A simplified Tamm-Dancoff density functional approach for the electronic excitation spectra of very large molecules

Two approximations in the Tamm-Dancoff density functional theory approach (TDA-DFT) to electronically excited states are proposed which allow routine computations for electronic ultraviolet (UV)- or circular dichroism (CD) spectra of molecules with 500-1000 atoms. Speed-ups compared to conventional time-dependent DFT (TD-DFT) treatments of about two to three orders of magnitude in the excited state part at only minor loss of accuracy are obtained. The method termed sTDA ("s" for simplified) employs atom-centered Löwdin-monopole based two-electron repulsion integrals with the asymptotically correct 1∕R behavior and perturbative single excitation configuration selection. It is formulated generally for any standard global hybrid density functional with given Fock-exchange mixing parameter ax. The method performs well for two standard benchmark sets of vertical singlet-singlet excitations for values of ax in the range 0.2-0.6. The mean absolute deviations from reference data are only 0.2-0.3 eV and similar to those from standard TD-DFT. In three cases (two dyes and one polypeptide), good mutual agreement between the electronic spectra (up to 10-11 eV excitation energy) from the sTDA method and those from TD(A)-DFT is obtained. The computed UV- and CD-spectra of a few typical systems (e.g., C60, two transition metal complexes, [7]helicene, polyalanine, a supramolecular aggregate with 483 atoms and about 7000 basis functions) compare well with corresponding experimental data. The method is proposed together with medium-sized double- or triple-zeta type atomic-orbital basis sets as a quantum chemical tool to investigate the spectra of huge molecular systems at a reliable DFT level.