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I have often wondered about diagonal relationships between elements on the periodic table, and the most often cited explanations revolve around charge-density considerations.

But other than that, what other factors could possibly contribute to this phenomenon?

EDIT: What I mean by "diagonal relationships" is that there are certain similarities in chemical properties that have been observed in diagonally adjacent neighbors in the 2nd and 3rd period example: Li-Mg, Be-Al, and B-Si.

Link to a wikipedia article (not much to be found here though)

The explanation that I personally have most often encountered is that the charge-to volume ratios (charge density), say for Li-Mg cations is roughly the same, and hence could account for some of the similarities in behaviors.

What I am looking for is what can be some other contributing factors (if any) to this phenomenon. I am not expecting very concrete answers because I believe this phenomenon is not very well understood.

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  • $\begingroup$ What do you mean by the "phenomenon" of "diagonal relationships"? How are "charge-density" considerations involved? All elements have at least one diagonal neighbor. $\endgroup$ – Curt F. Jun 8 '15 at 22:04
  • $\begingroup$ I looked up the term on Wikipedia: en.wikipedia.org/wiki/Diagonal_relationship You might want to link to or refer to this restricted definition in the Q. $\endgroup$ – Curt F. Jun 8 '15 at 22:04
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What I remember from studying C-P 'diagonal relationships' (for multiple bonds e.g. carbene vs phosphinidene, alkyne vs phosphaalkyne) is that similar electronegativity also played a role, also by affecting the valence orbitals.

However, perhaps it is better viewed from a different vantage point: the main group elements behave rather similarly from 3rd row onwards, but there is a distinct difference between the 2nd and 3rd row elements and the explanation is pretty straightforward: The 2s and 2p orbitals are roughly similar in 'size' since the 2p orbitals are the first p-orbitals and are pretty compact. Therefore 2s and 2p orbitals mix happily. Going to the third row, the 3p orbitals need to be orthogonal to the 2p orbitals and as a consequence they are much more diffuse than the 3s orbitals, resulting in less efficient s-p hybridization. This also manifests itself in the so-called 'inert pair' effect whereby e.g. Si will resist hybridization in favor of a lone pair. There is some beautiful work by Knutzelnigg from the 80s (?) describing these effects. This 2nd-3rd row discrepancy is somewhat counterbalanced if you step to right, increasing Z and thereby contracting the orbitals giving rise to this apparent diagonal relationship.

Similar arguments make that for the 3d TMs the hybridization is more efficient for 4s-3d than for the 4d/5d TMs. Consequently, 3d TMs tend to behave differently from their heavier sisters, which in turn are closer together (although for the 5d's the relativistic effects start to kick in more heavily...).

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The diagonal relationship is not a very good way to group elements, it makes sense only if we consider highly polar or ionic compounds. when you take compounds of 2nd and 3rd period following diagonal relationships where they are having their max oxidations state, the charge to volume ratio of the atoms/ions become more or less similar. Also when there is lot of positive charge on an atom say al3+, its orbitals become shorter and hence the bonding orbitals overlap in a similar ways as it does in the diagonally related 2nd period element(be2+). Hence the nature of compounds and the way the diagonally related elements react is similar.

EDIT: by Be2+ and Al3+ i am trying to say that Be is in +2 oxidation state and Al is in 3+ state

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