Fundamentally, forces on the atomic scale are caused the eletrostatic interaction, namely, the attraction between opposite charges (electron – nucleus) and the repulsion between like charges (electron – electron and nucleus – nucleus).
When two atoms bump into each other, their electron shells overlap which gives rise to a force that either attracts the atoms (forming a new bond) or driving them away from each other. Two atoms forming a bond are in sort of an equilibrium of forces, which means that the repulsive forces cancel the attractive forces on average. However, molecules always vibrate, even at zero Kelvin temperature. This is also a result of electrostatic interaction between the electrons and the nuclei in the molecule.
A molecule that is simply rotating or moving at constant speed does not experience any forces. A change of the rotational frequency or velocity is similarly caused by molecules bumping into each other.
There are other forces at work, namely the exchange and correlation force, which are consequences of the quantum mechanical nature of the electrons, but these forces are comparably smaller than the eletrostatic forces.
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