What is the force that holds two atoms together in a molecule?

Answer 1

Electrostatic attraction for electron pairs hold atoms together. When atoms bond into a molecule, they share electrons, each contributing one electron to a pair. Since the nuclei of the atoms are positive and the electrons are negative, both nuclei are attracted to the shared pair, and stay near each other.

Answer 2

Molecules are held together by covalent bonds ( these are different from ionic bonds which are a consequence of different electro-static values created by an imbalance between protons and electrons in the respective atoms.)

Covalent bonds are a consequence of electron sharing between atoms, and can be explained as an overlap of atomic orbitals. The force of "attraction" is a quantum mechanical effect sometimes called delocalistion energy.

Answer 3

They are called intermolecular forces. One is hydrogen bonding, in which hydrogen atoms bond with nearby fluorine, oxygen, or nitrogen atoms. Van der waals forces occur between dipole-dipole, dipole-induced dipole, and induced dipole-induced dipole molecules.