Is there any quick computational way using DFT or any other means to calculate the pKa of a compound? Is there any comprehensive database of pKa values of common chemicals?
It can be done in ChemAxon (https://docs.chemaxon.com/display/docs/pKa+Plugin). Academic version is available. Their web interface (https://chemicalize.com/) may also be used for ~30 calculations per month.
Quick with DFT - easy - calculate HA, H+ and A- in the same continuum solvent (solvent has huge effect on pKa). See for example https://www.researchgate.net/post/Can_someone_help_me_with_the_theoretical_pKa_calculations_using_DFT