Van Der Waals Surface Area
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The van der Waals surface of a
molecule A molecule is a group of two or more atoms that are held together by Force, attractive forces known as chemical bonds; depending on context, the term may or may not include ions that satisfy this criterion. In quantum physics, organic chemi ...
is an abstract representation or model of that molecule, illustrating where, in very rough terms, a surface might reside for the molecule based on the hard cutoffs of
van der Waals radii The van der Waals radius, ''r'', of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. It is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics, ...
for individual atoms, and it represents a surface through which the molecule might be conceived as interacting with other molecules. Also referred to as a ''van der Waals envelope,'' the van der Waals surface is named for
Johannes Diderik van der Waals Johannes Diderik van der Waals (; 23 November 1837 – 8 March 1923) was a Dutch theoretical physicist who received the Nobel Prize in Physics in 1910 "for his work on the equation of state for gases and liquids". Van der Waals started his car ...
, a Dutch theoretical physicist and thermodynamicist who developed theory to provide a liquid-gas equation of state that accounted for the non-zero volume of atoms and molecules, and on their exhibiting an
attractive force Attraction may refer to: * Interpersonal attraction, the attraction between people which leads to friendships, platonic and romantic relationships. ** Physical attractiveness, attraction on the basis of beauty ** Sexual attraction * Object or eve ...
when they interacted (theoretical constructions that also bear his name). van der Waals surfaces are therefore a tool used in the abstract representations of molecules, whether accessed, as they were originally, via hand calculation, or via physical wood/plastic models, or now digitally, via
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 ...
software. Practically speaking, CPK models, developed by and named for
Robert Corey Robert Brainard Corey (August 19, 1897 – April 23, 1971) was an American biochemist, mostly known for his role in discovery of the α-helix and the β-sheet with Linus Pauling. Also working with Pauling was Herman Branson. Their discoveries ...
,
Linus Pauling Linus Carl Pauling ( ; February 28, 1901August 19, 1994) was an American chemist and peace activist. He published more than 1,200 papers and books, of which about 850 dealt with scientific topics. ''New Scientist'' called him one of the 20 gre ...
, and Walter Koltun,Robert B. Corey & Linus Pauling, 1953, "Molecular models of amino acids, peptides, and proteins," '' Rev. Sci. Instrum.,'' 24(8), pp. 621–627, DOI 10.1063/1.1770803, se

accessed 23 June 2015.
were the first widely used physical molecular models based on van der Waals radii, and allowed broad pedagogical and research use of a model showing the van der Waals surfaces of molecules.


van der Waals volume and van der Waals surface area

Related to the title concept are the ideas of a ''van der Waals volume'', Vw, and a ''van der Waals surface area,'' abbreviated variously as Aw, vdWSA, VSA, and WSA. A van der Waals surface area is an abstract conception of the surface area of atoms or molecules from a mathematical estimation, either computing it from first principles or by integrating over a corresponding van der Waals volume. In simplest case, for a spherical monatomic gas, it is simply the computed surface area of a sphere of radius equal to the van der Waals radius of the gaseous atom: The ''van der Waals volume'', a type of ''atomic'' or ''molecular volume,'' is a property directly related to the
van der Waals radius The van der Waals radius, ''r'', of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. It is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics ...
, and is defined as the volume occupied by an individual atom, or in a combined sense, by all atoms of a molecule. It may be calculated for atoms if the van der Waals radius is known, and for molecules if its atoms radii and the inter-atomic distances and angles are known. As above, in simplest case, for a spherical monatomic gas, Vw is simply the computed volume of a sphere of radius equal to the van der Waals radius of the gaseous atom: For a molecule, Vw is the volume enclosed by the ''van der Waals surface''; hence, computation of Vw presumes ability to describe and compute a van der Waals surface. van der Waals volumes of molecules are always smaller than the sum of the van der Waals volumes of their constituent atoms, due to the fact that the interatomic distances resulting from
chemical bond A chemical bond is the association of atoms or ions to form molecules, crystals, and other structures. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds or through the sharing of electrons a ...
are less than the sum of the atomic van der Waals radii. In this sense, a van der Waals surface of a homonuclear diatomic molecule can be viewed as an pictorial overlap of the two spherical van der Waals surfaces of the individual atoms, likewise for larger molecules like methane, ammonia, etc. (see images). van der Waals radii and volumes may be determined from the mechanical properties of gases (the original method, determining the
van der Waals constant The van der Waals equation is a mathematical formula that describes the behavior of real gases. It is an equation of state that relates the pressure, volume, Avogadro's law, number of molecules, and temperature in a fluid. The equation modifies ...
), from the critical point (e.g., of a fluid), from
crystallographic Crystallography is the branch of science devoted to the study of molecular and crystalline structure and properties. The word ''crystallography'' is derived from the Ancient Greek word (; "clear ice, rock-crystal"), and (; "to write"). In J ...
measurements of the spacing between pairs of unbonded atoms in crystals, or from measurements of electrical or optical properties (i.e.,
polarizability Polarizability usually refers to the tendency of matter, when subjected to an electric field, to acquire an electric dipole moment in proportion to that applied field. It is a property of particles with an electric charge. When subject to an elect ...
or
molar refractivity Molar refractivity, R_m, is a measure of the total polarizability of a mole of a substance. For a perfect dielectric which is made of one type of molecule, the molar refractivity is proportional to the polarizability of a single molecule of the s ...
). In all cases, measurements are made on macroscopic samples and results are expressed as molar quantities. van der Waals volumes of a single atom or molecules are arrived at by dividing the macroscopically determined volumes by the
Avogadro constant The Avogadro constant, commonly denoted or , is an SI defining constant with an exact value of when expressed in reciprocal moles. It defines the ratio of the number of constituent particles to the amount of substance in a sample, where th ...
. The various methods give radius values which are similar, but not identical—generally within 1–2  Å (100–200  pm). Useful tabulated values of van der Waals radii are obtained by taking a
weighted mean The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The ...
of a number of different experimental values, and, for this reason, different tables will be seen to present different values for the van der Waals radius of the same atom. As well, it has been argued that the van der Waals radius is not a fixed property of an atom in all circumstances, rather, that it will vary with the chemical environment of the atom.


