The Modified Divide-and-Conquer Method

Ca are the a-spin MO coefficients for the A th fragment, and Ra are the nuclear positions of the atoms in fragment A. 

As discussed in the previous section, the relaxation of the orthonormality constraints allows one to solve for the MO coefficients through a series of small generalized eigenvalue problems (proportional to the size of a fragment) 

The inter-fragment coupling occurs through the interaction of their atomic multipoles which are determined from the fragment electron densities within the self-consistent-field (SCF) procedure. The a-spin Fock matrix for region A with inclusion of this coupling is 

The atomic multipoles are computed from the DFTB3 density matrix 

The atomic multipoles are obtained by inserting Eq. (1.7) into Eq. (1.2). If we restrict the contributions of the two-center densities to charge only, then the charge on atom a is 

---