Can I use nanotechnology to make the strongest possible non-nuclear explosive (when compared to the equal amounts of other explosives) or are we already at the peak-level of what can be achieved with chemicals?
I like the idea of nanotechnology Penning traps to hold antitmatter, but you need to supply the antimatter to be stored, so that’s probably not what you want. You want to fabricate it using atoms and assemblers in a normal way. (I’m making the technical reason explicit for reasons I’ll come back to.)
Nanotechnology could be used to safely store and contain some chemical or combination of separate molecules that would be impractical to use to make a bulk explosive. It's not an explosive but to get the idea, imagine having nanocells that safely store FOOF at room temperature, until intentionally released.
Things that are not normally explosives but are energy dense could be made to be explosive, through nanotechnology. The storage system would distribute the trigger for the reaction throughout the bulk at the speed of electronic signals, and not require a detonation style reaction to be the normal property of that chemical.
So if some other answers supply information on the energy density of chemicals, trust that nanotech can make that energy release instantly. Even common gasoline is more energy dense than dynomite, as I recall — it just doesn’t detonate in the desired manner. (Have to figure the density of gasoline and oxidizer combined to be a fair comparison.)
You might even be able to store energy in a scale associated with nuclear energy, well beyond chemical. This idea could count if you can create the exotic state using a nanotech device, putting energy in like charging a battery. This idea is a meta-stable excited nuclear state, which is kept long-term via quantum effects. I can imagine this invented with the intent of producing superbatteries, but he got bombs instead, or they are just too super for civilian use.
Another reasonably stable nuclear isomer, with a half-life of 31 years, is 178m2Hf, which has the highest excitation energy of any comparably long-lived isomer. One gram of pure 178m2Hf contains approximately 1.33 gigajoules of energy, the equivalent of exploding about 315 kg (694 lb) of TNT.
Strained-bond (or "strain energy") explosives.
When synthesizing... well, almost anything, the atomic and molecular bonds will settle into a minimum energy configuration. Only with careful coupling of two different species, one widely less energetic, with bonds of the appropriate length, and another that can both be bound to the first and then 'detached', so to speak, is it possible to create molecules where the bonds don't have the minimum possible energy.
When those molecules reorganize, the extra configurational energy is released, usually at very high speeds compared to conventional explosives.
One such molecule is octanitrocubane, which is the fastest known explosive, and has a projected brisance three to four times higher than C4 explosive. It makes an appearance (but with its brisance and yield considerably overestimated) in Douglas E. Richards' Split Second, where it is synthesized using
nanosecond-level time-travel duplication.
But these substances are exceedingly difficult or straight impossible to manufacture with ordinary chemistry: it's like trying to compress steel springs using tools made of putty. Pyramidanes are only theoretical, and this is the simple and intuitive pathway to azafenestrane achieved only a few years ago:
Nanotechnology, or rather the possibility of large-scale atom-level assembly, changes all that. With nanotechnology you can force atoms in configurations that they would never assume by themselves, no matter what undirected atoms around them might do, and achieve this without the rest of the structure, no matter how complex, collapsing on you and probably taking the whole manufacturing plant with it.
So you build your chemical explosive by arm-bending a very energetic molecule with very strong bonds, one branch at a time.
For example superphanes have an extra strain kick of 84 kJ/mol (compare that to the explosive energy of RDX, which is about 1300 kJ/mol. Not much, but that's extra - and that's for one singly-strained configuration).
It would be theoretically possible to arm-bend and produce a folded-up, densely packed poly-fenestrane compound with 6400 to 10000 kJ/mol strain energy alone (I wouldn't want to guess the stability of that), or even design completely new compounds with even higher energy content. Such a hypothetical polyfenestrane explosive would be around seven times more powerful than RDX or hexanitrobenzene, with a relative effectiveness factor around 13 compared to ordinary TNT.
(Sorry, I think I now have to go explain to the pair of helpful guys in black suits at my door what 'hypothetical' means).