There is quite abit of work going on in this field right now. Take a look at what Rogers et al. are doing using MP2 to derive all aspects of a force-field. They are also working on a DFT implementation, since DFT is alot faster and computationally cheaper.
I will assume that by interatomic, we are concerned with distant atoms interacting, and not near neighbors in the same molecules, ie. bonds/angles/torsions which are generally classed as intramolecular interactions. Interatomic interactions in classical molecular simulations are generally calculated as the interactions due to atom centered partial charges and Lennard-Jones (LJ) interactions, although sometimes LJ is replaced with a more expensive model such as the Buckingham (EXP-6) or other model.
For inter-atomic force-field parameters, you would want to ensure that the energies and forces between atoms are accurately calculated. You can regress the Lennard-Jones(or Buckingham, or whatever model you are using) parameters to minimize the error between the model and the energy/forces calculated using quantum mechanics (QM). Perhaps start with dimers/trimers and work your way up to bigger systems if needs be.
Part of the inter-atomic interactions is the partial charges, so you need to decide on a method for calculating the partial charges first( I prefer partitioning methods like MBIS or CM5, but you could use restrained-electrostatic potential (RESP) as well, or other). Once they are set in stone, you just optimize the LJ or exp-6 or other parameters.
Traditionally this optimization was done by fitting to experimental data for densities, enthalpy of vaporization, and free energy (and other data). You could also add in experimental data, but, as the paper I linked shows, we are now at a stage where quite good results can be obtained purely ab-initio.
Also look into the work being done by openFF