Why do atoms form bonds at all?

Why don't atoms just stay alone? What makes hydrogen grab hydrogen, or sodium grab chlorine, in the first place?

Systems roll downhill in energy — a ball settles in a valley, and atoms settle into arrangements where their electrons sit at lower total energy. For most atoms, being alone is not the valley.

The 'valley' usually corresponds to a full outer shell of electrons. Atoms get there in two ways: by transferring electrons outright (one atom gives, the other takes — an ionic bond) or by sharing pairs (a covalent bond). Either way, the bonded pair is lower in energy than the two loose atoms, and the difference is released — which is why forming bonds gives out energy and breaking them costs energy.

Ionic bonding: a metal with low ionisation energy (e.g. Na) transfers electrons to a nonmetal with high electron affinity (e.g. Cl); the resulting Na⁺ and Cl⁻ ions are held by electrostatic attraction in a lattice.

Covalent bonding: two nuclei share an electron pair; the shared electrons spend time between the nuclei, attracting both inward. The H₂ molecule sits about 436 kJ/mol lower in energy than two separate H atoms — that depth is what we call the bond energy: the H–H bond energy is 436 kJ/mol.

The octet rule (8 outer electrons, 2 for hydrogen) is a useful guide to which configurations are low-energy, though the deeper criterion is always minimum total energy — which is why exceptions to the octet rule exist.

Sodium chloride: Na ([Ne]3s¹) hands its lone outer electron to Cl ([Ne]3s²3p⁵). Both ions now have noble-gas configurations, and the +/− attraction locks them into the NaCl crystal. The energy released per mole formed from the ions (the lattice energy) is what makes table salt so stable and high-melting.

• Saying atoms 'want' full shells — atoms don't want anything; full shells simply correspond to lower-energy arrangements, and lower energy wins.
• Thinking energy is released when bonds break. It's the reverse: breaking bonds always costs energy; a reaction releases heat only when the new bonds formed are stronger than the ones broken.

• NCERT Class 11 Chemistry, Ch. 4 — Chemical Bonding and Molecular Structure
• Khan Academy — Chemical bonds