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–C60 triad.