A simplified time-dependent density functional theory approach for electronic ultraviolet and circular dichroism spectra of very large molecules

We present a simplified time-dependent density functional theory approach (sTD-DFT) that allows fast computation of electronic ultraviolet (UV) or circular dichroism (CD) spectra of molecules with 500–1000 atoms. The matrix elements are treated in the same way as in the recently proposed simplified Tamm-Dancoff approach (sTDA, S. Grimme, J. Chem. Phys., 138 (2013), 244104) but instead of applying the Tamm-Dancoff approximation, the standard linear-response density functional theory problem is solved. Compared to sTDA, the method leads to an increase in computation time (typically a factor of 2–5 compared to the corresponding sTDA) which is justified since the resulting transition dipole moments are in general of higher quality. This becomes important if spectral intensities (e.g. single-photon oscillator and rotatory transition strengths) are of interest. Comparison of UV and CD spectra obtained from sTD-DFT and sTDA for some typical systems employing standard hybrid functionals shows that both yield very similar excitation energies but the advantage of using the former approach for transition moments. In order to show the applicability of sTD-DFT to systems which are far beyond the scope of conventional TD-DFT, we present the CD spectrum of a substituted, chiral fullerene over a range of almost 1200 excited states. We propose this method as a more reliable alternative for the prediction especially of the more challenging CD spectra.