Bearing in mind that the charge density plots consider only the valence electrons, the fact that we observe some charge on the hydrogen atom but not on any of the others indicates that hydrogen is not ionised. That larger atoms are completely ionised is consistent with other reported experimental results [@186]. It is interesting that the same phenomenon occurs in both the cubic and hexagonal cases. The first ionisation energy of the intercalates are as follows: hydrogen 1.318 eV, lithium 0.526 eV, sodium 0.502 eV, potassium 0.425 eV, rubidium 0.409 eV, caesium 0.382 eV [@SI]. The high ionisation energy of hydrogen with respect to the other intercalates may be responsible for the differing behaviour.

![\[fig:cub\_hex\_chg\] Charge density maps of cubic (top) and hexagonal (bottom) tungsten oxide and bronzes. The largest tunnels are indicated, which are completely filled in each case. The oxygen atoms in-plane with the intercalated atom can be clearly seen, and only in the case of hydrogen is the charge still associated with the intercalated atom.](cub_hex_chg.eps){width="85mm"}

Energies of formation
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The energies of formation of the cubic and hexagonal tungsten bronzes are shown in Table \[table:bronze\_energies\] and Figure \[fig:bronze\_energ\]. These are calculated by subtracting the ground state energies 