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[...] Thus, it bonds to the oxygen atom of a solvent water molecule to give trigonal pyramidal hydronium ion, $\ce{H3O^+}$ $\ce{\{[H (H2O)]^+\}}$ (see box). In this chapter we shall use $\ce{H^+(aq)}$ and $\ce{H3O+(aq)}$ interchangeably to mean the same i.e., a hydrated proton.

Isn’t this the way to write coordinate compounds? This may sound dumb but is the hydronium ion a complex compound?

The box that this passage refers to:

Hydronium and Hydroxyl Ions
Hydrogen ion by itself is a bare proton with very small size (~$\pu{{e-15} m}$ radius) and intense electric field, binds itself with the water molecule at one of the two available lone pairs on it giving $\ce{H3O+}$, This species has been detected in many compounds (e.g., $\ce{H3O+Cl-}$) in the solid state. In aqueous solution the hydronium ion is further hydrated to give species like $\ce{H5O2+}$, $\ce{H7O3+}$, $\ce{H9O4+}$. Similarly the hydroxyl ion is hydrated to give several ionic species like $\ce{H3O2-}$, $\ce{H5O3-}$, $\ce{H7O4-}$, etc.

Source Chemistry Part 1, Textbook for Class XI National Council of Educational Research and Training (https://ncert.nic.in), NCERT Publications (version: October 2019 Ashwina 1941) https://ncert.nic.in/textbook/pdf/kech107.pdf

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    $\begingroup$ So... what is this question about? Notation? IUPAC rules? What is a coordination compound? $\endgroup$
    – Mithoron
    Commented Feb 8 at 15:17

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In water solution context, it is recommended and preferred to use $\ce{H+(aq)}$, as products of proton interaction with water are complex and still subject of research. $\ce{[H(H2O)]+}$ would be better to write as $\ce{[H(H2O)_n]+}$, what is nothing else than $\ce{H+(aq)}$.

An isolated, solvated hydronium is also possible in other protic solvents, where water is a minor/trace component. Hydronium is also abundant molecular ion in an interstellar space.

Solid structures with hydronium are known, like hydronium perchlorate [$\ce{H3O+}$][$\ce{ClO4-}$]. The corresponding bisulfate compound, $[\ce{H3O^+}][\ce{HSO4^-}]$, requires chilling to solidify, but even when melted the saltlike association of $\ce{H3O^+}$ and $\ce{HSO4^-}$ ions increases the viscosity and decreases the ionic conductivity of equimolar sulfuric acid-water solutions.

See hydronium and oxonium for more.

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$\ce{H3O+}$ does not exist in aqueous solution outside text books

Due to the strong hydrogen bonds the species is better described as a mixture of $\ce{H5O2+}$, $\ce{H19O9+}$ or maybe $\ce{H37O18+}$ (though I just made those up). The point is that there exists a network of regular water around this lone proton that arranges itself according to the electrostatic potential of this proton. This solvation effect has very concrete implications.

To me the $\ce{[H(H2O)]+}$ notation more strongly conveys this message. There is a free proton in there, transiently coordinated by the solvent, water. The same thing happens in other hydrated chalcogenids and halogens. $\ce{HF}$ is similarily coordinated in aqueous solutions - and this shielding contributes to the weak apparent acidity of $\ce{HF}$.

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    $\begingroup$ "H3O+ does not exist outside of textbooks". That is beyond the pale. Salts with that ion are known (and so are other salts with additional water molecules incorporated into the cation). Only in solution do the arguments given here apply. $\endgroup$ Commented Feb 8 at 11:48
  • $\begingroup$ @OscarLanzi Fair point, the idea was in aqueous solution. I'll amend. $\endgroup$
    – Stian
    Commented Feb 8 at 15:08
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    $\begingroup$ You'd think that the Grothuss mechanism would come naturally to an answer like this. And these "free" protons are far away from actually being free; they're just more mobile. I am trying to understand what you are saying, but I generally disagree with this interpretation to the point where I consider it wrong. $\endgroup$ Commented Feb 9 at 23:15

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