Quantum similarity measure framework

Remarkably, the question of quantifying similarity within a quantum mechanical framework has been addressed relatively late, in the early 1980s. The pioneering work of Carbd and co-workers [5,37] led to a series of quantum similarity measures (QSM) and indices (QSI). These were essentially based on the electron density distribution of the two quantum objects (in casu molecules) to be compared. The link between similarity analysis and DFT [38,39] built on the electron density as the basic carrier of information, and pervading quantum chemical literature at that time, is striking. 

Additional advantages have been pointed out in the Introduction. Since density domains play a major role in molecular shape analysis and in the construction of various molecular similarity measures [5], shape analysis and molecular similarity can be formulated in terms of quantum-chemically defined functional groups. This model is also compatible with a rather general, algebraic-geometrical framework discussed in ref. [6]. 

Measurements of the oxidation potentials yielded results which reflected the close proximity of the two phthalocyanine planes. The first two oxidation potentials (one-electron oxidations from each phthalocyanine ring) were 100 mV apart, suggesting the delocahzation of the cation radical over the two phthalocyanines jt-electronic framework. This behavior shows some similarity to that of the porphyrin dimers, and is expected to favor energy- and electron-transfer reactions. Another characteristic feature of this phthalocyanine dimer is that its fluorescence quantum yields are almost the same as those of the corresponding monomers (0.45, 0.26, and 0.76 for Zn(OBu), Zn(f-Bu), and Mg(f-Bu) phthalocyanines, respectively). Such a highly fluorescent phthalocyanine dimer has never been reported before. 

Abstract. Silica gel-bound crown ethers and aza macrocycles have been synthesized with the attaching arm connected to the carbon framework of the macrocycles. The interactions of these bound macrocycles with cations are almost identical to those involving the analogous free macrocycles. This has allowed for predictable cation separation, concentration, and removal processes to be performed on a small scale. Quantum mechanical calculations and NMR measurements indicate that similarly bound chiral macro-cycles will be capable of use in separating chiral organic amines. 

The paradox here is that if entropy is a state property of a system it cannot depend on what we happen to know about the system. Quantum mechanics has a similar-sounding, but quite different epistemological problem, which, in principle, placed limits on the precision by which certain pairs of properties are measured. Since measurement involves experimental design and choice of parameters of interest, in the quantum framework the observer is required to complete the phenomenon. In statistical thermodynamics, however, entropy is microscopic uncertainty and if we interpret entropy as lack of microscopic information about the macroscopic thermodynamic state we seem to get involved in the identity of that state alone, which would be a conflicting standpoint. Therefore, let us discuss all such viewpoints and inherent differences often arising from not fully congruous ideas, which try to enlighten the true interdisciplinary of the notion of entropy. 

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