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Atomic structure is predominantly determined by the Coulomb force.

The Coulomb force, i.e. force between charges is inversely proportional to distance, is the force of electrostatics.

The Coulomb force is the force of attraction between the nucleus and the electrons and it is the force of repulsion between the electrons.

Quantum mechanics is the theory which uses this force law in determining electronic structure of atoms and molecules.

If one wants to get picky and look for very small influences on atomic structure that are not due to the Coulomb force, then one has to investigate the subject of special relativity and some very weak nuclear interactions.

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