DFTB3 Parametrization for Copper: The Importance of Orbital Angular Momentum Dependence of Hubbard Parameters

We report the parametrization of a density functional tight binding method (DFTB3) for copper in a spin-polarized formulation. The parametrization is consistent with the framework of 3OB for main group elements (ONCHPS) and can be readily used for biological applications that involve copper proteins/peptides. The key to our parametrization is to introduce orbital angular momentum dependence of the Hubbard parameter and its charge derivative, thus allowing the 3d and 4s orbitals to adopt different sizes and responses to the change of charge state. The parametrization has been tested by applying to a fairly broad set of molecules of biological relevance, and the properties of interest include optimized geometries, ligand binding energies, and ligand proton affinities. Compared to the reference QM level (B3LYP/aug-cc-pVTZ, which is shown here to be similar to the B97-1 and CCSD(T) results, in terms of many properties of interest for a set of small copper containing molecules), our parametrization generally gives reliable structural properties for both Cu(I) and Cu(II) compounds, although several exceptions are also noted. For energetics, the results are more accurate for neutral ligands than for charged ligands, likely reflecting the minimal basis limitation of DFTB3; the results generally outperform NDDO based methods such as PM6 and even PBE with the 6-31+G(d,p) basis. For all ligand types, single-point B3LYP calculations at DFTB3 geometries give results very close (similar to 1-2 kcal/mol) to the reference B3LYP values, highlighting the consistency between DFTB3 and B3LYP structures. Possible further developments of the DFTB3 model for a better treatment of transition-metal ions are also discussed. In the current form, our first generation of DFTB3 copper model is expected to be particularly valuable as a method that drives sampling in systems that feature a dynamical copper binding site.