The eXact integral simplified time-dependent density functional theory (XsTD-DFT)

In the framework of simplified quantum chemistry methods, we introduce the eXact integral simplified time-dependent density functional theory (XsTD-DFT). This method is based on the simplified time-dependent density functional theory (sTD-DFT), where all semi-empirical two-electron integrals are replaced by exact one- and two-center two-electron integrals, while other approximations from sTD-DFT are kept. The performance of this new parameter-free XsTD-DFT method was benchmarked on excited state and (non)linear response properties, including ultra-violet/visible absorption, first hyperpolarizability, and two-photon absorption (2PA). For a set of 77 molecules, the results from the XsTDA approach were compared to the TDA data. XsTDA/B3LYP excitation energies only deviate on average by 0.14 eV from TDA while drastically cutting computational costs by a factor of 20 or more depending on the energy threshold chosen. The absolute deviations of excitation energies with respect to the full scheme are decreasing with increasing system size, showing the suitability of XsTDA/XsTD-DFT to treat large systems. Comparing XsTDA and its predecessor sTDA, the new scheme generally improves excitation energies and oscillator strengths, in particular, for charge transfer states. TD-DFT first hyperpolarizability frequency dispersions for a set of push-pull π-conjugated molecules are faithfully reproduced by XsTD-DFT, while the previous sTD-DFT method provides redshifted resonance energy positions. Excellent performance with respect to the experiment is observed for the 2PA spectrum of the enhanced green fluorescent protein. The obtained robust accuracy similar to TD-DFT at a fraction of the computational cost opens the way for a plethora of applications for large systems and in high throughput screening studies.