It is impossible to calculate quantum yield using Gaussian since there are a variety of rates of excited state decay which are caused by mechanisms other than photon emission and are, therefore, often called "non-radiative rates", such as dynamic collisional quenching, near-field dipole-dipole interaction (or resonance energy transfer), internal conversion, and intersystem crossing, Thus, if the rate of any pathway changes, both the excited state lifetime and the fluorescence quantum yield will be affected.
Therefore, the best way is to measure fluorescence quantum yields by comparison to a standard. The quinine salt quinine sulfate in a sulfuric acid solution is a common fluorescence standard.
Quantum Yield = Number of Photon Emitted/Number of Photon Absorbed.
Valeur, Bernard, Berberan-Santos, Mario (2012). Molecular Fluorescence: Principles and Applications. Wiley-VCH. ISBN 978-3-527-32837-6.