In
chemistry, topology provides a way of describing and predicting the
molecular structure
Molecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule. It includes the general shape of the molecule as well as bond lengths, bond angles, torsional angles and any other geometrical parameters that dete ...
within the constraints of three-dimensional (3-D) space. Given the determinants of
chemical bond
A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing o ...
ing and the
chemical properties
A chemical property is any of a material's properties that becomes evident during, or after, a chemical reaction; that is, any quality that can be established only by changing a substance's chemical identity.William L. Masterton, Cecile N. Hurley ...
of the
atoms, topology provides a model for explaining how the atoms ethereal
wave function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements m ...
s must fit together. Molecular topology is a part of
mathematical chemistry
Mathematical chemistry is the area of research engaged in novel applications of mathematics to chemistry; it concerns itself principally with the mathematical modeling of chemical phenomena. Mathematical chemistry has also sometimes been called c ...
dealing with the algebraic description of chemical compounds so allowing a unique and easy characterization of them.
Topology is insensitive to the details of a
scalar field
In mathematics and physics, a scalar field is a function associating a single number to every point in a space – possibly physical space. The scalar may either be a pure mathematical number (dimensionless) or a scalar physical quantity ...
, and can often be determined using simplified calculations. Scalar fields such as
electron density
In quantum chemistry, electron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial va ...
,
Madelung field,
covalent field and the
electrostatic potential
Electrostatics is a branch of physics that studies electric charges at rest (static electricity).
Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for ambe ...
can be used to model topology.
[Brown, David; Topology and Chemistry; Structural Chemistry Volume 13, Numbers 3–4, 339–355, ]
Each scalar field has its own distinctive topology and each provides different information about the nature of chemical bonding and structure. The analysis of these topologies, when combined with simple electrostatic theory and a few empirical observations, leads to a quantitative model of localized chemical bonding. In the process, the analysis provides insights into the nature of chemical bonding.
Applied topology explains how large molecules reach their final shapes and how biological molecules achieve their activity.
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 formation of contacts of vari ...
is a topological property of folded linear polymers. It describes the arrangement of intra-chain contacts. Contacts can be established by intra-chain interactions, the so called hard contacts (h-contacts), or via chain entanglement or soft contacts (s-contacts). This notion has been applied to structural analysis of biomolecules such as proteins, RNAs, and genome.
Topological indices
It is possible to set up equations correlating direct quantitative structure activity relationships with experimental properties, usually referred to as
topological indices (TIs). Topological indices are used in the development of
quantitative structure-activity relationship
Quantitative may refer to:
* Quantitative research, scientific investigation of quantitative properties
* Quantitative analysis (disambiguation)
* Quantitative verse, a metrical system in poetry
* Statistics, also known as quantitative analysis ...
s (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure.
References
*Francl, Michelle
Stretching topologyNature Chemistry 1, 334–335 (2009) {{doi, 10.1038/nchem.302
*Rouvray, D. H.; A rationale for the topological approach to chemistry; Journal of Molecular Structure: THEOCHEM Volume 336, Issues 2–3, 30 June 1995, pages 101–114
See also
*
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 formation of contacts of vari ...
*
Theoretical chemistry
Theoretical chemistry is the branch of chemistry which develops theoretical generalizations that are part of the theoretical arsenal of modern chemistry: for example, the concepts of chemical bonding, chemical reaction, valence, the surface o ...
*
Molecular geometry
Molecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule. It includes the general shape of the molecule as well as bond lengths, bond angles, torsional angles and any other geometrical parameters that det ...
*
Molecular graph
In chemical graph theory and in mathematical chemistry, a molecular graph or chemical graph is a representation of the structural formula of a chemical compound in terms of graph theory. A chemical graph is a labeled graph whose vertices corresp ...
*
Molecular geometry
Supramolecular chemistry
Topology
Cheminformatics
Mathematical chemistry