The first ionization energy of hydrogen is $1312\;\mathrm{kJ\cdot mol}^{-1}$, which is larger than that of halogens such as chlorine, bromine, and iodine.

Given that observation, why don't halogens form $\ce{X+}$ ions like $\ce{H+}$?

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    $\begingroup$ It is a subtle matter. The halogens do exist in the +1 oxidation state, for example, in $\ce{OCl-}$. However, you aren't likely to see a naked $\ce{X+}$ cation. It is electron-deficient and would greatly prefer to form a bond to something else. "Well, why does hydrogen form $\ce{H+}$ then?" In fact, the naked $\ce{H+}$ ion does not exist either. In water, any naked $\ce{H+}$ ion will immediately form $\ce{H3O+}$. We only write $\ce{H+}$ as shorthand notation for "a Bronsted acid"; $\ce{H+}$ itself does not actually exist. Not in solution, at least. $\endgroup$
    – orthocresol
    Nov 4 '15 at 13:55
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    $\begingroup$ @orthocresol What if we consider a case other than solution? $\endgroup$ Nov 4 '15 at 14:00
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    $\begingroup$ Even in superacidic media people have problems formulating true $\ce{H+}$. Superacids will protonate just about anything, showing how very unhappy the hydrogen would be to form a $\ce{H+}$ ion. $\ce{CH5+}$, anyone? $\endgroup$
    – Jan
    Nov 4 '15 at 14:03
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    $\begingroup$ One context where $\ce{X+}$ form fairly readily is in ionizing plasma. But, just about everything forms cations in ionizing plasma, so ... $\endgroup$
    – hBy2Py
    Nov 4 '15 at 14:05
  • $\begingroup$ Iodine does form some compounds of $\ce{I+}$ in which it acts kinda like a metal. $\endgroup$ Nov 4 '15 at 14:22

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