Why do elements on the right side of the periodic table tend to form covalent bonds with each other

TLDR: Stability of molecules and compatibility.

Energy is the universal "policeman" that dictates the natural order; every activity that has ever been performed, every breath that you take, every action that will continue throughout the lifetime of the universe is governed by energy - how much is present, and how much of that energy it takes to perform work.

When elements attempt to form more complex structures, simple limitations inhibit their capacity to do so; electrons and protons attract to one another, but two electrons together and two protons together repel one another. It is for this reason that nothing is ever considered "stable". The atoms that comprise your screen allowing you to read this text are emitting energy from an excited state in a particular fashion, and you are using your own energy to interpret these words.

Binding atoms together require an action to offset these counteracting principles; protons are relatively large and bulky, and they are combined with neutrons by the nuclear force, meaning that they really can't move around in any fashion; electrons, however, can move much more freely. When messing with left-bound elements on the periodic table, these compounds tend to want to get rid of electrons to achieve the stable octet; in doing so, they can't bind with another one like them to become stable, it'll just become much worse. Instead, they can bind with an element that is electron-affinitive and completely give that second element the electron to make both of them stable.

Elements on the right side of the table, however, are a little more complex. Because it's easier to fill the rest of the shell rather than remove a bunch of electrons like a left-bound element (remember that electrons and protons attract, meaning that it takes A LOT of energy to change the atom in that fashion), these right side elements will actively seek out free electrons as well as other electron-dense atoms to bind to. Instead of trading electrons like a left-bound atom would, these two electron-dense atoms can "share" those electrons to make them both stable. Keep this in mind:

-electron sharing between a left-right molecule: not good, the left-bound atom wants to get rid of those electrons.

-electron sharing between a right-right molecule: much better, both of these atoms need the electrons for themselves but sharing can make both of them more stable

If you tried to form an ionic bond between two right molecules, you'd be stabilizing one of them but jeopardizing the other by depriving it of those electrons it needs for stability. Thus, covalent bonding increases the stability of those right-right molecules and proves to be much more compatible instead of forcing an ionic bond or not bonding altogether.

Hope this helps, sorry for rambling a little bit!

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