Chemical space is a concept in cheminformatics referring to the property space spanned by all possible molecules and chemical compounds adhering to a given set of construction principles and boundary conditions.
Theoretical Chemical Spaces
A chemical space often referred to in cheminformatics is that of potential pharmacologically active molecules. Its size is estimated to be in the order of 1060 molecules. There are no rigorous methods for determining the precise size of this space. The assumptions  used for estimating the number of potential pharmacologically active molecules, however, use the Lipinski rules, in particular the molecular weight limit of 500. The estimate also restricts the chemical elements used to be Carbon, Hydrogen, Oxygen, Nitrogen and Sulfur. It further makes the assumption of a maximum of 30 atoms to stay below 500 Daltons, allows for branching and a maximum of 4 rings and arrives at an estimate of 1063. This number is often misquoted in subsequent publications  to be the estimated size of the whole organic chemistry space, which, however, will be much larger through considering the potential introduction of the halogens and other elements.
Concrete Chemical Spaces
As of July 2009, there were 49,037,297 organic and inorganic substances registered with the Chemical Abstracts Service, indicating that they have been reported in the scientific literature. Chemical libraries used for laboratory-based screening for compounds with desired properties are examples for real-world chemical libraries of small size (a few hundred to hundreds of thousands of molecules).
Generation of Chemical Spaces
Systematic exploration of chemical space is possible by creating in silico databases of virtual molecules, which can be visualized by projecting multidimensional property space of molecules in lower dimensions. Generation of chemical spaces may involve creating stoichiometric combinations of electrons and atomic nuclei to yield all possible topology isomers for the given construction principles. In Cheminformatics, software programs called Structure Generators are used to generate the set of all chemical structure adhering to given boundary conditions. Constitutional Isomer Generators, for example, can generate all possible constitutional isomers of a given molecular gross formula.
In the real world, chemical reactions allow us to move in chemical space. The mapping between chemical space and molecular properties is often not unique, meaning that there can be very different molecules exhibiting very similar properties. Materials design and drug discovery both involve the exploration of chemical space.
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