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Andreas Orthaber, Ferdinand Belaj and Rudolf Pietschnig, Comptes Rendus Chimie 13 (2010), 923–928. Section 3.2 analyses the strongly polar P–O sigma bond and oxygen lone-pair negative hyperconjugation; this is not a claim that every orbital-localization scheme assigns the same bond order.

Negative hyperconjugation is donation from an occupied lone-pair or related orbital into an antibonding sigma orbital. Nitrogen-to-P–X sigma-star donation contributes to phosphazene bonding. Short P–N bonds therefore do not require a model dominated by phosphorus $3d$ pi orbitals.

In a boroxine, each boron has three sigma bonds and is approximately trigonal planar, with an $s{p}^2$ description for its sigma framework and an available perpendicular $2p$ orbital. oxygen can be described approximately as $s{p}^2$: two in-plane hybrids form B–O sigma bonds, one contains an in-plane lone pair, and a perpendicular $2p$ lone pair overlaps with neighbouring boron $2p$ orbitals. These three oxygen donor pairs supply a six-electron pi system around the alternating ring. The combination of good same-shell overlap and a low-strain six-membered ring favours planarity and partial B–O multiple-bond character. The bonds remain polar; a six-electron diagram alone does not establish benzene-like aromatic stabilization quantitatively.

In a siloxane, each silicon instead has four sigma bonds, two to oxygen and two to its organic groups, giving an approximately tetrahedral $s{p}^3$ sigma framework. oxygen has two sigma bonds and two lone pairs, so an approximately $s{p}^3$ localized description is a useful starting point, although actual Si–O–Si angles and lone-pair hybrids vary considerably. There is no comparable ring of vacant silicon $2p$ orbitals. A description based on strong oxygen-$2p$ to silicon-$3d$ pi bonds is also misleading: those orbitals have poor energy and radial matching. Strongly polar Si–O sigma bonding, supplemented by negative hyperconjugation from oxygen lone pairs into appropriate Si–R antibonding orbitals, gives a better account. The ring can therefore pucker rather than requiring continuous planar pi overlap. This follows the broader conclusion that strong main-group bonds and apparently expanded valence do not imply dominant valence $d$-orbital participation.^[ref]

$\mathrm{OP}(\mathrm{OMe}{)}_3$ also has approximately tetrahedral molecular geometry at phosphorus, now with three P–O–C sigma linkages and a terminal phosphoryl O. Only the latter is being compared with the terminal O of Me${}_3$PO; the three P–O–C bonds are chemically distinct.

The electronegative alkoxy substituents withdraw electron density from P and improve its capacity to accept donation from terminal O into the surrounding antibonding framework. The elementary substituent argument therefore predicts a stronger, stiffer terminal P–O bond in $\mathrm{OP}(\mathrm{OMe}{)}_3$ than in $\mathrm{M}{\mathrm{e}}_3\mathrm{PO}$. A description invoking polar bonding and negative hyperconjugation avoids assigning a literal localized d-orbital double bond solely because the formula is written P=O.

Measure the terminal P–O stretching vibration by infrared or Raman spectroscopy under comparable, non-hydrogen-bonding conditions. In an approximate local-mode comparison the reduced mass is the same, so a larger terminal stretching wavenumber indicates a larger force constant, $k\propto {\tilde{\nu }}^2$. Mode assignment can be checked by ${}^{18}$O substitution at the terminal oxygen or by a normal-mode calculation; otherwise an alkoxy P–O–C vibration could be compared by mistake. X-ray diffraction can supply a supporting bond-length comparison, but neither bond length nor a single coupled vibrational frequency directly measures an isolated bond-dissociation enthalpy.

The unequal P–N distances reflect unequal local bonding interactions in the alternating-chain conformation, rather than an extended conducting P=N pi system. nitrogen is much more electronegative than phosphorus, so the backbone sigma bonds are strongly polar. nitrogen lone-pair density can also donate into appropriately oriented antibonding P–substituent orbitals: negative hyperconjugation, schematicallyThe strengths of these interactions depend on the orientation of the donor and acceptor orbitals. In a planar cis–trans backbone, the P–N links are not all geometrically equivalent. Different overlap and charge redistribution give alternating greater and smaller effective P–N bond orders, hence shorter and longer bonds. A formal alternating P=N/P–N drawing is a useful shorthand for this inequality, but does not imply that isolated textbook single and double bonds are present with no electronic communication.

The historical island picture captures the limitation of pi interaction to local P–N–P regions rather than a continuous band along the whole chain. A modern description need not invoke strong phosphorus $3d$–nitrogen $2p$ bonding; polar bonding and donation into sigma-star orbitals provide the useful explanation. Calculations on oligomers found bond alternation for planar cis–trans conformations but not for optimized helices. Bond alternation is therefore conformation dependent, not a universal consequence of the repeat formula alone.^[ref]

The six P–N bonds are not well described as three permanently localized single bonds alternating with three ordinary double bonds. The strongly polar P–N framework has contributions from ionic bonding and nitrogen lone pair donation into neighboring phosphorus-centered acceptor combinations, including P–Cl ${\sigma }^{\ast }$ orbitals. This negative hyperconjugation supplies additional P–N bonding and equivalent environments around the ring. Approximate planarity is compatible with these interactions, but equal lengths and planarity alone do not establish benzene-like aromaticity. Large phosphorus $3d$ participation is not required.^[ref]

Gallium binds to a ring nitrogen, and the two P–N bonds flanking that nitrogen lengthen. Formation of the N$\to$GaCl${}_3$ coordinate covalent bond changes the available nitrogen electron density and local geometry, weakening its contribution to the adjacent P–N interactions. The other four P–N bonds retain greater multiple-bond character and are correspondingly shorter. Loss of the threefold equivalence and altered local geometry permit the ring to pucker. This is a Lewis acid-base adduct, not replacement of a P–Cl bond by GaCl${}_3$. Single-crystal structures and variable-temperature multinuclear nuclear magnetic resonance establish this class of nitrogen-bound group-13 adducts.^[ref]

A phosphazene contains phosphorus–nitrogen bonding often represented with formal P=N units. Ionic bonding and negative hyperconjugation provide a modern account; formal double-bond drawings do not require phosphorus $3d$ pi bonding.