Development of Density Functional Tight-Binding Parameters Using Relative Energy Fitting and Particle Swarm Optimization

We provide a strategy to optimize density functional tight-binding (DFTB) parameterization for the calculation of the structures and properties of organic molecules consisting of hydrogen, carbon, nitrogen, and oxygen. We utilize an objective function based on similarity measurements and the Particle Swarm Optimization (PSO) method to find an optimal set of parameters. This objective function considers not only the common DFTB descriptors of binding energies and atomic forces but also incorporates relative energies of isomers into the fitting procedure for more chemistry-driven results. The quality in the description of the binding energies and atomic forces is measured based on the Ballester similarity index and relative energies through a similarity index induced by the Levenshtein edit distance to quantify the correct energetic order of isomers. Training and testing datasets were created to include all relevant chemical functional groups. The accuracy of this strategy is assessed, and its range of applicability is discussed by comparison against our previous parameterization [A. Krishnapriyan, et al., J. Chem. Theory Comput. 13 , 6191 (2017)]. The improved performance of the new DFTB parameterization is validated with respect to the density functional theory large datasets QM-9 [R. Ramakrishnan, et al., Sci. Data 1 , 140022 (2014)] and ANI-1 [J. S. Smith, et al., Sci. Data 4 , 170193 (2017)], where excellent agreement is found between the structures and properties available in these datasets, and the ones obtained with DFTB.