The relationship among the standard reaction Gibbs free energy ΔG°, the standard reduction potential E°, and the atomic structure parameters of radius, nuclear charge, and isoelectronic orbitals nl is accomplished through the attraction electric force F elec. In relationship with E°, it was necessary to define two new reference scales: E 0 ° with a final state of E° in the element, which allowed to have a parabolic trend of ΔG° versus F elec, and E °,0 whose final state is the ion with a more negative charge (e.g., −1, –2, −3). The relationship with ΔG° is related to the concept of chemical stability, and the relationship with E °,0 is more related to the concept of electronegativity. In relationship with ΔG°, it was necessary to predict the values of possible new cations and noncommon cations in order to find a better trend of ΔG° versus F elec, whose stability is analyzed by Frost diagrams of the isoelectronic series. This dependence of ΔG° on F elec is split into two terms. The first term indicates the behavior of the minimum of ΔG° for each isoelectronic orbital nl, while the second term deals with the parabolic trend of this orbital. For the minima of the configuration np6, a hysteresis behavior of the minima of ΔG° is found: an exponential behavior from periods 1 and 2 and a sigmoidal behavior from periods 5 and 4 to interpolate period 3. It is also found that the proximity of unfilled np or (n + 1)s orbitals induces instability of the ion in configurations ns2/nd2/4f2 and nd10/nd8(n + 1)s2, respectively. On the contrary, the stability of the orbitals np6 does not depend on the neighboring empty (n + 1)s0 orbitals. Both phenomena can be explained by the stability of the configuration of noble gas np6 and the nd10(n + 1)s2 configuration. We have also found that it is possible to increase the reduction potential E °,0 (macroscopic electronegativity), although the electric force F elec decreases because the orbital overlap influences the electronegativity.
In this work, we propose a new representative electronegativity scale χ DC based on a statistical analysis of 11 electronegativity scales associated with electric ionic resonance energy, ionization potential, electron affinity, polarizability, electric force, average orbital energy, chemical potential, electrochemical reduction potential, and electric potential energy. Among these scales, it is the new PE° electronegativity scale, which relates the reduction potential E ° to Pauling’s electronegativity scale. The scale χ DC gives more weight to the physicochemical factors, which influence the electronegativity, but this scale is not necessarily the best electronegativity scale for the element. This scale is based on (1) the average of the experimental electronegativity values; (2) the proximity of an experimental value to the average given by the difference and the ratio to this average; (3) in critical cases, the periodicity network of the periods and the groups; and (4) the periodicity of the sequence of the ratios of the experimental electronegativity values to the best-selected electronegativity value. We have also taken as probe scales Nagle’s, Allred and Rochow’s, Allen’s (Hoffman’s and Politzer’s), PE°, Gordy’s, and Ghosh’s electronegativity scales in order to investigate the trend of the physicochemical factors which influence the electronegativity. With this trend, we have determined zones where a physicochemical property influences the electronegativity more. We have also found that physicochemical perturbations such as the orbital overlap, the stable configurations, the nephelauxetic effect, the width of the band gap, the ligand field stabilization energy, the penetration of the orbitals, and the lattice energy influence the electronegativity. Besides, we have analyzed the exactness of the electronegativity of the scales through the periodical ranking, the chemical tripartite separation among ionic, covalent, or metallic bond (taking into account the amplitude of the metalloid band), and the physicochemical property of bond force. The representative χ DC electronegativity scale is the best in periodicity, followed by Batsanov’s and Pauling’s scales. In the type of chemical bond, the ranking depends on the number and kind of compounds in the sample, but in general, Pauling’s, the ARS, and Batsanov’s electronegativity scales are the best with a confidence interval of 95%. On the other hand, in the physical bond force, Batsanov’s, Pauling’s, Mulliken’s, Nagle’s, Allen’s, the ARS, and the χ DC electronegativity scales are the best scales. Also, we have considered the free atom and the in situ hypotheses of electronegativity and used the low and high oxidation states to verify these hypotheses. Besides, as an example of the utility of this ranking of scales, we have analyzed the relation of lanthanum La and lutetium Lu to Group 3, lanthanides, and hafnium Hf. We also analyze the vertic...
The nonlinear optical (NLO) properties of meta-nitroaniline (m-NA) are evaluated via Huckel−Agrawal's approximation in a solvent environment. In this context, both the 1 B and the intramolecular charge transfer (ICT) electronic transitions are considered. The benzene ring currents on the clockwise or counterclockwise direction and the corresponding Brillouin zone from 0 to π are also considered. Besides, the Bloch equations were applied to a single cell n = 1 defined on the benzene ring. We have considered that the light beam was directed along the ring benzene bonds of m-NA; this topological hypothesis changed the crystal structure to a linear chain and the calculated optical properties were found near the experimental ones. In addition, the Fermi's golden rule was applied to the crystal state and then the calculated refraction index of m-NA had an error of less than 3% of the experimental one. On the other hand, the molar absorptivity ε of m-NA in acetonitrile for the 1 B and intramolecular ICT transitions was experimentally determined to be 11 981 and 1192 L mol −1 cm −1 , respectively. With this methodology, we found that the change of the charge in the NO 2 group has also a strong influence on the linear and NLO properties. In addition, the dipole transition moments, which are originated from the carbon between the carbons joined to NO 2 and NH 2 , are mainly involved in the NLO properties. Thus, the first hyperpolarizability β z was 1.69 × 10 −30 esu at λ Laser = 1064 nm, 27% of the experimental value. We attribute this difference to the evaluation of the excited dipole moment. If we attribute a separation of charge of 0.1 e in the excited state, the new dipole moment allows for the simulation of the experimental value. Besides, the calculated value of χ (3) for m-NA in a solution of acetonitrile is 2.9 × 10 −13 esu at λ Laser = 1064 nm, 158% of the experimental value. The discrepancy between these values is attributed to the influence of the electronic correlation effects, that is, because of resonance structures of the aromatic ring and the zwitterionic pair of nitro and aniline. Besides, we have also evaluated the second hyperpolarizability γ, the second-order susceptibility χ (2) of m-NA and their values have similar differences to the experimental values. This type of approach is important because it reduces computing time and gives insight into the molecular causes responsible for linear and NLO properties in this type of functional groups, which can be used as building blocks in more complex polymer systems.
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