Gallery

File:3D ammoniac.PNG, alt=Ammonia, van-der-Waals-based model, Ammonia, NH3, space-filling, van der Waals-based representation, nitrogen (N) in blue, hydrogen (H) in white. File:Phosphine-elpot-transparent-3D-balls.png, alt=Phosphine, van-der-Waals-based model with ball-and-stick model superimposed, Phosphine, PH3, space-filling, van der Waals-based representation, ball-and-stick model superimposed, phosphorus (P) in orange, hydrogen (H) in white. File:Octane.qutemol.png, alt=N-octane, van-der-Waals-based model, A space-filling model of ''n''-octane, the straight chain (normal)
hydrocarbon In organic chemistry, a hydrocarbon is an organic compound consisting entirely of hydrogen and carbon. Hydrocarbons are examples of group 14 hydrides. Hydrocarbons are generally colourless and Hydrophobe, hydrophobic; their odor is usually fain ...
composed of 8 carbons and 18 hydrogens, formulae: CH3CH2(CH2)4CH2CH3 ''or'' . Note, the representative shown is of a ''single conformational "pose"'' of a population of molecules, which, because of low
Gibbs energy In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure–volume work, that may be performed by a ther ...
barriers to rotation about its carbon-carbon bonds (giving the carbon "chain" great flexibility). normally is composed of a very large number of different such conformations (e.g., in solution). File:Thc.pdb.gif, alt=THC, van-der-Waals-based model, rotating, An example of a three-dimensional, space-filling, van der Waals-based model of a complex molecule, THC, the active agent in medical marijuana. ''You may have to click on the image to see rotation.'' File:Hydrogen-sulfide-elpot-transparent-3D-balls.png, alt=Hydrogen sulfide, van-der-Waals-based model with ball-and-stick model superimposed, with electrostatic potential surface, Hydrogen sulfide, H2S, space-filling, van der Waals-based representation, ball-and-stick model superimposed, sulfur (S) in yellow, hydrogen (H) in white over-shaded with blue. It also shows on its surface the electrostatic potential surface, (computed for the molecule in unknown fashion), using
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 ...
tools. It is shaded from blue for
electropositive Electronegativity, symbolized as , is the tendency for an atom of a given chemical element to attract shared electrons (or electron density) when forming a chemical bond. An atom's electronegativity is affected by both its atomic number and the d ...
areas to red for
electronegative Electronegativity, symbolized as , is the tendency for an atom of a given chemical element to attract shared electrons (or electron density) when forming a chemical bond. An atom's electronegativity is affected by both its atomic number and the d ...
areas.


See also

* Molecular surface (disambiguation) *
van der Waals force In molecular physics and chemistry, the van der Waals force (sometimes van der Waals' force) is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical elec ...
*
van der Waals molecule A van der Waals molecule is a weakly bound complex of atoms or molecules held together by intermolecular attractions such as van der Waals forces or by hydrogen bonds. The name originated in the beginning of the 1970s when stable molecular clust ...
*
van der Waals radius The van der Waals radius, ''r'', of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. It is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics ...
*
van der Waals strain Van der Waals strain is strain resulting from Van der Waals repulsion when two substituents in a molecule approach each other with a distance less than the sum of their Van der Waals radii. Van der Waals strain is also called Van der Waals repul ...


References and notes

{{reflist


Further reading

*DC Whitley
van der Waals surface graphs and molecular shape
''Journal of Mathematical Chemistry'', Volume 23, Numbers 3-4, 1998, pp. 377–397(21). *M. Petitjean
On the Analytical Calculation of van der Waals Surfaces and Volumes: Some Numerical Aspects
''Journal of Computational Chemistry'', Volume 15, Number 5, 1994, pp. 507–523.


External links


VSAs for various molecules
by Anton Antonov,
The Wolfram Demonstrations Project The Wolfram Demonstrations Project is an open-source collection of interactive programmes called Demonstrations. It is hosted by Wolfram Research. At its launch, it contained 1300 demonstrations but has grown to over 10,000. The site won a Pa ...
, 2007.
van der Waals radii
Structural Biology Glossary, Image Library of Biological Macromolecules.

of van der Waals surfaces and volumes. Intermolecular forces Physical chemistry
Surface A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...