Accurate Hydrogen Bond Energies within the Density Functional Tight Binding Method A. Domínguez,* ,† T. A. Niehaus, ‡ and T. Frauenheim † † Bremen Center for Computational Materials Science, Universitä t Bremen, Am Fallturm 1, 28359 Bremen, Germany ‡ Department of Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany ABSTRACT: The density-functional-based tight-binding (DFTB) approach has been recently extended by incorporating one-center exchange-like terms in the expansion of the multicenter integrals. This goes beyond the Mulliken approximation and leads to a scheme which treats in a self-consistent way the fluctuations of the whole dual density matrix and not only its diagonal elements (Mulliken charges). To date, only the performance of this new formalism to reproduce excited-state properties has been assessed (Domínguez et al. J. Chem. Theory Comput., 2013, 9, 4901-4914). Here we study the effect of our corrections on the computation of hydrogen bond energies for water clusters and water-containing systems. The limitations of traditional DFTB to reproduce hydrogen bonds has been acknowledged often. We compare our results for a set of 22 small water clusters and water- containing systems as well as for five water hexadecamers to those obtained with the DFTB3 method. Additionally, we combine our extension with a third-order energy expan- sion in the charge fluctuations. Our results show that the new formalisms significantly improve upon original DFTB. 1. INTRODUCTION Density functional theory (DFT) has become the method of choice to simulate a wide range of processes in quantum chemistry and computational material science due to its well- balanced compromise between accuracy and efficiency. To address those problems still escaping from the scope of DFT due to their highly demanding computing resources, several approximate schemes have been developed. The density functional tight-binding (DFTB) approach 1,2 has been shown to be a very useful tool, combining, in many cases, the accuracy typical of DFT with the efficiency representative of semi- empirical methods. DFTB was originally based on the expansion of the DFT total energy up to the zeroth order in the charge density fluctuations around an input density, which is chosen as the sum of the densities of the isolated atomic constituents of the system in question. This original approach 1 had limitations regarding the description of some molecular systems with an electronic density different from the mere superposition of neutral atomic contributions. With the self-consistent-charge (SCC) extension (expansion of the energy up to the second- order), the method was significantly improved, thus accounting for charge transfer among atoms. Afterward, DFTB has been extended in multiple ways to gradually broaden its applicability. For example, to allow for the study of spin-polarized systems, the method was generalized to a spin-unrestricted formalism. 3,4 Broadening the number of chemical elements (and the combination of elements) that can be investigated within the approach has also been a consistent focus. In this sense, relativistic effects have been incorporated in the parametrization process, thus widening the number of atomic species covered by the formalism. 5 Furthermore, there have been some attempts to automatize the generation of the needed param- eters, one recent effort being the development of a semi- automatic parametrization approach for the electronic part of DFTB. 6 Other extensions include the development of QM/MM schemes based on DFTB 7,8 and the implementation of empirical corrections to account for dispersion forces. 9,10 Recently, the level of approximation in DFTB has taken a step forward with the inclusion of third-order terms in the energy expansion, which introduces a higher degree of self- consistency and accuracy. 11-14 This extension becomes particularly important for highly charged molecules, and combined with an empirical correction, it has been shown to improve the parameter transferability to reproduce hydrogen bonding energies and proton affinities. 13 Whereas many efforts seem to be now devoted to what appears to be the next generation of DFTB, we believe that there is still plenty of room for improvements in second-order DFTB. Indeed, at this level of theory, two main approximations are applied, namely, the monopole approximation of the density fluctuations and the Mulliken approach for the evaluation of the multicenter integrals. Possible corrections to these approaches have, how- ever, just started to be exploited. For the former approach, a refinement has been proposed, where dipole-monopole inter- actions are considered, 15 whereas we have recently improved on the Mulliken approximation with the so-called onsite correc- tion. 16 In this approach, we propose a more accurate evaluation of multicenter integrals within DFTB, which does not imply additional computational effort. This scheme has been shown Published: March 12, 2015 Article © 2015 American Chemical Society 3535 DOI: 10.1021/acs.jpca.5b01732 J. Phys. Chem. A 2015, 119, 3535-3544