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The bonding in $\ce{(NPCl2)3}$ (and other compounds of the form $\ce{(NPR2)3}$) has historically been described using the ‘Dewar island model’.

By analogy to benzene, $\ce{(NPCl2)3}$ is π-electron precise, containing 6-electrons in the π-system, and as such was thought to exhibit some degree of aromaticity.

The Dewar model accounted for this benzene-like structure by allowing phosphorous to use an occupied d-orbital to engage in a dπ(P)–pπ(N) interaction, forming the delocalised π-system of the phosphazene ring. This rationalised experimental observations that $\ce{(NPCl2)3}$ is (almost) planar and has equal P-N bond lengths which are somewhere between standard P-N (single) and P=N (double) bond lengths. What it fails to explain however is why other members of the series $\ce{(NPR2)n}$ do not show planarity.

Despite these flaws, and despite it being widely acknowledged that the d-orbitals aren’t capable of being involved in bonding to any great extent, the Dewar island model is still commonly found in inorganic chemistry textbooks and taught to undergraduates (possibly because its an easy to understand explanation and draws analogy to the familiar).

Is there a better model to explain the bonding in $\ce{(NPR2)3}$ that is (1) consistent with the observed properties of the molecule, (2) makes sense in terms of the orbitals/interactions used (i.e. no invoking d-orbitals) and (3) can be backed up by calculation? [*]

[*]: My understanding is that negative hyperconjugation can be invoked, but this doesn't seem to be widely accepted and possibly isn't the most intuitive explanation for bonding by itself.

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The bonds between the phosphorus and nitrogen in phosphazenes are best described as having a significant ionic component with each of the N atoms having a negative charge and each of the phosphorus atoms having a positive charge. There is also some negative hyperconjugation resulting from the donation of electrons from the nitrogen atoms' lone pairs to antibonding orbitals between the P atoms and the R groups. The degree of negative hyperconjugation increases with the electronegativity of the R groups and it imparts a partial double bond character to the bonds between the P and N atoms. For more information see http://pubs.acs.org/doi/abs/10.1021/ic0511266

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    $\begingroup$ It would be nice if you could summarise how the authors got to this conclusion. $\endgroup$ – orthocresol Nov 25 '17 at 15:35

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