The second term in equation 1 is the energy due to charge fluctuations and is parameterized analytically as a function of the orbital charges and γ AB , which is a function of the interatomic separation and Hubbard parameter, U . ∆q A = q A -q 0 A is the self-consistent induced Mulliken charge on atom A; for details see reference 21. The remaining contribution to the total DFTB energy in equation 1 is E rep , which corresponds to the distancedependent diatomic repulsive potential and contains the core electron effects, ion-ion repulsion terms, as well as some exchange-correlation effects. This term can be considered as a practical equivalent to an xc-functional in DFT as it approximates the many-body correlation interactions with simple functions. The total repulsive energy of a system in DFTB is a sum of contributions of repulsive potentials V rep (r) from each atom pair: