Trends in pi backbonding for main group elements across a period

Recently, I have been re-reading some undergraduate notes and found that there's a period trend in pi backbonding of main group elements (i.e. no transition metals involved) but no explanation were given other than it correlates with the increase in number of nonbonding pairs (lone pairs?):


$\pi$ backbonding strength: Si>P>S>Cl.


While it is well known that the lewis acidity of boron halides are explained by the strength of $\pi$ backbonding which decreases down the *group*, the same kind of explanation cannot be used for period trends like those above (especially B-P, B-S and B-Si are almost unheard of to check that) as across a period,orbitals in the same principal quantum number will be involved mainly in bonding, thus we should not expect a large difference in the size of the orbitals across a period and hence their extent of overlap due to spatial overlap alone.


In [Chemwiki usdavis](http://chem.libretexts.org/Textbook_Maps/Inorganic_Chemistry_Textbook_Maps/Map%3A_Inorganic_Chemistry_(Wikibook)/Chapter_05%3A_Coordination_Chemistry_and_Crystal_Field_Theory/5.04%3A_%5C(%5Cpi%5C)-bonding_between_metals_and_ligands) an explanation of the periodic trend for the same ligand but different *metals* were provided as an increase in the energy gap of the d, $\pi^\*$ orbitals. However since we are not talking about d orbitals here, that is not very relevant


I suspect that since periodic trends have orbital energies in general decreases across the period, that it might be down to the increase in energy gap of the overlapping orbitals in the $\pi$ bonding between a given electron deficient atom and the donor atom of the type listed above. However this explanation has a problem in that the role of nonbonding pairs are not accounted for in the trend. I then suspect it might be due to an increase in repulsion of the nonbonding pairs, but a repulsion argument seemed to be too simple to explain since the oribtals involve in the same period should have roughly the same size



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> What is the mechanism or underlying explanation of $\pi$ backbonding periodic trends in main group chemistry?
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