Knight’s move

This is the operation of clockwise rotation by 2w/ about an axis followed by reflection in a plane perpendicular to that axis (or vice versa, the order is not important). If this brings the molecule into coincidence with itself, the molecule is said to have a n-fold alternating axis of symmetry (or improper axis, or rotation-reflection axis) as a symmetry element. It is the knight s move of symmetry. It is symbolized by Sn and illustrated for a tetrahedral molecule in Fig. 2-3.3.f... 

The child s mind is autistic, a rich texture of free synthesis, hal1 uncinatory and unlimited. His mind can skip over syllogisms with ease, in a non-logical, dream-sequence kind of "knight s move" continuum. He nevertheless shows a strong desire to participate in a world of others. 

Maturity, or becoming reality adjusted, restricts and diminishes that "knight s move" thinking, and tends to make pawns of us in the process. The kind of adult logic that results is dependent on the kinds of demands made on the young mind by parents and society. 

Thought disorder manifest by failure in the organisation of speech such that it drifts away from the point (tangentiality), never reaches the pome (circumstantiality), moves from one topic to the next illogically (loosened associations, knight s move chinking), breaks off abruptly only to continue on an unrelated topic (derailment) or moves from one topic to the next on the basis of a pun or words which sound similar (clang association). 

The trends within rows and columns of the periodic table are quite well known and are not repeated here. Instead, I concentrate on a number of other chemical trends, some of which challenge the form of reductionism that attempts to provide explanations based on electronic configurations alone.In the case of one particular trend described here, the knight s move, the chemical behavior defies any theoretical understanding whatsoever, at least at the present time. 

The knight s move relationship is perhaps the most mysterious one among all the unusual relationships involving the periodic table (figure 10.11). It takes its name from the knight s move in the game of chess, meaning a move of one step in any... 

FIGURE 10.11 Elements that show knight s move relationships. For example, zinc and tin or silver and thaUium. 

Based on M. Laing,The Knight s Move in the Periodic Table Education in Chemistry, 36, p. 160-161,1999, table 1. 

FIGUKE 10.12 The inorganic chemist s periodic table,designed by G.Rayner Can-ham. Shadings indicate relationships ( ) and (n + 10) relationships diagonal relationships knight s move relationships aluminum—iron link actinoid relationship lanthanide-actinide relationship combination elements pseudoelements. 

Of the eight possible knights moves available in the game of chess, it appears that the chemical knight s move represents just one of these. In all cases, it involves a movement of one step down in the periodic table, followed by two steps to the right. 

Laing made the discovery of the knight s move relationship in the course of teaching a chemistry course for engineers that caused him to emphasize the similarity between zinc and tin (M. Laing, personal communication). 

M. Laing,The Knight s Move in the Periodic Table, Education in Chemistry, 36,160— 161, November 1999 M. Laing, chapter 4, in D. Rouvray, R.B. King, Patterns in the Periodic Table, The Periodic Table Into the 21st Century, Research Studies Press, Bristol, UK, 2004, pp. 123-141... 

The chemical reactions of the bromides and iodides resemble those of the chloride. Light darkens them all. The periods 3-5 anionic complexes of TC in water are less stable in the series Cl > Br > 1 . The similarities of T1 to Ag, and some resemblances of In to Cu, Sn to Zn, Pb to Cd, Sb to Ga, and Bi to In, albeit more in physical than in chemical properties, are reminiscent of the knight s move in chess [1]. 

One more periodic chart [6] shows in one place some additional similarities, mentioned separately in this text. It has the pseudohalogen CN with the halogens, NH4 with the alkali metals, and some p-block elements and early actinoids with the d-block. It also suggests the similarity of Al to Fe (as Fe ) (although it could well include Cr too), as well as some diagonal and knight s move (Cu through In, Bi etc.) relationships. We now know Uun as Ds and Uuu as Rg. See Fig. A. 11. 

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