Drastically reducing the cost of the XsTD-DFT family of methods using a minimal auxiliary basis set (ηXsTD-DFT) to efficiently treat ultra large systems.

This contribution introduces the ηXsTD-DFT family of methods in which the exact integral simplified time-dependent density functional theory (XsTD-DFT) is adapted considering the resolution of identity (RI) approximation with a minimal auxiliary basis set. The main goal of this is to provide to the community the most efficient simplified quantum chemistry method to compute excited states and response properties for all-atom quantum mechanical (AQM) methodologies. This auxiliary set is composed of 1s orbitals with the square of the atomic chemical hardness η scaled by a global factor θ as parameters into the exponent. This approximation allows a drastic reduction of the computational cost. The θ in the ηXsTDA was globally fitted to reproduce reference excitation energies and oscillator strengths for the 17 first molecules of the XsTD-DFT benchmark set. The method was then tested for the entire set of 77 molecules. For B3LYP, the ηXsTDA scheme deviates on average by only 0.12 eV with respect to TDA, similarly to the TDA-ris scheme. Thanks to the fitting of the θ parameter that absorbs some of the error, MADs with respect to TDA are slightly lower than those for the XsTDA method. For this set, on average, the ηXsTDA is 147 times faster than TDA, outperforming both TDA-ris (32×) and XsTDA (82×) schemes. These results highlight the computational efficiency and robustness of the ηXsTD-DFT and suitability for applications in AQM methodologies. To showcase the performance of the method, three increasingly-large systems were selected: a mixed donor/acceptor ligand Pd(II) double cage (395 atoms), photoactive yellow protein (PYP, 1931 atoms), and bacteriorhodopsin (bR, 3835 atoms). In all cases, striking comparisons with respect to experiment were obtained. For bR, the largest system of this study, one- and two-photon absorption spectra were computed at the ηXsTD-DFT level in only 2 h 25 min on a desktop computer using ∼500 GB of RAM. The ηXsTDA shows also excellent performance in computing core-valence excitations, well reproducing the oxygen K-edge NEXAFS spectrum of collagen. A spin-flip version was also implemented and tested for 9 diradicals and a large μ-hydroxo-bridged dimer of corrole tape Ga(III) complexes derivative.