulations are t3pically empirically determined. The description presented here will therefore treat this approach as an empirical method. The first step in determining the potential is to define a local electron density at each atomic site in the solid. A simple sum of atomic electron densities has proven to be adequate, and so in most cases a sum of free atom densities is used . The second step is to determine an embedding... 

Nano-scale and molecular-scale systems are naturally described by discrete-level models, for example eigenstates of quantum dots, molecular orbitals, or atomic orbitals. But the leads are very large (infinite) and have a continuous energy spectrum. To include the lead effects systematically, it is reasonable to start from the discrete-level representation for the whole system. It can be made by the tight-binding (TB) model, which was proposed to describe quantum systems in which the localized electronic states play an essential role, it is widely used as an alternative to the plane wave description of electrons in solids, and also as a method to calculate the electronic structure of molecules in quantum chemistry. 

To this point there has been a review of the description of the electrons on free atoms and their interaction with an external magnetic field. There has also been a discussion of the two principal approaches to a quantitative description of the outer electrons of atoms that have condensed into molecules or solids the MO or collective-electron approach and the IIL localized-electron approach. 

Biradical (Synonymous with diradical) An even-electron molecular entity with two (possibly delocalized) radical centres which act nearly independently of each other. Species in which the two radical centres interact significantly are often referred to as biradicaloids. If the two radical centres are located on the same atom, they always interact strongly, and such species are called carbenes, nitrenes, etc. The low-est-energy triplet state of a biradical lies below or at most only a little above its lowest singlet state (usually judged relative to kT, the product of the Boltzmann constant k and the absolute temperature T). The states of those biradicals whose radical centres interact particularly weakly are most easily understood in terms of a pair of local doublets. Theoretical descriptions of low-energy states of a biradical display the presence of two unsaturated valences (biradicals contain one fewer... 

---