I would like to know where did you find the set of parameters for that force-field. Also, I want to know if you applied the charge equilibritation method to compute atomic charges. In that case, how did you solve the Coulomb integrals mentioned by Rappé and Goddard in their publication? They do not say how to solve them neither give the atomic parameters for all elements.
For the UFF force field, I re-used the parameters from RDKit, although the parameter files are available from multiple sources:
The UFF method does not use the QEq charges. There are a number of sources out there for this fact, but the best discussion comes from MCCS Towhee
The UFF parameters were derived without the use of point charges on the atoms and I believe the consensus of the original authors is to use this force field without any additional charges. One notable proponent of not using partial charges for UFF is A.K. Rappe who states this quite strongly in his UFF FAQ (no longer available).
Your question is about the Coulomb integrals in QEq. These are Coulomb integrals using Slater-type orbitals and there are plenty of references about this. An open source implementation of QEq is available in Open Babel:
That implementation re-casts the Slater-type integrals into approximate Gaussian integrals with fairly reasonable accuracy.