The effectiveness of solar energy capture and conversion materials derives from their ability to absorb light and to transform the excitation energy into energy stored in free carriers or chemical bonds. The Thomas-Reiche-Kuhn (TRK) sum rule mandates that the integrated (electronic) oscillator strength of an absorber equals the total number of electrons in the structure. Typical molecular chromophores place only about 1% of their oscillator strength in the UV-vis window, so individual chromophores operate at about 1% of their theoretical limit. We explore the distribution of oscillator strength as a function of excitation energy to understand this circumstance. To this aim, we use familiar independent electron model Hamiltonians as well as first-principles electronic structure methods. While model Hamiltonians capture the qualitative electronic spectra Associated with pi electron chromophores, these Hamiltonians mistakenly focus the oscillator strength in the fewest low-energy transitions. Advanced electronic structure methods, in contrast, spread the oscillator strength over a very wide excitation energy range, including transitions to Rydberg and continuum states, consistent with experiment. Our analysis rationalizes the low oscillator strength in the UV-vis spectral region in molecules, a step toward the goal of oscillator strength manipulation and focusing.