Organic chemistry | Lecture 1 | part 2

Interesting lecture, thanks! Could you please explain, how can we calculate the number of structural isomers of an alkane based on the number of carbons in the skeleton?

Hi, sure!

It isn't easy but it is an interesting research topic

Determining the number of possible structures for a given range of chemical formulae isn't simple even for saturated hydrocarbons. The number of possible structural isomers rises rapidly with the number of carbons and soon exceeds your ability to enumerate or identify the options by hand. Wikipedia, for example, lists the numbers of isomers and stereoisomers for molecules with up to 120 carbons. But the counts are getting silly even at 10 carbons where there are 75 isomers and 136 stereoisomers.

Structural isomers start from butane.

Formula is 2^(n-4) + 1 for up to n=7

n is number of carbon atoms

For octane it's 18

For more than n=7 the formula is

2^(n-4) + 3

But this formula doesn't take into account the stereoisomers as far as I know.

Generally speaking, graph-theoretical enumeration aims at counting chemical compounds as graphs (2D structures). In other words, it is concerned with constitutional (or structural) isomers.

• • The most famous method for combinatorial enumeration of graphs is based on Polya's theorem: G. Polya and R. C. Read,
    Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds (Springer, 1987).
  • G. Polya, R. E. Tarjan, and D. R. Woods, Notes on Introductory Combinatorics (Birkhauser, 1983) Chapter 6.
  • An introduction to the practical uses of Polya's theorem from a chemical viewpoint has appeared: O. E. Polansky, Polya's method for the Enumeration of Isomers (MATCH Commun. Math. Comput. Chem. 1, 11--31 (1975)). free access.
  • Many examples of chemical application of Polya's theorem have been described in the following book: A. T. Balaban (Ed.), Chemical Applications of Graph Theory (Academic Press, 1976).

Thanks for the detailed answer!