Quantitative Property-Periodicity Correlations

There raises the idea that the atomic number has to be related, in principle, with all physical and chemical properties an atomic stmcture carries, or in a more phenomenological order, it appears as an effect or as a consequence of a certain existential elemental property. From this remark until the endeavor of viewing Z as the atomic activity/property that may be cast in terms of a plethora of structural indices is just a step and this is to be unveil in this communication, while testing one particular quantitative structure-property relationship (QSPR) for certain element leads, in fact, with testing the elemental periodicity of the Periodic System along a given period (Putz et al., 2011). 

The streamline of QSPR analysis resides in evaluating the coefficients of the expansion 

Quantum Nanochemistry—Volume II Quantum Atoms and Periodicity 

The results are presented in Tables 4.19-4.21, where the obtained QSPR equations are supplemented with the associate correlation factors (r) and tested for the remaining element of each considered period Ne (Z=10), Ar (Z=18), Sc (Z=21) for the second, third and transitional metals from the forth period, respectively. Individually, the predicted Z in Tables 2.19-4.21 reveals the important feature of the atomic structure that the electronegativity and chemical hardness related indices are the most appropriate for modeling the periodicity, beside the expected Z=Z(A) relationship, when combined both the closest computational result respecting the observed one with the highest correlation factors (Putz et al., 2011). 

Conversely, there was shown that the so-called macroscopic physicochemical structural features such as melting or boiling point or density are not the best indicators for rational ordering of the elemental periodicity this perhaps in all these cases all atomic electrons and levels are perturbed or regarded as equivalent when averaging for density, in contrast with the electronic frontier behavior quantified by electronegativity and related reactivity indices. 

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The extrema of Vs(r) are, however, only the beginning of the useful information that can be gleaned from it. The question is how to characterize the key features and overall pattern of Vs(r) sufficiently to permit quantitative correlations with physical properties. Over a period of several years, we have identified a group of statistically-defined quantities that are effective for this... 

However, the long range effectiveness of polymer additives remains, due to the mechanical degradation, a hitherto unsolved problem. By application of the above-mentioned theoretical approaches and the influence of laminar and elongational flow on polymer stability described in Sect. 6.3.4, it seems possible to retain the flow features over a longer period. It is therefore necessary to reinforce investigations which enable a more quantitative description of turbulent flow, so that in the future structure-property relationships can be established which permit a correlation of the microscopic structure of the macromolecules with the observed flow phenomena. 

Calculations using the methods of non-relativistic quantum mechanics have now advanced to the point at which they can provide quantitative predictions of the structure and properties of atoms, their ions, molecules, and solids containing atoms from the first two rows of the Periodical Table. However, there is much evidence that relativistic effects grow in importance with the increase of atomic number, and the competition between relativistic and correlation effects dominates over the properties of materials from the first transition row onwards. This makes it obligatory to use methods based on relativistic quantum mechanics if one wishes to obtain even qualitatively realistic descriptions of the properties of systems containing heavy elements. Many of these dominate in materials being considered as new high-temperature superconductors. 

Ionic potential — Function defined by = zjr, where z and r are the valence and radius of an ion, respectively. This function was introduced by G.H. Cartledge [i,ii], who used it as a quantitative basis of the periodic classification of elements. The ionic potential is directly connected with the heat of hydration of ions (see - Born equation), and thus related to the heat of solution of salts, acidic properties of ions, and others. It is also known that the ionic potential is correlated with electrochemical redox potentials (e.g., for solid metal hexacyanomet-allates [iii]). 

Metal electrodes are divided into 4 groups in accordance with the product selectivity indicated in Table 3. Pb, Hg, In. Sn, Cd, Tl, and Bi give formate ion as the major product. Au. Ag, Zn. Pd, and Ga, the 2nd group metals, form CO as the major product. Cu electrode produces CH4, C2H4 and alcohols in quantitatively reproducible amounts. The 4th metals, Ni, Fe, Pt, and Ti. do not practically give product from CO2 reduction continuously, but hydrogen evolution occurs. The classification of metals appears loosely related with that in the periodic table. However, the correlation is not very strong, and the classification such as d metals and sp metals does not appear relevant. More details of the electrocatalytic properties of individual metal electrodes will be discussed later. 

The fundamental issue of elemental periodicity is here addresses through quantitative-structure-property-relationship (QSPR) by assuming the atomic number as the atomic activity/property to be correlated with structural indicators, among which those relating with outermost orbitals, electronegativity, chemical hardness, ionization potential and electronic... 

Therefore, the statistical quantitative structure-property relationship (QSPR) methodology may be undertaken towards checking the elemental periodicity on the 2nd, 3rd, and transitional 4th chemical periods through correlating the atomic order s number Z with various physical-chemical properties, including various formulations for electronegativity and chemical hardness. 

On the experimental side much more numerous and more accurate data are required. It will be necessary to know with exactitude how Z>, Dq and E in the expression D = vary with composition in alloy systems. Many more selfdiffusion coefficients obtained by the radioactive indicator method are required. The connections between polarisation, atomic radius and density, position in the periodic table, alloy formation, melting-point, and degree of lattice loosening must be placed upon a more quantitative basis than the present data permit. When these properties have been correlated among themselves, and with existing X-ray data on crystal structure, it should be possible to understand more clearly phenomena of diffusion in metallic and non-metallic lattices. 

In chapter 2 we provided the justification for the single-particle picture of electrons in solids. We saw that the proper interpretation of single particles involves the notion of quasiparticles these are fermions which resemble real electrons, but are not identical to them since they also embody the effects of the presence of all other electrons, as in the exchange-correlation hole. Here we begin to develop the quantitative description of the properties of solids in terms of quasiparticles and collective excitations for the case of a perfectly periodic solid, i.e., an ideal crystal. 

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