In all the above-presented expressions, the T (n) mod (r i , R QM ) is the n-th order derivative of modified interaction tensor with respect to the QM coordinate (either electronic r or nuclear R k ) as presented in Eq. 16, where r cov,i and r i is a covalent radius and position vector of i-th MM atom, respectively. Summation runs over the N QM and N M M , which are the number of atoms in QM and MM subsystems, respectively. The analytical derivatives of T (n) mod (r i , R QM ) with n = 1, 2 are provided in the Supplementary Information of this article.