Quantum similarity measures particular cases

In previous papers [1,2] the authors have worked out the theoretical foundation of Quantum Similarity (QS). In this paper, several practical results will be listed. All of them came from some of the Quantum Similarity Measures (QSM) defined previously and are particular cases of the general QSM definition obtained in reference [1]. 

Abstract This contribution reviews a selection of findings on atomic density functions and discusses ways for reading chemical information from them. First an expression for the density function for atoms in the multi-configuration Hartree-Fock scheme is established. The spherical harmonic content of the density function and ways to restore the spherical symmetry in a general open-shell case are treated. The evaluation of the density function is illustrated in a few examples. In the second part of the paper, atomic density functions are analyzed using quantum similarity measures. The comparison of atomic density functions is shown to be useful to obtain physical and chemical information. Finally, concepts from information theory are introduced and adopted for the comparison of density functions. In particular, based on the Kullback-Leibler form, a functional is constructed that reveals the periodicity in Mendeleev s table. Finally a quantum similarity measure is constructed, based on the integrand of the Kullback-Leibler expression and the periodicity is regained in a different way. 

The analysis of atomic density functions can be furthered by comparing them in pairs. Specifically, the use of quantum similarity measures and indices as defined by Carbo [5] has shown that particular influences on the density functions can be estimated in this way. Here this feature is demonstrated by reviewing three case studies (1) the LS -term dependence of Hartree-Fock densities, (2) the comparison of atoms throughout the periodic table [6], and (3) the quantitative evaluation of the influence of relativistic effects, via a comparison of non-relativistic Hartree-Fock densities with Dirac-Hartree-Fock relativistic densities [7]. 

After discussing the definition of atomic density functions, quantum similarity measures are introduced and three case studies illustrate that specific influences on the density function of electron correlation and relativity can be quantified in this way. Although no periodic patterns were found in Mendeleev s table, the methodology is particularly successful for quantifying the influence of relativistic effects on the density function. 

A general definition of the Quantum Molecular Similarity Measure is reported. Particular cases of this definition are discussed, drawing special attention to the new definition of Gravitational-like Quantum Molecular Similarity Measures. Applications to the study of fluoromethanes and chloro-methanes, the Carbonic Anhydrase enzyme, and the Hammond postulate are presented. Our calculations fully support the use of Quantum Molecular Similarity Measums as an efficient molecular engineering tool in order to predict physical properties, lMok>gical and pbarraacdogical activities, as well as to interpret complex chemical problems. 

NOx as it is in the gas phase, in spite of the fact that the nature of nitrate at the ice surface is not well established. Recent spectroscopic experiments indicate that nitrate exists at the ice surface in solvated form with a local environment similar to that in concentrated solution [302]. Still, this does not rule out a reduced solvent cage compared to dilute nitrate solution that would allow NO2 to escape, more likely due to recombination being suppressed, as has been suggested based on quantum yield measurements for frozen nitrate solutions [192]. Since in snow the nitrate anion is often co-located with other ions, e.g., halogenide ions, in a brine solution, ion specific effects may lead to enhancement of nitrate ions at the aqueous brine-air interface. Such effects have been shown to lead to enhanced nitrate photolysis rates in aqueous solution [303, 304]. In some contrast to the case of H2O2, the particular enviromnent in snow or ice makes photolysis of nitrate more efficient than in solution. Such effects would help to explain the significant cycling of NOx mediated by nitrate photolysis in polar snow [276, 298, 305-308]. 

In steady-state PL, the shape of the spectrum is determined by the level of excitation intensity as the defect-related PL often saturates at power densities on the order of to 10 Wcm, and the overall PL spectrum may be skewed in favor of the excitonic emission at higher excitation densities. Similarly, focusing the laser beam and using small monochromator slit widths would also skew the PL in favor of excitonic transitions. In such a case, the chromatic dispersion of the lenses used to collect the PL, as well as the different effective sizes of the emission spots for the ultraviolet (UV) and visible emission attributed in particular to photon recycling process [24], may lead to a noticeable artificial enhancement of the UV (near band edge) over the visible part in the PL spectrum (mainly defect related). Qualitative terms such as "very intense PL attesting to the high quality of the material are omnipresent in the literature on ZnO. In contrast to the wide use of PL measurements, relatively little effort has been made to estimate the absolute value of the PL intensity or its quantum efficiency (QE) for a quantitative analysis. 

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