How does Civilization 4 calculate the amount of gold recieved on a city capture?

I don't know but I think it go on what gold the civ has and the size of the city

You may have to experiment... I would say that the gold is partially related to the AI's cash on hand plus the sale price of buildings destroyed. Hrm, I will have to look at that...

I believe the size of the city matters.I don't see any relation to the amount of cash the AIs have around (because there isn't anymore the amplitude in sums which was present in former civ installations); however, it is hard to tell, since the figures displayed in the diplomacy screen are just what they are willing to use in trade (they have a hidden stack for paying upgrades etc.)