The Symmetry of Electron Configurations

The ground-state configuration of N2, with its 14 electrons, is read from Fig. 3.5 to be  

The notation just introduced is rather more than a convenient shorthand for specifying which orbitals are occupied and by how many electrons. It expresses the fact that the MO approximation to the molecular wave function is a product of one-electron wave functions, i.e. orbitals, each taken to a power equal to the number of electrons occupying it. We recall that the irreducible representation of a product of coordinates is the direct product of their irreps extending the same idea to the product of orbitals, we see that the irrep of an electron configuration is simply the direct product of the irreps of its occupied 

Chapter 3. Diatomic Molecules and their Molecular Orbitals 

Two more points should be noted before going on to characterize the configurations fully by symmetry species  

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Figure 2. New proposed form of the periodic table based on symmetry of electronic configurations and quantum numbers.

So that for the fixed nuclear configuration which defines the molecule s symmetry, the change of electronic configuration caused by H, - X l( leaves K i unchanged. The rest of the proof of eqn (8-2.14) is the same as the proof of eqn (8-2.15). 

The application of MOssbauer spectroscopy to silicate mineralogy has been well described in two papers by Bancroft et al, in which the influences of electronic configuration, oxidation state, and coordination symmetry of the iron cations were correlated firstly with silicates of known structures [212], and latterly with silicates of unknown and complex structures [213]. Most of the data discussed here are taken from these works, but references are given where appropriate to other data available. Silicate minerals of lunar origin are discussed on p. 294. 

In summary, a high-spin state results from dispersion or 3d electrons to all orbitals and a low-spin state is due to 3d electrons being restricted to low-energy orbitals. The microstates of electron configuration can be determined by electron spin resonance and by Mossbauer spectroscopy (recoil-free y-ray resonance absorption), procedures that provide additional information about the redox state of the metal center, spin configuration, symmetry of the ligand field, and type of ligand [2]. 

Aspects of the Jahn-Teller symmetry argument will be relevant in later sections. Suppose that the electronic states aie n-fold degenerate, with symmetry at some symmetiical nuclear configuration Qq. The fundamental question concerns the symmetry of the nuclear coordinates that can split the degeneracy linearly in Q — Qo, in other words those that appeal linearly in Taylor series for the matrix elements A H B). Since the bras (/1 and kets B) both transform as and H are totally symmetric, it would appear at first sight that the Jahn-Teller active modes must have symmetry Fg = F x F. There... 

Electronic absorption spectra are produced when electromagnetic radiation promotes the ions from their ground state to excited states. For the lanthanides the most common of such transitions involve excited states which are either components of the ground term or else belong to excited terms which arise from the same 4f" configuration as the ground term. In either case the transitions therefore involve only a redistribution of electrons within the 4f orbitals (i.e. f—>f transitions) and so are orbitally forbidden just like d—>d transitions. In the case of the latter the rule is partially relaxed by a mechanism which depends on the effect of the crystal field in distorting the symmetry of the metal ion. However, it has already been pointed out that crystal field effects are very much smaller in the case of ions and they... 

The periodic table may be seen to take on a more symmetrical or systematic form with respect to these numbers if the elements are arranged so that the alkaline earths occur at the right-hand edge of the table as shown below. It is claimed that in the conventional form of the periodic table the inherent symmetry in electronic configurations is not emphasized and that the order of filling of electronic orbitals takes on a puzzling form (15). The proposed new fdps version shown in... 

X-ray absorption spectroscopy combining x-ray absorption near edge fine structure (XANES) and extended x-ray absorption fine structure (EXAFS) was used to extensively characterize Pt on Cabosll catalysts. XANES Is the result of electron transitions to bound states of the absorbing atom and thereby maps the symmetry - selected empty manifold of electron states. It Is sensitive to the electronic configuration of the absorbing atom. When the photoelectron has sufficient kinetic energy to be ejected from the atom It can be backscattered by neighboring atoms. The quantum Interference of the Initial... 

High-valent iron can occur in a wide variety of electronic configurations. Figure 8.25 (a-c, e-i) presents a summary of the corresponding one-electron crystal-field states for the 3(/, 3J, and 3J electron configurations, allocated to HS and LS states in distorted octahedral and tetrahedral symmetry. Part d, in addition, depicts the case of low-low-spin iron(IV) found in some trigonal... 

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