Automated Generation of Optimized Auxiliary Basis Sets for Long-Range-Corrected TDDFT Using the Cholesky Decomposition.

Range-separated hybrid functionals making use of a smooth separation of the Coulomb operator in terms of the error function and its complement have proven to be a valuable tool for improving Kohn-Sham density functional theory (DFT) calculations. This holds in particular for obtaining accurate excitation energies from linear-response time-dependent DFT. Evaluating the long-range exchange contributions represents one of the most time-consuming tasks in such calculations. Prefitted auxiliary basis sets can be employed to speed up this step. Here, we present a way to generate auxiliary basis sets optimized to fit the long-range exchange contributions only, contrary to the common optimization strategies on the basis of the full Coulomb operator. For this purpose, we use the atomic Cholesky decomposition technique. The basis sets are generated on-the-fly using the specific range-separation parameter defined in the exchange-correlation functional. We obtain excitation energies and oscillator strengths which are of similar or better accuracy than those obtained with conventional resolution-of-the-identity auxiliary basis sets while drastically reducing the number of auxiliary functions required. This is demonstrated for the QUESTDB#5 benchmark set. In addition, we outline the benefits of this approach in sequences of calculations employing varying range-separation parameters, as is the case in the optimally tuned range-separation strategy. Finally, we illustrate the efficiency of this approach for real-world examples, namely, a chlorophyll tetramer from photosystem II and a carotenoid-porphyrin-C triad.