If you are using reaxff, you will get interactions between all atoms as defined by the fundamental bond length/ bond order relationship used. In addition, nonbonded interactions (van der Waals, Coulomb) are calculated between every atom pair, irrespective of connectivity. Excessive close-range nonbonded interactions are avoided by shielding.
So, all the interactions in your carbon cluster are intrinsic to your calculation using reaxff.
Here’s a good primer:
http://www.wag.caltech.edu/home/duin/Reax/ch121ReaxFF_introduction.pdf
The good reaxff stuff starts on page 16 and following.
Jim
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