UV-visible absorption spectroscopy probes the electronic structure of molecules in their ground and excited states. Numerous studies have examined electronic structure methods' ability to reproduce molecular light-absorption energies. Comparatively few studies have addressed the intensities (probabilities) of the predicted transitions. This is the topic of this dissertation.

We looked at the oscillator strengths (OSs or f-values) predicted by four wavefunction methods (CIS, TD-HF, EOM-CCSD, and LR-CCSD) and the time-dependent (TD) implementation of nineteen DFT functionals. These included eight pure, eight hybrid, and three long-range-corrected hybrid functionals. We also tested the Tamm--Dancoff approximation (TDA) for nine of the functionals. For all methods, transition dipole moments were obtained in the length, velocity, and mixed gauges. Different basis sets (Pople, Dunning, and Jensen's) were tested as well.

We compared the computations to 85 OSs derived from the experimental absorption spectra of 69 small organic molecules in solution. Most transitions in this comparison set come from conjugated molecules and have $\pi\rightarrow\pi^*$ character. In the comparison, we account for the effect of the solvent on i) the molecular wavefunctions, by using different polarizable continuum model (PCM) implementations, ii) on the electromagnetic field driving the absorption, by modeling the cavity field acting on the molecules, and iii) on the light's energy flux, by multiplying experimental OSs (f_{exp}) times the refractive index of the solvent n.

OSs computed (f_{comp}) using the TDA, CIS, or EOM-CCSD exhibit a strong gauge dependence, which is diminished in linear response theories (TD-DFT, TD-HF, and to a smaller degree LR-CCSD). Overall, for TDA and the wavefunction methods, the length gauge reproduces experiments better. LR-CCSD, EOM-CCSD, and TD-DFT f_{comp} values have ~10--20% MAEs relative to n f_{exp}. CIS and TD-HF present significantly larger errors. The TDA results in roughly twice the error of full TD for nine functionals tested. LR-CCSD and pure functionals' f_{comp} values present a 1:1 ratio with n f_{exp} while hybrid functionals systematically overestimate experimental OSs by a magnitude that increases with the % of HF exchange included in the functional.