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I am trying to teach myself about Electron Ionization, and am very confused about the formation of the CH4+ Ion.

enter image description here

Do the dotted lines between the C and the H, and between the two Hydrogens indicate a resonance structure of sort? I have taken organic chemistry, but cannot wrap my head around this.

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The dotted lines in this structure could be thought of as partial bonds. In other words, none of those three bonds has a bond order of 1 with two electrons attributable to that bond.

Another way to look at this structure is that the dashed lines represent multicenter bonding. A common example of multicenter bonding is diborane $\ce{B2H6}$. The structure of diborane features 3-center-2-electron bonds (often abbreviated 3c2e bonds - in this notation, a typical single sigma bond is a 2c2e bond) with two hydrogen atoms shared by both boron atoms: enter image description here

These bonds in $\ce{CH4+}$ could be considered a 3-centered-3-electron bond as originally each C-H bond would have had two electrons. The radical cation is one electron short, so there are only three electrons shared between those three atoms.

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