Mathematical chemistry is the area of research engaged in novel applications of
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
to
chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...
; it concerns itself principally with the
mathematical modeling
A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical m ...
of chemical phenomena. Mathematical chemistry has also sometimes been called computer chemistry, but should not be confused with
computational chemistry
Computational chemistry is a branch of chemistry that uses computer simulations to assist in solving chemical problems. It uses methods of theoretical chemistry incorporated into computer programs to calculate the structures and properties of mol ...
.
Major areas of research in mathematical chemistry include
chemical graph theory
Chemical graph theory is the topology branch of mathematical chemistry which applies graph theory to mathematical modelling of chemical phenomena.
The pioneers of chemical graph theory are Alexandru Balaban, Ante Graovac, Iván Gutman, Haruo ...
, which deals with
topology
Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...
such as the mathematical study of
isomerism
In chemistry, isomers are molecules or polyatomic ions with identical molecular formula – that is, the same number of atoms of each element (chemistry), element – but distinct arrangements of atoms in space. ''Isomerism'' refers to the exi ...
and the development of
topological descriptors or indices which find application in
quantitative structure-property relationships; and chemical aspects of
group theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...
, which finds applications in
stereochemistry
Stereochemistry, a subdiscipline of chemistry, studies the spatial arrangement of atoms that form the structure of molecules and their manipulation. The study of stereochemistry focuses on the relationships between stereoisomers, which are defined ...
and
quantum chemistry
Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions ...
. Another important area is molecular knot theory and
circuit topology
The circuit topology of a folded linear polymer refers to the arrangement of its intra-molecular contacts. Examples of linear polymers with intra-molecular contacts are nucleic acids and proteins. Proteins fold via the formation of contacts of v ...
that describe the topology of folded linear molecules such as proteins and nucleic acids.
The history of the approach may be traced back to the 19th century.
Georg Helm published a treatise titled "The Principles of Mathematical Chemistry: The Energetics of Chemical Phenomena" in 1894.
[Helm, Georg. The Principles of Mathematical Chemistry: The Energetics of Chemical Phenomena. translated by J. Livingston R. Morgan. New York: John Wiley & Sons, 1897]
/ref> Some of the more contemporary periodical publications specializing in the field are MATCH Communications in Mathematical and in Computer Chemistry, first published in 1975, and the Journal of Mathematical Chemistry, first published in 1987. In 1986 a series of annual conferences MATH/CHEM/COMP taking place in Dubrovnik
Dubrovnik, historically known as Ragusa, is a city in southern Dalmatia, Croatia, by the Adriatic Sea. It is one of the most prominent tourist destinations in the Mediterranean Sea, Mediterranean, a Port, seaport and the centre of the Dubrovni ...
was initiated by the late Ante Graovac.
The basic model
A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin , .
Models can be divided in ...
s for mathematical chemistry are molecular graph and topological index.
In 2005 the International Academy of Mathematical Chemistry (IAMC) was founded in Dubrovnik (Croatia) by Milan Randić. The Academy has 82 members (2009) from all over the world, including six scientists awarded with a Nobel Prize.
See also
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Bibliography
* ''Molecular Descriptors for Chemoinformatics'', by R. Todeschini and V. Consonni, Wiley-VCH, Weinheim, 2009.
* ''Mathematical Chemistry Series'', by D. Bonchev, D. H. Rouvray (Eds.), Gordon and Breach Science Publisher, Amsterdam, 2000.
* ''Chemical Graph Theory, by N. Trinajstic'', CRC Press, Boca Raton, 1992.
* ''Mathematical Concepts in Organic Chemistry'', by I. Gutman, O. E. Polansky, Springer-Verlag, Berlin, 1986.
* ''Chemical Applications of Topology and Graph Theory'', ed. by R. B. King, Elsevier, 1983.
* "Topological approach to the chemistry of conjugated molecules", by A. Graovac, I. Gutman, and N. Trinajstic, ''Lecture Notes in Chemistry'', no.4, Springer-Verlag, Berlin, 1977.
Notes
References
* N. Trinajstić, I. Gutman, Mathematical Chemistry, Croatica Chemica Acta, 75(2002), pp. 329–356.
* A. T. Balaban, Reflections about Mathematical Chemistry, Foundations of Chemistry, 7(2005), pp. 289–306.
* G. Restrepo, J. L. Villaveces, Mathematical Thinking in Chemistry, HYLE, 18(2012), pp. 3–22.
Advances in Mathematical Chemistry and Applications. Volume 2. Basak S. C., Restrepo G., Villaveces J. L. (Bentham Science eBooks, 2015)
External links
Journal of Mathematical Chemistry
MATCH Communications in Mathematical and in Computer Chemistry
International Academy of Mathematical Chemistry
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