Empirical Self-Consistent Correction for the Description of Hydrogen Bonds in DFTB3

The description of hydrogen bonds in the density-functional tight-binding (DFTB) method continues to be a challenging task because the approximations that make the method computationally efficient compromise already the first-order electrostatic contribution to the interaction. So far, the best results have been achieved with fully empirical corrections such as the recently reparametrized DFTB3-D3H4 method. This approach has, however, important limitations that arise from its independence of the actual electronic structure. Here, we present a novel correction denoted as D3H5, which is integrated deeper in the DFTB method, correcting the problem at the place of its origin. It is applied within the self-consistent evaluation of electrostatic interactions, where it empirically models the missing contributions of atomic multipoles and polarization. Despite being very simple and using fewer parameters than D3H4, it is both more accurate and more robust. In data sets of small model systems, it yields errors below 1 kcal/mol, and it performs comparably well in larger systems. Unlike D3H4, it can describe cooperativity in H-bond networks, which makes it more transferable to more complex systems.