Delocalization errors in a hubbard-like model: Consequences for density-functional tight-binding calculations of molecular systems
International Journal of Quantum Chemistry
It has previously been shown that self-consistent-charge density-functional tight-binding (SCC-DFTB) suffers from a self-interaction error that leads to artificial stabilization of delocalized states. The effects of the error are similar to those appearing for many density functionals. In SCC-DFTB the delocalization error is inherently related to the use of a Hubbard-like term to describe on-site charge interactions. The mathematical simplicity of this Hubbard-like term makes it easy to
... if a complex system is subject to artificial stabilization of delocalized states, and to quantitatively predict the delocalization error in the system energy at large fragment separation. The error is directly proportional to the on-site charge interaction term, but decreases as the fragments become more asymmetric. The difference in orbital energies required to eliminate the delocalization error becomes equal to the Hubbard-like parameter of the fragment with the highest electron affinity. However, in most cases the localized state will be favored by spin polarization, fragment repulsion, solvent effects and large reorganization energies, in analogy to density functional theory (DFT), from which SCC-DFTB is derived. The presented analysis gives an early indication whether the standard approach is suitable, or if a different method is required to correct the delocalization error. In addition to cationic dimers, we discuss the effects of the delocalization error for asymmetric systems, bond dissociation of neutral molecules, and the description of mixed valence transition metal systems, exemplified by the enzyme cytochrome oxidase.