Absorption Intensities\nof Organic Molecules from Electronic\nStructure Calculations versus Experiments: the Effect of Solvation,\nMethod, Basis Set, and Transition Moment Gauge

Recently, we derived experimental oscillator strengths\n(OSs) from\nwell-defined UV–visible absorption spectral peaks of 100 molecules\nin solution. Here, we focus on a subset of transitions with the highest\nreliability to further benchmark the OSs from several wave function\nmethods and density functionals. We consider multiple basis sets,\ntransition moment gauges (length, velocity, and mixed), and solvent\ncorrections. Most transitions in the comparison set come from conjugated\nmolecules and have π → π* character. We use an\nautomated algorithm to assign computed transitions to experimental\nbands. OSs computed using the Tamm–Dancoff approximation (TDA),\nCIS, or EOM-CCSD exhibited a strong gauge dependence, which is diminished\nin linear response theories (TD-DFT, TD-HF, and to a smaller degree\nLR-CCSD). OSs calculated from TD-DFT with PCM solvent models are systematically\nlarger than apparent OSs derived from experimental spectra. For example, <i>f</i><sub>comp</sub> from hybrid functionals and PCM have mean\nabsolute errors that are ∼10% of <i>n</i>·<i>f</i><sub>exp</sub>, where <i>n</i> is a solvent refractive\nindex factor that arises from the energy flux of the radiation field\nin a dielectric (solvent). Theoretical cavity field corrections considering\nspherical cavities do not improve the agreement between computed and\nexperimental data. Corrections that account for the molecular shape\nand the direction of transition dipole moments, or that explicitly\naccount for the effect of solvent molecules on the local field, should\nbe more appropriate.