Absorption Intensities of Organic Molecules from Electronic Structure Calculations versus Experiments: the Effect of Solvation, Method, Basis Set, and Transition Moment Gauge

Recently, we derived experimental oscillator strengths
(OSs) from
well-defined UV–visible absorption spectral peaks of 100 molecules
in solution. Here, we focus on a subset of transitions with the highest
reliability to further benchmark the OSs from several wave function
methods and density functionals. We consider multiple basis sets,
transition moment gauges (length, velocity, and mixed), and solvent
corrections. Most transitions in the comparison set come from conjugated
molecules and have π → π* character. We use an
automated algorithm to assign computed transitions to experimental
bands. OSs computed using the Tamm–Dancoff approximation (TDA),
CIS, or EOM-CCSD exhibited a strong gauge dependence, which is diminished
in linear response theories (TD-DFT, TD-HF, and to a smaller degree
LR-CCSD). OSs calculated from TD-DFT with PCM solvent models are systematically
larger than apparent OSs derived from experimental spectra. For example, fcomp from hybrid functionals and PCM have mean
absolute errors that are ∼10% of n·fexp, where n is a solvent refractive
index factor that arises from the energy flux of the radiation field
in a dielectric (solvent). Theoretical cavity field corrections considering
spherical cavities do not improve the agreement between computed and
experimental data. Corrections that account for the molecular shape
and the direction of transition dipole moments, or that explicitly
account for the effect of solvent molecules on the local field, should
be more appropriate.