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I'm interested in

  • How many unique molecules (of all types: organic and inorganic, etc), exist in the world accessible by man (let's exclude black holes and the centers of stars etc)?
  • What subset of those distinct types are only in existence because of synthesis by man?

To make it simpler, ignore variants such as molecules with different atom isotopes and different bond configurations (e.g. cis, trans). E.g. standard water and "heavy water" are both $\ce{H2O}$ and count as one.

I'm looking for a theoretical estimate, so orders of magnitude only are required. I'm not looking for a count of records in some database catalogue of chemicals.

Please explain methods for determining your estimates. This isn't really helpful.

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    $\begingroup$ I can't even begin to imagine how an appropriate answer can be offered to this question. Given the vastness of the Universe and how much of it we don't actually know, and given the multitude of chemical environments that are possible, it would be difficult to answer this question without make a variety of gross approximations. Also, what do you mean by distinct types? $\endgroup$
    – LordStryker
    Commented Oct 1, 2014 at 14:41
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    $\begingroup$ Could we ask what is the motivation for this question? It seems like you want an estimate of synthetic molecules vs. all molecules. Why? Curiosity or something else? $\endgroup$
    – user467
    Commented Oct 1, 2014 at 22:40
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    $\begingroup$ I'm inclined to estimate over 9000. $\endgroup$
    – Sherlock Holmes
    Commented Oct 2, 2014 at 8:16
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    $\begingroup$ Depending on the precise definition of the terms "molecule" and "unique", the answer can be either a very large finite number, or countable infinity, or even uncountable infinity. $\endgroup$
    – Ivan Neretin
    Commented Apr 8, 2016 at 7:24
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    $\begingroup$ The answer is likely to be uncountably big (bigger, for example, the the number of particles in the observable universe). For simple unsaturated hydrocarbons alone the number of structural isomers is thought to exceed 10^22 for just 50 carbons. And that is just two types of atom with restrictions on connectivity. The possibilities grow faster than exponentially for more atom types. And we can do longer chains. $\endgroup$
    – matt_black
    Commented Nov 22, 2017 at 22:00

6 Answers 6

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Polymers make this question more or less unanswerable.

Consider human chromosome 1, which contains about 249,000,000 base pairs. There is nothing that says we couldn't order those pairs in any way we like, so for DNA alone, in a quantity that exists in every person on Earth, there exists the possibility for 4249000000 different molecules. Include things like alternative nucleotides (there are almost surely at least thousands of these that are possible) and longer chains and the number gets even more enormous, and that's only including DNA (and close relatives.)

There's no real way to include all of them, since there have to be an enormous number of ways to put these molecules together that we haven't found yet.

How many exist? An awful lot. How many only exist in our minds? Almost all of them (the universe only contains about 1080 particles, after all.

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    $\begingroup$ That's a great explanation for a theoretical maximum. I was thinking about DNA combinations in the same way. As for actual numbers that exist, can you get any closer precision than "an awful lot"? Any idea of the proportion of those that only exist because they're man-made? $\endgroup$
    – poshest
    Commented Oct 1, 2014 at 20:02
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    $\begingroup$ I think amount of particles is very unstable in the universe. You know, black holes, black mass and stuff. $\endgroup$
    – Tomáš Zato
    Commented Oct 1, 2014 at 20:21
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    $\begingroup$ Awful lot? Actually, you mean infinite. There is no upper bound for chainlength of polymers, therefore their number itself is infinite. The only real upper bond is the size of universe and the number of atoms in it. $\endgroup$
    – Greg
    Commented Oct 2, 2014 at 0:09
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    $\begingroup$ Well, that gives us a reasonable upper bound. Each atom is or is not bound to each other atom, so we're looking at ways to partition N=10^80 elements, i.e. the upperbound is Bell(10^80) = e^(e^(10^80)). Writing out that number is impossible in this universe, though, as it contains more than 10^80 digits (!) $\endgroup$
    – MSalters
    Commented Oct 2, 2014 at 8:04
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    $\begingroup$ @Greg If we're going to be picky, it wouldn't really be infinite, but it's going to be absurdly large. Above a certain limit the molecule's behavior will be dominated by gravitational affects. Make it large enough and it will collapse into a star and begin fusion, messing up the chemical bonds. The best you could do for something that would qualify as a single molecule would be an upper mass limit for a white dwarf star. That's going to limit your chain length to roughly 10^57 atoms total. There are a ton of ways to arrange those, but it's not infinite. I love this stuff... $\endgroup$
    – Jason Patterson
    Commented Oct 2, 2014 at 12:12
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Without some constraint on the number of atoms/molecular weight, the number of possible theoretical compounds is infinite, for the reason given by Jason Patterson: you can always extend a polymer by one more unit.

It has been estimated that there are 10^60 possible organic compounds with molecular weight less than 500 The art and practice of structure-based drug design: a molecular modelling perspective. CAS may have duplicates, but it is still the best database of all known compounds in the literature, and yet is not comprehensive. Almost all of the CAS database is wholly synthetic. A search for entries in CAS with molecular weight <500 gives 61,026,438 hits, about half of the entire database. The reference above suggests that life can exist with a few thousand small molecules (i.e. compounds with molecular weight <500). Nature produces far more compounds than the absolute minimum, but I expect that we have only scratched the surface of what is out there.

That should give you an idea of the orders of magnitude that we are talking about. Keep in mind that the numbers will grow exponentially as the constraint of MW < 500 is relaxed. In short, chemists have synthesized literally millions of different compounds, but essentially none relative to the possibilities.

I suggest you research the topic of "chemical space" if you want to know more about this area.

