A covalent bond is formed when two atoms share electrons between them. Covalent bonds typically are only formed between pairs of nonmetal atoms, for example H with Br, C with H, Cl with H, C with Cl. The simplest covalent bond is the single bond.

A single bond exists between two atoms when they share one pair of electrons. A double bond exists between two atoms when they share two electron pairs and triple covalent bond exists between atoms that share 6 electrons in three pairs. .

Graph in annimation shows how the separation between 2 H atoms changes their energy

Low energy favors stability.

The more negative the energy (energy is released) the more stable the bond. When energies are negative between two atoms this favors bond formation.

The graph below shows how the energy of two H atoms changes when the atoms approach each other. At long distance the energy is near zero. As the atoms get closer the energy decreases. The energy goes to a low point or minimum at a separation that matches the average bond length of 0.74 Angstroms and a negative energy of -436 kilojoules/ mol.

When the atoms get too close the energy increases and goes positive, above zero. If the atoms get too close the energy of repulsion gets too big. The total energy crosses over to positive energy which is unstable combination and the atoms do not form a bond.

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Bringing atoms together:

When a pair of atoms are brought close to each other the electric fields around the positively charged nuclei and around the negatively charged electrons interact.  These interactions change the energy of the atoms. The positively charged nuclei attract the negatively electrons and energy is released. The energy of the 'system goes down because of these attractions.

Remember particles with the same sign electrical charge repel one another. This means the positively charged nuclei repel each other and the negatively charged electrons repel each other.

The size of these energies and forces changes as the atoms are brought closer and closer.

If the total energy reaches a minimum that separation of nuclei is equal to the bond length distance or bond length IF A BOND FORMS.

The separation or bond length depends on the size of the atoms and the number of shared electrons. The bond length is consistent for a specific pair of atoms.

The C-H bond length is roughly the same 109 picometers in all organic molecules. This allows us to predict the size of molecules if we know their composition.

When a pair of atoms don't form a bond, the total energy simply gets bigger and bigger. The two atoms will not stay together, but will bounce off one another and fly apart if left on their own.

A covalent bond exists because the two nonmetal atoms both get the shared electrons in their valence shell some of the time. That is what the sharing means. The formulas for compounds result from these limitations on bonding.

Examples:

hydrogen and oxygen only form H₂O and H₂O₂.

There are no other combinations like H₂O₅, H₃O₄, etc.

Molecules are groups of atoms that are held together by covalent bonds.  A molecule can have as few as two atoms like H₂ or as many as millions, like proteins and polymers in plastics.