The first three terms correspond to the DFTB2 energy expression, whereas the last term is the QM/MM interaction. The first term is E rep is a parameterized repulsion-like energy collecting all terms depending on ρ0. The second term is the core Hamiltonian expanded in atom-centered molecular orbitals (indexed Aµ for the atom and atomic shell labels respectively). The third term approximates the electron repulsion integrals using a γ function that is an integral over a product of two normalized Slater-type spherical charge densities and the Mulliken fluctuation charges, ∆qA = qAq 0 A is the net charge of atom A, while qA is given by the usual Mulliken atomic orbital expression,