  The energies of molecular excited states arise as solutions to the electronic
Schr\"{o}dinger equation and are often compared to experiment. At the same
time, nuclear quantum motion is known to be important and to induce a red-shift
of excited state energies. However, it is thus far unclear whether
incorporating nuclear quantum motion in molecular excited state calculations
leads to a systematic improvement of their predictive accuracy, making further
investigation necessary. Here we present such an investigation by employing two
first-principles methods for capturing the effect of quantum fluctuations on
excited state energies, which we apply to the Thiel set of organic molecules.
We show that accounting for zero-point motion leads to much improved agreement
with experiment, compared to `static' calculations which only account for
electronic effects, and the magnitude of the red-shift can become as large as
1.36 eV. Moreover, we show that the effect of nuclear quantum motion on excited
state energies largely depends on the molecular size, with smaller molecules
exhibiting larger red-shifts. Our methodology also makes it possible to analyze
the contribution of individual vibrational normal modes to the red-shift of
excited state energies, and in several molecules we identify a limited number
of modes dominating this effect. Overall, our study provides a foundation for
systematically quantifying the shift of excited state energies due to nuclear
quantum motion, and for understanding this effect at a microscopic level.
