READING Mendeleevs Periodic Table

Mendeleev s paper did not evoke much interest either when it was published two months later in the journal of the Chemical Society. However, matters were different when Mendeleev published another paper, The Natural System of the Elements, two years later. This paper, which contained a revised periodic table (Mendeleev now listed elements in vertical columns rather than horizontal rows), had a much greater response. Russian chemists read it with great interest, as did foreign chemists when the paper was translated into German the same year. 

For chemists working with several elements, the periodic chart of the elements is so indispensable that one is apt to forget that, far from being divinely inspired, it resulted from the hard work of countless chemists. True, there is a quantum mechanical basis for the periodicity of the elements, as we shall see shortly. But the inspiration of such scientists as Mendeleev and the perspiration of a host or nineteenth-century chemists provided the chemist with the benefits or the periodic table about half a century before the existence of the electron was proved The confidence that Mendeleev had in his chart, and his predictions based on it, make fascinating reading.16... 

The periodic table shown in Figure 3.14 is on the end wall of the four storey building in which Mendeleev worked from 1893 onwards. It was erected in 1934 to celebrate the centenary of Mendeleev s birth. The title is written in Russian Cyrillic script and reads Periodic System of Elements, D.l. Mendeleev. The elements whose symbols are blue were discovered between Mendeleev s death in 1907 and 1934. Blanks were left for francium and astatine, still to be discovered. J represents iodine and A represented argon until 1958. At the bottom of the periodic table are the group formulas for the hydrides and oxides, emphasizing that the table is based on chemical properties. 

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. 

In recent years, the present authors have developed an interest in obtaining chemical information from atonic density functions. The application of concepts from quantum chemistry shows that some particular aspects of physical and chemical interest can be read from the density functions. In particular the comparison of density functions using quantum similarity measures or functionals from information theory plays an important role. The original goal of the work was to find a way of regaining the periodicity in Mendeleev s table through the comparison of density functions. 

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