Periodic table/system representation

E. G. Mazur.S, Graphic Representation of the Periodic System during One Hundred Years, University of Alabama Press. Alabama, 1974. An exhaustive topological classification of over 700 forms of the periodic table. 

It should also be said that the reason why Bent and Weinhold devote such attention to the n + ( rule is that, as mentioned earlier, the rule is clearly represented on the left-step table, the form of the periodic table that they favor. In addition, as was mentioned, the authors believe that the best representation of the periodic system should be based on the electronic structure of the neutral atoms of all the elements and not on their macroscopic properties. 

Subgroup. A subdivision of a vertical group in the periodic system of the elements, made necessary in order to group together similar elements in the short-period representation. The long-period table has no subgroups. 

In Fig. 2 is an attempt to give a general idea of how far the enumerations of benzenoid isomers have been advanced up to now. The position of a formula C HS in the dot-diagram representation of the periodic table is marked by an asterisk if the corresponding numbers of isomers are known (at least) for the Kekulean and non-Kekulean systems separately. 

The accuracy of calculations on transition metal systems has lagged behind that of the first and second rows of the periodic table.One problem for the transition metal compounds is that an SCF wave function is often a much poorer representation of the system than for those compounds only composed of first- and second-row elements. In fact, for some transition metal systems, large CASSCF calculations are required even for a qualitatively correct description, and a quantitative description requires lengthy Cl expansions. In addition to extensive n-particle basis requirements, experience has shown that transition metals also require considerably larger one-particle basis sets than for the first and second rows. As transition metals have such stringent one- and n-particle requirements, FCI benchmark calculations and ANO basis sets have given considerable insight into how to improve the accuracy of calculations on transition metal systems. 

Figure 10.1 shows the corresponding section of the periodic table. Pressure-induced superconductors are marked by a solid triangle. One may notice that instead of La the last rare earth metal Lu appears below Y in the third column. This is different from standard representations of the periodic system. The reason for this exchange will be given in section 3.3. 

Perhaps this is a good place to discuss some other points of terminology. How is a periodic table different from a periodic system The term periodic system is the more general of the two. The periodic system is the more abstract notion that holds that there is a fundamental relationship among the elements. Once it becomes a matter of displaying the periodic system, one can choose a three-dimensional arrangement, a circular shape, or any number of different two-dimensional tables. Of course, the term table strictly implies a two-dimensional dimensional representation. So although the term periodic table is by fiu- the best known of the three terms law, system, and table, it is actually the most restricted. 

Another recent departure has been the invention of periodic tables designed to summarize the properties of compounds rather than elements. In 1980, Ray Hef-ferlin produced a periodic system for aU the conceivable diatomic molecules that can be formed between the first 118 elements. In order to represent this vast number of entries, Hefferlin used four three-dimensional blocks of varying sizes. His representation reveals that interatomic distances, spectroscopic frequencies, and molecular ionization energies are periodic properties. It also provided successful predictions regarding the properties of diatomic molecules. 

But I conclude with a less controversial proposal. Let us imagine that the various representations of the periodic system he on a continuum. At one end of thk continuum is the unruly Rayner Canham table (figure 10.14) that attempts to do justice to many unusual relationships of the kind that have been highhghted in this chapter. At the other end of the continuum hes what I call the Platonic periodic table, or what is usually called the left-step or Janet periodic table (figure 10.13). Somewhere near the middle of thk continuum of representations, one can locate the currently popular medium-long representation. It is not altogether surprising that thk fbrm has been so popular since it appears to capture the correct... 

The final comment k rather controversial, with many chemists believing that there k no one best representation.These authors consider representation to be a secondary issue, which is dictated by convention.The present author takes issue with this view and supports a more realist interpretation whereby the grouping of troublesome elements such as hydrogen has an objective aspect and is not merely a manner of convenience. See E.R. Scerri,The Best Representation of the Periodic System The Role of the n + /Rule and the Concept of an Element as a Basic Substance, in D. Rouvrary, R.B. King (eds.). The Periodic Table Into the 21st Century, Science Studies Press, Bristol, 2004,143—160. 

While on this subject, it should be remembered that Mendeleev rendered a great service which has not really been heeded. Although he considered various possible representations he also emphasized that the important aspect of the periodic system was the existence of the periodic law. The fact that Mendeleev attached so much importance to the periodic law, qua law, has been especially stressed by Bernadette Bensaude-Vincent in her many articles on the periodic table (Bensaude-Vincent, Mendeleev s Periodic System ). 1 believe that she is correct to do so and that the modem tendency to not even mention the periodic law, as such, is regrettable. The reason for this omission is presumably because of the prevalent notion that this law has now been explained away by the deeper laws of quantum mechanics (Scerri, Explanation ). This is just not true and 1 will return to the issue later in this article. 

So I would like to see this representation used as a challenge to theoretical chemists and physicists and to serve as a reminder of a feature that is not yet fully explained from quantum mechanics. Rather than claiming that the periodic table does not reduce to quantum mechanics I am really trying to encourage physicists to dig deeper and give an even more reductionist explanation of the periodic system. 

When all is said and done, I suppose I am still maintaining that the model or the representation of the periodic table is indeed secondary. From a theoretical point of view it is a means to an end since the goal is a theoretical deduction of the observed facts. To the chemist of course representation must offer something useful which suits his or her particular purpose. So the demand for representation, not surprisingly is context dependent. It depends on what purpose one is putting the periodic system to. 

The periodic table is a physical representation of two more abstract notions, namely the periodic law and the periodic system, both of which are more fundamental that the familiar periodic table. Nevertheless, the terms periodic table and periodic system will be used somewhat interchangeably in what follows. 

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