In optimising proteins with DFT/B3LYP, how can we detect the charge and multiplicity of the protein?
Sometimes the protein has been studied experimentally (or thoroughly by theory), and a consensus has been made about the most common charge and multiplicity for the molecule. In most cases, I would recommend to look at the literature to find such established values.
When not much is known about the molecule, you can do calculations with various different multiplicities to see which one provides the most stable molecule (if your calculations on a triplet state of the molecule are considerably lower than anything you're able to obtain with a singlet or quintuplet, etc. state, then it probably makes most sense to treat the molecule as having a triplet spin multiplicity).
Unfortunately for the charge, it's not as easy, because simply by adding more electrons, your molecule's energy will drop, so H2O-9 has a lower energy than H2O, but that doesn't mean that H2O-9 is more stable. You could still try to look at energetics, such as the depth and width of the deepest well of the potential energy surface, but that may be very impractical to do, especially for a protein, and it might not be accepted by people working in your field. Alternatively, you can determine the charge with as much knowledge about charges as you have (I've worked with some people in the past who were very good at this, as well as determining oxidation states and partial charges of atoms in the molecule). When in doubt, if there's no good reason available to believe that the molecule is charged, I would assume it's neutral and proceed with the analysis to determine the most energetically favorable spin multiplicity.
Unless there are transition metals (e.g. Fe, Mn, Cu, Ni) present in the active site, proteins typically have singlet state. There are several programs out there, such as propka, that can propose protonation states of the different amino acid residues. And as Nike already mentioned, often there could be experimental information about the protonation state of His residues. With the protonation state of the different residues, you then obtain the overall charge of the protein.