I have always doubted the use of a nuclear bomb to dominate. Why destroy the riches you wish to dominate?
I figure it will be biologic, stealthy invasion or destruction of the infrastructure thru the internet/satellites.
I'll be back...I'm going to hide under my desk.
It wasn't so much to dominate as provide the sort of shock and awe that would lead to a surrender, rather than an invasion and fighting for every inch of the Japanese home islands. The argument can be made that the sheer terror of an entire city going up in a flash saved millions of allied and Japanese lives in the long run, millions who would have attacked and defended and fought over every foot of soil.
Even though we did not want the Soviets, who after the war were the most likely to develop atomic weapons to have them (because there was deep distrust of the Soviets, and with good reason), I question whether we actively used them or anything but the quiet threat of being the only nation on Earth to have workable Atomic weapons to dominate. If we did, we did a poor job of it, as we gave most of Eastern Europe to the Soviets, rather than taking them actively under our own penumbra. That division might have gone quite differently otherwise.
Had we not supplied the Soviets with the materiel and knowledge to help them develoop their weapons industry, they would not have been quite the force they were on the Eastern Front, effectively splitting the Nazi war effort into three fronts: Eastern, Western, and the domestic front of extermination camps and secret police, which had to consume tremendous resources that could have been diverted to the war effort were they not used to kill more civilians than the total number of combat troops KIA for the entire Axis.
The only bomb that made sense for seizing territory or riches would be the neutron bomb (kills people but leaves most infrastructure). Nowadays, however, all that would need to be done is disrupt shipping, computer transactions, and banking (all interlaced), and wait for the survivors to kill each other over the scraps. All of those systems are seriously dependent on electronics, and a few large EMP devices would make a mess of things.