How do I model non-covalent interactions in Gaussian?
As hBy2Py, Greg, and others have pointed out in their comments, the cation is just a counter ion for your benzothiazole-based cyanine dyes.

I suggest to be reasonably lazy and perform the calculations on the cyanine dye only. 

Even for calculations in solvents of sufficient polarity (from an experimental photochemical perspective, acetonitrile seems to be a good choice), I would just ignore the cations.