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.