Time-dependent density functional theory based upon the fragment molecular orbital method.

Time-dependent density functional theory (TDDFT) was combined with the two-body fragment molecular orbital method (FMO2). In this FMO2-TDDFT scheme, the system is divided into fragments, and the electron density for fragments is determined self-consistently. Consequently, only one main fragment of interest and several fragment pairs including it are calculated by TDDFT. To demonstrate the accuracy of FMO2-TDDFT, we computed several low-lying singlet and triplet excited states of solvated phenol and polyalanine using our method and the standard TDDFT for the full system. The BLYP functional with the long-range correction (LC-BLYP) was employed with the 6-31G() basis set (some tests were also performed with 6-311G(), as well as with B3LYP and time-dependent Hartree-Fock). Typically, FMO2-TDDFT reproduced the full TDDFT excitation energies within 0.1 eV, and for one excited state the error was about 0.2 eV. Beside the accurate reproduction of the TDDFT excitation energies, we also automatically get an excitation energy decomposition analysis, which provides the contributions of individual fragments. Finally, the efficiency of our approach was exemplified on the LC-BLYP6-31G(*) calculation of the lowest singlet excitation of the photoactive yellow protein which consists of 1931 atoms, and the obtained value of 3.1 eV is in agreement with the experimental value of 2.8 eV.