Yes, it is possible to predict or estimate the photoluminescence quantum yield (PLQY) of organic compounds using density functional theory (DFT) calculations. I am not a Gaussian user so I can't give you the details to perform such calculation, but the general procedure will incldue the following steps:
To calculate the PLQY using DFT, you would need to perform electronic structure calculations on the organic compound of interest. This typically involves optimizing the molecular geometry and calculating the electronic excited states. The latter is important for understanding the energy levels involved in the absorption and emission processes.
Once you have obtained the electronic excited states, you can use them to calculate the transition rates between the excited states involved in emission and other competing processes, such as non-radiative decay pathways. The PLQY can then be estimated by comparing the radiative and non-radiative decay rates.
It's worth noting that accurately predicting the PLQY using DFT can be challenging due to the inherent limitations of the method, such as the approximate treatment of electron correlation.
Just to add another (important) point to Jaafar A Mehrez 's answer: DFT is a ground state theory, and we normally employ some approachs, as the TDDFT formalism, to calculate excited states, but the results aren't usually very accurate. Don't get me wrong, TDDFT is great for getting insights into transitions, but predicting behaviours is not as "black-box" as usual (for DFT) and demands a very detailed work that might not be of your interest Syeda Aaliya Shehzadi