Multipole Expansion of Atomic Electron Density Fluctuation Interactions in the Density-Functional Tight-Binding Method

Abstract

The accuracy of the density-functional tight-binding (DFTB) method in describing noncovalent interactions is limited due to its reliance on monopole-based spherical charge densities. In this study, we present a multipole-extended second-order DFTB (mDFTB2) method that takes into account atomic dipole and quadrupole interactions. Furthermore, we combine the multipole expansion with the monopole-based third-order contribution, resulting in the mDFTB3 method. To assess the accuracy of mDFTB2 and mDFTB3, we evaluate their performance in describing noncovalent interactions, proton transfer barriers, and dipole moments. Our benchmark results show promising improvements even when using the existing electronic parameters optimized for the original DFTB3 model. Both mDFTB2 and mDFTB3 outperform their monopole-based counterparts, DFTB2 and DFTB3, in terms of accuracy. While mDFTB2 and mDFTB3 perform comparably for neutral and positively charged systems, mDFTB3 exhibits superior performance over mDFTB2 when dealing with negatively charged systems and proton transfers. Overall, the incorporation of the multipole expansion significantly enhances the accuracy of the DFTB method in describing noncovalent interactions and proton transfers.

Three-Center Tight-Binding Together with Multipolar Auxiliary Functions

“…Going beyond the monopole approximation in conjunction with Mulliken mapping is possible, however. ,− In ref a different mapping is used, together with nonminimal auxiliary basis sets, in a method that otherwise resembles DFTB. The mapping coefficients are calculated as the overlap between the AO product and the associated auxiliary basis functions.…”

Obtaining Robust Density Functional Tight-Binding Parameters for Solids across the Periodic Table

“…Nonetheless, being an approximation to DFT, DFTB preserves the capability to calculate band structures and other common electronic properties. Unlike empirical interatomic potentials, it can thus be applied to systems where charge transfer, excitations, and/or chemical reactions are of interest, e.g., in catalysis. − In this context, the development of extensions such as self-consistent charge (SCC) DFTB (also known as DFTB2) and DFTB3 , has been highly influential. Recently, the development of hybrid functionals and machine learning (ML) approaches in DFTB have further expanded its domain of applicability. , However, being a semiempirical method, the lacking availability of general parametrizations remains a bottleneck toward more widespread adoption.…”

“…Unlike empirical interatomic potentials, it can thus be applied to systems where charge transfer, excitations, and/or chemical reactions are of interest, e.g., in catalysis. 3−6 In this context, the development of extensions such as self-consistent charge (SCC) DFTB (also known as DFTB2) 7 and DFTB3 8,9 has been highly influential. Recently, the development of hybrid functionals and machine learning (ML) approaches in DFTB have further expanded its domain of applicability.…”