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  • $\begingroup$ I think stratification into molecular weights is a good way to break the problem down. Who estimated the 10^60? And how? I don't have the book, sorry. +1 for "chemical space" too! The magic search formula! :) $\endgroup$
    – poshest
    Commented Oct 2, 2014 at 7:13
  • $\begingroup$ This has some references to your numbers and a lot of other good stuff ncbi.nlm.nih.gov/pmc/articles/PMC3447393 $\endgroup$
    – poshest
    Commented Oct 2, 2014 at 7:32
  • $\begingroup$ Reymond (in the link above) suggested the 10^60, but others have agreed the number is probably in that range. These questions usually fall into the range of cheminformatics. $\endgroup$
    – Geoff Hutchison
    Commented Oct 2, 2014 at 12:39
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According to the Chemical Abstracts Service, CAS REGISTRY (SM) contains more than 90 million unique organic and inorganic chemical substances, such as alloys, coordination compounds, minerals, mixtures, polymers and salts, and more than 65 million sequences—more than any other database of its kind. It includes substances reported in the literature back to the early 1800s, and is updated daily with about 15,000 substances.

The CAS registry does not include substances yet to be thought of or discovered. It does indeed include your five examples.

This is about as close to an answer as I can think of.

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  • $\begingroup$ well, I specifically asked not for a "count of records in some database catalogue of chemicals", but I do appreciate your answer. Is there any way of knowing the proportion of CAS that comprises wholly unnatural (synthetic) molecules? $\endgroup$
    – poshest
    Commented Oct 1, 2014 at 20:22
  • $\begingroup$ I think the proportion of naturally occurring substances is a relatively small proportion of the total. My reasoning: Note that while many substances exist in nature, not very many exist in nature in pure, bulk form. Note also that "natural products chemistry" is a specialty within organic chemistry dealing with substances that are produced within living organisms. There are a lot of natural products out there that have not yet been discovered--but this is still a small subset of possible substances. $\endgroup$
    – iad22agp
    Commented Oct 2, 2014 at 14:01
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In a database of currently available synthetic compounds that i built, there are 9.8 milion synthetic and natural compounds available to purchase, and an additional 27 milion compounds that the vendors think they can produce if needed.

This explicitly includes only pure compounds that can be described by drawing a structure, so no mixtures, and no stuff like DNA where you can only guess at the exact structure.

I included only around 30 trustworthy vendors, and this set is specifically not the same as the CAS register, mind you, as that one is very heavily polluted with gazillions of duplicates and variations in notation. Also, as a nice to know: nearly all vendors lie about the number of compounds they have.

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    $\begingroup$ You built that? Nice work! The Alibaba of chemicals. :) This is a great angle on the commerical numbers. Any idea what proportion only exist synthetically? $\endgroup$
    – poshest
    Commented Oct 2, 2014 at 6:47
  • $\begingroup$ Thanks for the compliment :-) The natural compounds can be either synthetized to be exactly as they are in nature, or actually filtered out of a natural source. Still, those are only a very small fraction of the total available compounds. I do not have a count at hand, but i would say an upper limit of 5% would be very royal. Of all the others, most compounds could, by chance, exist 'in the wild' in very very small quantities. So there is our next definition hurdle: when do you declare that a compound 'exists' in nature? If you have one molecule? $\endgroup$
    – Ellert van Koperen
    Commented Oct 2, 2014 at 8:35
  • $\begingroup$ It is not available online, sorry. This data represents a lot of work and tools that are not free either. $\endgroup$
    – Ellert van Koperen
    Commented Oct 2, 2014 at 19:38
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You don't need to go to polymers. You can already create a huge amount of molecules in the realm of small molecules (MW < 900 Da). It is an interesting field since most of today's drugs are small molecules.

Here is the link to a research group in Bern, Switzerland that enumerates virtual compounds and tries to classify to many different categories. One is synthetic availability.

This is where they explain what they do

Here are the tools they offer

They have a lot of tools with fancy visualization for some. Happy playing.

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  1. Choose an upper limit on number of atoms in a molecule. (e.g. max_a=500)
  2. Choose which of the atomic elements you wish to allow (e.g. els=1..92)
  3. Select atom from els list
  4. What possible number of bonds can this atom type make (e.g. b_el1 = {2,3,4})
  5. Select how many bonds in this instance (e.g. current_b = 3)
  6. Select next bond number (bond_num = 1 in first iteration)
  7. Select next add-on atom from els list, to be attached at current bond num
  8. Check add-on atom for compatibility: bond type, electrons avail, space fit
  9. If pass all tests, then add-on. Index atom counter +1.
  10. If not pass, return to step 7.
  11. If pass, return to step 6.
  12. If all bonds full, return to step 7
  13. If atom counter exceeds max_atoms, STOP
  14. Eliminate redundancies (which will equal quant of termini-1)

For anyone with access to reaction compatibility data, this algorithm generates the total number of possible molecules up to a chosen limit. Not all details are provided for an 'exhaustive search' procedure, such as tracking all branches, and how to handle double bonds. but these can be added in a straight forward manner. The 'set limit' feature is necessary to avoid putting your computer to millennia of number crunching.

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    $\begingroup$ This doesn't really answer the question, which is very difficult to answer anyway. Also, actually implementing this algorithm is a lot more difficult than you seem to imagine. For example Check add-on atom for compatibility: bond type, electrons avail, space fit is a highly non trivial task and there is also a question as to how compatible is 'compatible'. $\endgroup$
    – bon
    Commented Nov 24, 2015 at 11:32
  • $\begingroup$ Also, this algorithm can not create rings. As it happens, rings and fused rings make up the majority of carbon based natural compounds. $\endgroup$
    – Ellert van Koperen
    Commented Feb 23, 2018 at 22:26

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