Fast and Accurate Calculation of the UV-Vis Spectrum with the Modified Local Excitation Approximation

The local excitation approximation (LEA), a method for the calculation of electronic excitations localized in a specific region of a molecule, has been modified with new approaches to enhance the accuracy of the original method. The primary concept behind LEA involves isolating the region of interest as a submolecule from the full molecule using a localization method, followed by calculating electronic excitations solely within this submolecule. In this study, we examined approaches that improve the accuracy in describing the region of interest, particularly its molecular orbital energies. Additionally, the localization method was extended with a new projection technique to accelerate calculations. These approaches were studied in time-dependent density functional theory (TDDFT) calculations applied to four testing systems with a chromophore as the region of interest: two basic linear molecules, acrolein surrounded by 24 water molecules, and a model of a green fluorescent protein. For all studied systems, the results of TDDFT calculations combined with LEA exhibited near-zero error when groups of atoms adjacent to the chromophore were explicitly included in the submolecule. This was achieved with at least a quadratic speedup of the calculation time as a function of the submolecule size.