Quantum numbers, chemical conventions

The conventional chemical nomenclature for these orbitals is given on the right hand side, and the X-ray nomenclature used in Auger spectroscopy appears on the left. The designation of levels to the K, L, M,... shells is based on their having principal quantum numbers of 1,2,3,... respectively. 

Theories of chemical bonding based on the properties of degenerate states with fixed I assume independent behaviour of the electrons in these states. In particular, for three electrons in the three-fold degenerate /i-state with 1=1, they are assumed to have distinct values of m, without mutual interference. To make this distinction it is necessary to identify some preferred direction in which the components of angular momentum are quantized. By convention this direction is labeled as Cartesian Z. If the electrons share the degenerate p-state with parallel spins, they must share the same direction of quantization. This being the case, only one of the electrons can have the quantum number m = 0, characteristic of the real function (7). 

Overall the present article seeks to meld chemical graph-theoretic (chemicalbonding) ideas with conventional quantum-chemical approaches, all within the framework of traditional VB theory here extended to encompass more recent results and models. Thence use is made of some quantum-chemical nomenclature, which, however, is standard fare in any of a number of quantum chemistry texts, though they seldom seriously discuss VB models for Jt-network systems. Some effort is made to incorporate solid-state theoretic results on one of the models which has arisen with different applications in mind. As such, the present article offers a novel global perspective which (as is so often the case) emphasizes the author s own work in the area. 

In spite of the impressive progress which has been achieved with conventional ab-initio methods as the Configuration-Interaction or Coupled-Cluster schemes in recent years density functional theory (DFT) still represents the method of choice for the study of complex many-electron systems (for an overview of DFT see [1]). Today DFT covers an enormous variety of fields, ranging from atomic [2,3], cluster [4,5] and surface physics [6,7] to the material sciences [8-10]. and theoretical biophysics [11-13]. Moreover, since the introduction of the generalized gradient approximation DFT has become an accepted method also for standard quantum chemical applications [14,15]. Given this tremendous success of nonrelativistic DFT the question for a relativistic extension (RDFT) arises quite naturally in view of the large number of problems in which relativistic effects play an important role (see e.g. Refs.[16,17]). 

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