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Ideal gaseous phosphorus pentachloride is a trigonal bipyramid with D3h molecular point group symmetry. There are five chlorine sites and three 3p orbitals per site, hence a fifteen-dimensional basis. A moved atom contributes zero to the character; each fixed chlorine contributes the trace of the three-dimensional polar-vector matrix acting on its local p orbitals.For example, a $C_2^{\prime }$ axis through one equatorial chlorine fixes that site but rotates its p-vector basis with trace $1-1-1=-1$. Counting that atom as $+1$ would be incorrect.

Apply molecular character reduction with class sizes $(1,2,3,1,2,3)$ and group order twelve:For $A_1^{\prime }$, this gives $(15-3+3+9)/12=2$; for $E^{\prime }$, $(30+6)/12=3$. The full result isThe dimension check is $2+1+6+2+4=15$. As an additional transparent separation, the two axial chlorines supply $A_1^{\prime }+E^{\prime }+A_2^{\prime \prime }+E^{\prime \prime }$, while the three equatorial ones supply $A_1^{\prime }+A_2^{\prime }+2E^{\prime }+A_2^{\prime \prime }+E^{\prime \prime }$. These are all chlorine 3p orbitals, including both radial and tangential functions; a five-orbital ligand-sigma basis would answer a different question.

Prepare a chlorophosphazene ring from phosphorus pentachloride and ammonium chloride, isolate the cyclic trimer, open the rings to make the linear chloropolymer, and finally replace P–Cl by P–OEt:The first stage can produce a mixture of cyclic oligomers, so isolation of hexachlorocyclotriphosphazene is important. Controlled thermal ring-opening polymerization, conventionally around $250{}^{\circ }\mathrm{C}$ for the classical route, gives soluble linear polydichlorophosphazene before excessive cross-linking. Moisture exclusion avoids uncontrolled hydrolysis of the reactive P–Cl precursor.

The target is poly[bis(ethoxy)phosphazene]. The final step is nucleophilic substitution with an ethoxide salt in a compatible dry medium, replacing two chlorides per phosphorus. Polymerize the chlorinated ring first, then substitute the linear polymer: complete ethoxylation of the isolated ring does not by itself produce the requested high polymer. The primary macromolecular-substitution work explicitly includes the ethoxy derivative.^[ref]