Electronic states, relationship

Calculation of Thermodynamic Properties We note that the translational contributions to the thermodynamic properties depend on the mass or molecular weight of the molecule, the rotational contributions on the moments of inertia, the vibrational contributions on the fundamental vibrational frequencies, and the electronic contributions on the energies and statistical weight factors for the electronic states. With the aid of this information, as summarized in Tables 10.1 to 10.3 for a number of molecules, and the thermodynamic relationships summarized in Table 10.4, we can calculate a... 

Fig. 5. Relationship between the logarithm of the bond stretching force constant, f, of a sulfur-sulfur bond and the logarithm of its length, d j. The data were taken from (7 electronic states), S (in BaSj), S, Sg, Sj, S, and SgO...

Additional experimental evidence for the preservation of electronic states upon formation of molecules is the insensitivity of X-ray spectra to the chemical enviromnent of an atom, implying that the ionization potentials of inner electrons are relatively unaffected by bonding. Indeed, Moseley s classic experiments on the relationship between X-ray frequencies and atomic number were carried out on atoms in a variety of states of chemical combination. 

An X-ray atomic orbital (XAO) [77] method has also been adopted to refine electronic states directly. The method is applicable mainly to analyse the electron-density distribution in ionic solids of transition or rare earth metals, given that it is based on an atomic orbital assumption, neglecting molecular orbitals. The expansion coefficients of each atomic orbital are calculated with a perturbation theory and the coefficients of each orbital are refined to fit the observed structure factors keeping the orthonormal relationships among them. This model is somewhat similar to the valence orbital model (VOM), earlier introduced by Figgis et al. [78] to study transition metal complexes, within the Ligand field theory approach. The VOM could be applied in such complexes, within the assumption that the metal and the... 

Fradin has considered the question recently and emphasized the relationship between particular measurements and the way they project out the localized and the band nature of the 5f electron states. 

Local chemical composition from areas less than 1 nm in diameter can be measured by energy dispersive X-ray spectroscopy (EDS) or electron energy loss spectroscopy (EELS). Such spectroscopic information may be presented in 2D maps showing the spatial element distribution in the specimen (13). Furthermore, information about the local density of unoccupied electron states of a specific element can be extracted from EELS data and used to estimate the oxidation state and the local coordination geometry of the excited atoms (14). In some favorable cases, electronic structure information with a resolution of about 1 eV from individual atomic columns has been attained (15,16). Recent developments of monochromators and spectrometers have brought the resolution down to 0.1 eV (17,18), and this capability may offer new opportunities to determine relationships between electronic structure information, the atomic arrangements and the catalytic activities of solids. 

One may argue that for molecular systems in their ground electronic state, an eigenstate has no obvious relationship to a chemical species. The problem of isomerism is often invoked to sustain this criticism. In the BO approach, such a criticism is sustainable [5-7] and, since current molecular theory is apart of the BO approximation scheme [8], it is the whole molecular theory which would require anew foundation. This amounts to defining the molecular structure problem from a different perspective, as it is discussed in the following sections. 

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