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I know that some chemical substances are used as explosives. Amongst the most famous nitroglycerin in dynamite and cyclonite in C-4. Which chemical properties (I suspect that physical properties have less of an effect) make a substance a good explosive? If we know, for example, the formula and its geometry, is it easy to predict how explosive it can be?

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    $\begingroup$ @TylerBailey - Those kinds of reactions are certainly dangerous, but the salient feature of an explosion is a rapid expansion of volume, usually by the rapid production of many equivalents of gas. $\endgroup$ – Ben Norris Mar 2 '13 at 13:06
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    $\begingroup$ I think it's interesting to cite silver acetylide exemplifying an explosive where none the products are gaseous. $\endgroup$ – Nicolau Saker Neto May 10 '13 at 2:57
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There are, actually, several types of explosives by use: initiating (primary) explosives, secondary explosives and blasting agents.

Initiating explosive must be sensitive to shock/friction, but not too sensitive. The most famous primary explosive is mercury fulminate, but others are known. To act as primary explosive, substance must have hi-energetic unstable groups, like peroxides, azides and similar.

Secondary explosives are substances, that are not sensitive to shock/friction and requires initiating blast to explode. Unlike primary explosives, they can be manufactured as hi-density blocks with high speed of detonation. It is exactly what is needed for military applications. The most common type of secondary explosives are (substituted) polynitroarenes. Most well-known examples are TNT and picric acid. It is very beneficial to have zero oxygen balance for such explosives, i.e. to explode without extra oxygen produced and without extra reducing gases produced. TNT, for example, has negative oxygen balance, producing much carbon on explosion, and dinitromethane has positive oxygen balance, producing extra oxygen on explosion. A less stable class of secondary explosives is nitroamines, with hexo/octo-gen as most well-known example. Anyway, main variables here are relative stability and high density paired with medium-high energy of explosion.

Tertiary explosives or blasting agents are explosives, used to move hight amounts of materials. They are usually used in big amounts in mining/engineering and must be cost-effective and produce much gases in explosion. The most common typeы of blasting agents are oxyliquits and compositions, based on ammonia nitrate.

There are also special kinds of explosives/pyrotechnic mixtures. For example, a mixture used in car airbags must produce much gases very quickly, but said gases must have low temperature.

If we know, for example, the formula and its geometry - is it easy to predict how explosive it can be?

Actually, not that easy. Di/Trinitroarenes are usually explosive, but their stability and performance may vary greatly and depends on crystal structure, density and form (crystals/fine dust/puffy things).

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I'm going to assume by 'good explosive' you mean 'high energy to mass ratio', which by no means implies anything about whether the explosive is 'good' in the 'won't suddenly explode when thought about' sense.

This is not intended to be a full answer as it doesn't touch on the terrifying explosivity of organic peroxides, however it's a start. The presence of nitro ($\ce{R-NO2}$) or azide ($\ce{R-N=N=N}$) groups in a molecule is strongly suggestive of explosivity. This has a lot to do with the large negative free energy change of formation of dinitrogen and (I guess) oxides of nitrogen upon decomposition of these molecules. $\ce{N2}$ has one of the strongest bonds known and releasing a lot of $\ce{N2_{(g)}}$ entails a large increase in entropy. Inorganic nitrates and azides are also likely to be explosive.

The state of the art in explosive research seems to involve cramming as many consecutive nitrogen atoms as possible into a molecule, as showcased on Derek Lowe's blog:

$\ce{C4H4N8}$

$\ce{C2N14}$ (what?!)

Alternatively, you can take a highly strained polyhedrane of some description and stick nitro groups all over it. The ur example of this sort of philosophy is octanitrocubane.

Bonus: tetranitrotetrahedrane

Disclaimer: Explosives are deadly and people who prepare them are either highly trained experts with exquisite safety infrastructure, or morons. Nothing in my answer should be taken by any person as an endorsement to attempt to synthesise anything described.

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    $\begingroup$ Your link to C2N14 is part of Lowe's "Things I won't work with" series, which includes some great links to explosives research. $\endgroup$ – Colin McFaul Mar 2 '13 at 19:02
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It is extremely difficult to look at a molecule and know whether it is explosive.

But, generally speaking, highly exothermic chemical reactions are the "explosive" ones.

A --> B + C

What makes the reaction exothermic? Either A is very unstable, or B and C are very stable. Any molecule that has lots of very stable B's and C's is going to be very explosive. Examples of very stable B and C could be carbon soot, water, and also NO2. (Actually there are lots of them)

The trick is to keep A stable enough (metastable) to use it for some practical purpose. So, this somewhat limits how "unstable" A can be.

Said another way, I would design an explosive A to be an effective delivery mechanism of B's and C's just waiting to be formed.

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I would add that explosive reactions are extremely rapid reactions. It is hard to judge rapidity of a reaction just by knowing the structure of a molecule.

A given substance can qualify as an explosive under special conditions. For example we cook with methane gas. It burns nicely and gives us no problems. But mix it with the proper amount of oxygen and toss in a match and there goes the neighborhood.

The proper amount is often a range of concentrations, wide or narrow depending on the molecules involved.

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