= Phosphoric anhydride
A \b[phosphoric anhydride] contains an acid-anhydride linkage involving <phosphoric acid>. One type joins two phosphoric groups through <oxygen>, giving P–O–P connectivity. A mixed anhydride joins a phosphoric group to a different acid-derived group, such as one derived from a <carboxylic acid>. These are distinct from the P–O–C connectivity of a <phosphoric ester>.<Nomenclature of Phosphorus-Containing Compounds of Biochemical Importance by IUPAC and IUBMB>[§3, phosphoric anhydrides, types(a) and(b)]{ref}
A formal neutral-molecule balance illustrates the first type:
$$
2\,\mathrm{H_3PO_4}\rightleftharpoons
\mathrm{H_4P_2O_7}+\mathrm{H_2O}.
$$
Two phosphorus centers remain, but one oxygen now bridges them. Both sides contain six hydrogens, two phosphorus atoms and eight oxygens. This is an atom balance, not a claim that dilute aqueous <phosphoric acid> spontaneously undergoes substantial condensation. Actual speciation and reaction direction depend on conditions.
The P–O–P connections between phosphoric groups in <ATP> illustrate anhydride connectivity, whereas the connection from its sugar to the first phosphoric group is an ester linkage.<Nomenclature of Phosphorus-Containing Compounds of Biochemical Importance by IUPAC and IUBMB>[§3 and Table2, ATP and other oligophosphoric esters]{ref} One molecule can therefore contain more than one linkage class. Identifying the atoms on either side of a bridging <oxygen> is more informative than merely counting its phosphorus atoms.
<Hydrolysis> changes both chemical connectivity and the surrounding solution's products. Whether it releases useful free energy is a property of the whole reaction under its stated conditions, rather than energy being released by breaking an isolated bond alone.
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