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

Abstract

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 (∼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.

Copper Oxidation/Reduction in Water and Protein: Studies with DFTB3/MM and VALBOND Molecular Dynamics Simulations

“…This is consistent with our previous finding 18 that for the interaction between copper and charged ligands (e.g., deprotonated Cys sidechain), the current DFTB3 model still has considerable errors, due most likely to the use of minimal basis. Improvement of polarization using chemical potential equalization 127–129 (or a larger basis for the charged ligands) is likely to reduce the deviations observed here.…”

“…18 By including orbital angular momentum dependence of the Hubbard parameter and its charge derivative, we were able to describe the structural properties of both oxidation states in generally good agreement with “first principle” density functional theory (DFT) methods such as B3LYP 19–21 and B97-1, 22 which were shown to give adequate description for copper complexes of biological relevance (see discussion in Ref. 18 in relation to previous work 23–25 ). We note that the DFTB3 model in the current form has PBE 26 as its “parent functional”, which was shown 18 to be less accurate than B3LYP and B97-1 for copper.…”

“…For comparison, hybrid QM/MM simulations are performed using DFTB3 17 and the 3OB parameterization for ONCH 47 and copper 18 is used. The metal complex is described by DFTB3 whereas the water molecules are treated by TIP3P.…”

“…In our previous work, 18 the DFTB3 method was tested only against DFT and, in some cases, CCSD(T) methods for gas phase molecules. The computational efficiency of DFTB3 over DFT and ab initio methods makes it an attractive QM approach in QM/MM applications.…”

QM/MM free energy simulations: recent progress and challenges

“…For metalloenzyme applications, recent developments have led to promising parameterizations for several metal ions that include the alkali metals, 57 magnesium, zinc 58 and copper. 59 The DFTB3 method in the current form is most reliable for structural properties, including for fairly complex bi-metallic motifs in several enzymes; 40,41,58,60,61 for energetic properties, the results are less robust as compared to DFT/GGA 62,63 but can often be improved to satisfying accuracy with single point energy calculations at high QM(/MM) level, making DFTB3 a promising low-level approach in dual-level QM/MM free energy simulations, a topic that we will also discuss here.…”