This has to do with the electron correlation effect and is quantum mechanical in nature. Present in all molecules and atoms. When two molecules get close enough their electron clouds will start to repel each other, causing a very sharp increase in potential energy. Hydrogen bonding in water, this is somewhere in between induction and chemical bond formation. Present in only a few types of molecules.
Charge transfer is another example.
Model Potentials Let us assume that pair-wise additivity is accurate. Quantum mechanics says that the repulsive potential can be modeled by and the attractive or dispersion forces can be modeled as an infinite series where each of the coefficients must be identified for a specific type of molecule. We assume that the molecule is spherically symmetric in such a treatment, but not really because we can define an angle averaged potential that is a function of temperature that is rigorous. Empirical potential models have been developed. Some of them are listed here.