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A covalent bond is pictured as two electrons shared by two different atomic nuclei, which means that each of the two nuclei has two electrons. The problem I see with it is that it implies that if a hydrogen atom is neutral then a hydrogen nucleus in a covalent bond must be negatively charged since it has one more electron than a hydrogen atom. Which implies that a hydrogen molecule is negatively charged which is a contradiction (molecules are neutral).

Alternatively, one can say that the covalent bond is composed out of a single electron, which acts as a negative potential for both hydrogen nuclei hence it exerts negative potential of two in the molecule. But then the question is, where does the second electron go when two hydrogen atoms form a covalent bond?

My question does not relate only to this specific example, it's about covalent bonds in general.

enter image description here

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  • $\begingroup$ You are overthinking it. A covalent bond kinda "consists of" two electrons, but it belongs jointly to two atoms. $\endgroup$ – Ivan Neretin Oct 16 '17 at 14:44
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    $\begingroup$ This would be an extremely conservative view saying that a covalent bond consists of two electrons (Lewis mad that famous). However, bonding interactions are not localised and it is impossible to tell how many electrons form a bond; or what is a bond in the first place. In this specific example though, there are two protons, two electrons, everything is neutral. By necessity the bond consists of two electrons. $\endgroup$ – Martin - マーチン Oct 16 '17 at 14:44
  • $\begingroup$ @Martin-マーチン What you say is reasonable. I was interpreting the pictures literally since both atoms are removed an equivalent distance apart from the electrons. So, I assume, I must see the electrons completely delocalized? There is no geometry involved then? $\endgroup$ – mechanicious Oct 16 '17 at 14:50
  • $\begingroup$ As you may know, electrons are not only particles. They are not at all like in the picture $\endgroup$ – Martin - マーチン Oct 16 '17 at 14:53
  • $\begingroup$ @Martin-マーチン Is the covalent bond formed because it is energetically optimal for both atoms? $\endgroup$ – mechanicious Oct 16 '17 at 15:12
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The bond in your picture is made up of two electrons, and in the Lewis formalism so is every single bond. Yet there is no negative charge. We can think of this in two ways:

  1. Remember that the bond electrons are shared. So each atom contributed one electron and, upon dissociation, would usually take back that one electron. Counting only that one electron will give a neutral hydrogen atom, not a hydride ion.

  2. Charges on an atomic or molecular level are due to a mismatch of the numbers of protons and electrons. In the hydrogen molecule, you have two nuclei consisting of one proton each, meaning an overall $2+$ charge. Furthermore, you have two electrons that get shared in the covalent bond giving an overall $2-$ charge. $+2 + -2 = 0$, so the overall molecule is neutral.

    If you wanted to place both electrons on one atom to form a hydride anion, that would mean the other atom is left with zero. Instead of a hydrogen molecule $\ce{H-H}$ you would have a separated ion pair $\ce{\overset{-}{H}\bond{...}\overset{+}{H}}$.

Once you leave the very simplified Lewis formalism and turn to theories such as molecular orbital theory which explain molecules much more accurately, this way of thinking will be lost altogether since there is no longer an obvious localisation of two electrons to a single bond.

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