Just a few of the interesting tidbits:
The point to be made here is that, literally speaking, there is no upper limit to the mass of a thermonuclear device. Why would mankind choose to produce the extreme sized devices described above is anyone’s guess. However, it may be useful to point out that the cosmos over long time frames is a metaphorical shooting gallery. One has to merely recall the event that supposedly wiped out the dinosaurs and realize that over a long enough time period, most probably, even larger threats will present themselves. If we are going to plan for the survival of mankind for the next thousand years, why not plan for our survival essentially for eternity.
A much more practical 1,000 megatons to safety destroy a 1/4 mile wide or even a 1/3 mile wide asteroid might be doable providing at least one third of the bombs energy can be deposited within the asteroid’s material composition. 1,000 megatons of TNT releases the energy required to completely vaporize 2 cubic kilometers of water ice and because of the relatively lower specific heat and heat of vaporization of many solid minerals and metals, roughly, an equal volume of rock and metal may be vaporized depending on the minerals and metals in question. Note that even though it is relatively easy to bring water from freezing to boiling, the heat of vaporization of water is about 1.85 megajoules/kilogram as opposed to the 0.420 megajoules/kilogram necessary to heat liquid water just above freezing to boiling temperature. The specific heat of water and its heat of vaporization is about as high as they come for ordinary materials.
Our first use of space based nuclear bombs might be our first self-saving act of deflecting a large rouge asteroid with our name on it. Afterward, Project Orion star ships that use low yield atomic bombs, perhaps even low yield pure fusion bombs, can probably get us to the stars within this century if a concerted global effort were to be undertaken to develop the flight hard ware, mission plans, and operational protocol.
I strongly feel that we definitely have the explosive means for dealing with large rouge asteroids given enough lead time and human ingenuity.