Covalent Bond
A covalent bond forms when two atoms share one or more pairs of electrons, the type of bond found in water, carbon dioxide, and most molecules.
Definition
A covalent bond is when two atoms share electrons instead of one taking them, and the shared electrons hold both atoms together. It forms when two nonmetal atoms share a pair of electrons so that each reaches a full outer shell; a single bond shares one pair, a double bond two, and a triple bond three, and the resulting molecular compounds generally have lower melting and boiling points than ionic compounds and do not conduct electricity. The bond arises from the overlap of atomic orbitals, which lets a shared electron pair be attracted to both nuclei and lowers the energy of the system: sigma bonds form from end-on overlap and pi bonds from side-on overlap of $p$ orbitals, so a double bond is one sigma plus one pi and a triple bond is one sigma plus two pi. Bond polarity depends on the electronegativity difference, and molecular orbital theory describes bonding and antibonding combinations whose occupancy gives the bond order.
Example
In a water molecule, the oxygen atom shares electrons with two hydrogen atoms, and neither one gives up its electrons. Oxygen gas, $O_2$, has a double bond, since each oxygen has $6$ valence electrons and shares $2$ pairs to reach $8$; nitrogen gas, $N_2$, has a triple bond, and methane, $CH_4$, has four single bonds from carbon to hydrogen. The $N$-$N$ triple bond in $N_2$ has a bond energy of $945\text{ kJ/mol}$ and a length of $110\text{ pm}$, versus $418\text{ kJ/mol}$ and $125\text{ pm}$ for the double bond and $160\text{ kJ/mol}$ and $145\text{ pm}$ for the single bond, and that strength is why nitrogen gas is inert enough to dilute the oxygen we breathe and why nitrogen fixation requires either enzymes or the high pressures of the Haber process.
Key Insight
Covalent bonds usually form between two nonmetals, and since neither atom wants to give electrons away, sharing is the compromise. When atoms with different pulling power share electrons, the sharing is unequal and one end of the bond becomes slightly negative, which is why water is polar and sticks to itself, and why ice floats. Lewis proposed the shared electron pair in 1916, a decade before quantum mechanics could explain why sharing lowers energy; the explanation is that a shared electron's wavefunction spreads over two nuclei, reducing its kinetic energy while keeping it close to positive charge.