Figure 10.5 Comparative nonrelativistic and relativistic energies for the s- and p-orbitals of tin and lead (adapted from Ref. [26]).
As can be seen, there is a small (yet significant) decrease in the energy of the 5s orbital for tin while there is a dramatic decrease in the energy of the 6s orbital for lead, that is, the 6s2 electron pair is exceptionally strongly bound to the nucleus. Thus, it would seem that there is indeed a satisfactory explanation for most aspects of the knight’s move relationship.
Commentary
The indication of a periodic pattern is the consistent applicability of a phenomenon to a subset of the Periodic Table of Elements. On this basis, the justification of the knight’s move relationship should be made primarily on the basis of similarities in formulas and chemistry of compounds of knight’s move pairs of elements in the lower right quadrant of the Periodic Table.
Though there are a few specific resemblances in melting and boiling points among pairs of “Knight’s Move” compounds, they are not widespread and consistent enough to be regarded as evidence of a systematic pattern. Thus, it is the chemical, rather than the physical, properties that should be emphasized as evidence for this relationship.
References
1.M. Laing, “The Knight’s Move in the Periodic Table,” Educ. Chem. 36, 160–161 (1999).
2.J. Shorter, “Vernon Harcourt: A Founder of Chemical Kinetics and a Friend of ‘Lewis Carroll’,” J. Chem. Educ. 57, 411–416 (1980).
3.M. C. King, “The Chemist in Allegory: Augustus Vernon Harcourt and the White Knight,” J. Chem. Educ. 60, 177–180 (1983).
4.L. Carroll, More Annotated Alice: Alice’s Adventures in Wonderland and Through the Looking Glass and What Alice Found There, with notes by Martin Gardner; Random House, New York, 277 (1990).
5.R. Eichler et al., “Indication for a Volatile Element 114,” Radiochim. Acta 98, 133–139 (2010).
6.D. H. Rouvray and R. B. King (eds.), The Periodic Table: Into the 21st Century, Research Studies Press Ltd., Hertfordshire, England, 135–136, 177–179 (2004).
7.E. R. Scerri, The Periodic Table: Its Story and Its Significance, Oxford University Press, New York, NY, 272–275 (2007).
8.G. B. Kauffman and L. M. Kauffman, “Michael J. Laing (1937–2012), Obituary of a Lovable, Inspirational Inorganic Chemist, Chemical Educator, and Science Popularizer,” Chem. Educ. 20, 183–193 (2015).
9.F. J. Arnáiz, “The Preparation of TlBF4,” J. Chem. Educ. 74(11), 1332–1333 (1997).
10.J. L. Lambert and M. W. Lambert, “The Alums: Interchangeable Elements in a Versatile Crystal Structure,” J. Chem. Educ. 47(6), 465 (1970).
11.K. T. Douglas, M. A. Bunni, and S. R. Baindur, “Thallium in Biochemistry,” Int. J. Biochem. 22(5), 429–438 (1990).
12.G. Rayner-Canham and M. Oldford, “The Chemical ‘Knight’s Move Relationship: What Is Its Significance?” Found. Chem. 9, 119–125 (2007).
13.J. C. Bailar et al., (eds.), Comprehensive Inorganic Chemistry, Pergamon Press, Oxford (1973).
14.F. A. Cotton, G. Wilkinson, C. A. Murillo, and M. Bochmann, Advanced Inorganic Chemistry, 6th ed., Wiley-Interscience, New York, NY (1999).
15.N. N. Greenwood and A. Earnshaw, Chemistry of the Elements, 2nd ed., Butterworth-Heinemann, Oxford (1997).
16.A. G. Massey, Main Group Chemistry, 2nd ed., John Wiley, Chichester (2000).
17.M. Laing. “The Periodic Table — A New Arrangement,” J. Chem. Educ. 66, 746 (1989).
18.Ref. 16, A. G. Massey, p. 174.
19.Ref. 16, A. G. Massey, p. 208.
20.R. C. Brasted, Comprehensive Inorganic Chemistry, vol. 8, Van Nostrand, New York, NY, 250 (1961).
21.A. S. Bahrou et al., “Volatile Dimethyl Polonium Produced by Aerobic Marine Microorganisms,” Environ. Sci. Technol. 46(20), 11402–11407 (2012).
22.N. V. Sidgwick, The Electronic Theory of Valency. Clarendon Press, Oxford, 178–181 (1927).
23.L. E. Orgel, “The Stereochemistry of B Subgroup Metals. Part II. The Inert Pair,” J. Chem. Soc. 3815–3819 (1959).
24.R. S. Drago, “Thermodynamic Evaluation of the Inert Pair Effect,” J. Phys. Chem. 62(3), 353–357 (1958).
25.K. S. Pitzer, “Relativistic Effects on Chemical Properties,” Acc. Chem. Res. 12, 271–276 (1977).
26.P. Pyykkö, “Relativistic Effects in Structural Chemistry,” Chem. Rev. 88(3), 563–594 (1988).
27.J. S. Theyer, “Relativistic Effects and the Chemistry of the Heaviest Main-Group Elements,” J. Chem. Educ. 82, 1721–1727 (2005).
Chapter 11
Isodiagonality
Diagonal relationships in the Periodic Table were recognized by both Mendeléev and Newlands. More appropriately called isodiagonal relationships, the same three examples of lithium with magnesium; beryllium with aluminum; and boron with silicon; are commonly quoted. Here these three pairs of elements are discussed in detail, together with evidence of isodiagonal linkages elsewhere in the Periodic Table.
Though the vertical groups and horizontal periods are emphasized as being the key relationships in the Periodic Table (see Chapters 7 and 8), chemistry historian Ihde has noted that both Mendeléev and Newlands had reported the diagonal similarities of lithium with magnesium; beryllium with aluminum; and boron with silicon; as early as 1860 [1].
Isodiagonality
It was in 1937 that French explored the diagonal relationship in detail. In fact, he considered diagonality to extend further down the Periodic Table [2]:
In chemical behavior, bismuth bears a much greater resemblance to silicon and boron than to nitrogen.
This diagram, from French’s article, was probably the first to illustrate the diagonal linkages (Figure 11.1).
Figure 11.1 French’s diagram of the isodiagonal linkages (from Ref. [2]).
Figure 11.2 The first three Periods of French’s slanting periodic table to illustrate group and diagonal linkages (adapted from Ref. [2] — note “A” was the former symbol for argon).
French was concerned that diagonality not be overemphasized, adding:
… silicon for instance, resembles neither carbon nor boron in chemical properties but might be said to lie between the two.
Thus, French suggested that the best mode of display of the “cross relationships” might be that shown in his “warped” Periodic Table in the following (Figure 11.2).
More recently, Rich proposed the term isodiagonal for species related on an upper-left to lower-right diagonal [3]. He subsequently authored a version of the Periodic Table to specifically emphasize isodiagonalities (Figure 11.3) [4].
Here the following definition of isodiagonal will be used:
An isodiagonal relationship is identified by similarity in chemical properties between an element and that to the lower right of it in the periodic table.
Isodiagonality is, in some ways, a general attribute of the properties of the chemical elements. For example, Edwards and Sienko commented that the metal–nonmetal divide forms an “almost
