The most important shortcoming of the MFCC scheme is its neglect of intramolecular interactions. Several extensions of the MFCC scheme have been proposed to alleviate this issue (see also Ref. 61 and references therein). One approach for systematically improving the MFCC scheme is its combination with the many-body expansion. To include pairwise interactions (i.e., two-body contributions), fragment-fragment (ff) interaction energies are calculated akin to the second-order eb-MBE. To take account of the accruing interactions between fragments and caps as well as interactions between caps, one additionally needs to account for fragment-cap (fc) and cap-cap (cc) interactions.