View source for Van der Waals surface

{{Short description|Molecule interaction model}}
{{refimprove science|date=June 2015}}
{{Lowercase title}}

{| class="wikitable" style="float:right; margin-top:0"
|+ van der Waals radii
|-
! Element !! radius ([[angstrom|Å]])
|-
| [[Hydrogen]] || 1.2 (1.09)<ref name="RowlandRS1996">{{cite journal |title=Intermolecular nonbonded contact distances in organic crystal structures: comparison with distances expected from Van der Waals radii |author=Rowland RS, Taylor R |journal=J. Phys. Chem. |year=1996 |volume=100 |issue=18 |pages=7384–7391 |doi=10.1021/jp953141+}}</ref>
|-
| [[Carbon]] || 1.7
|-
| [[Nitrogen]] || 1.55
|-
| [[Oxygen]] || 1.52
|-
| [[Fluorine]] || 1.47
|-
| [[Phosphorus]] || 1.8
|-
| [[Sulfur]] || 1.8
|-
| [[Chlorine]] || 1.75
|-
| [[Copper]] || 1.4
|-
| colspan=2 | <small>van der Waals radii taken from<br/>Bondi's compilation (1964).<ref name="Bondi1964">{{cite journal | first = A. | last = Bondi | year =1964 | title = Van der Waals Volumes and Radii | journal = [[Journal of Physical Chemistry|J. Phys. Chem.]] | volume = 68 | issue = 3 | pages = 441–51 | doi= 10.1021/j100785a001}}</ref><br/>Values from other sources may<br/>differ significantly (''see text'')</small>
|-
|}
{{redirect-synonym|Molecular volume|Amount of substance}}
The '''van der Waals surface''' of a [[molecule]] 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]] for individual atoms, and it represents a surface through which the molecule might be conceived as interacting with other molecules.{{citation needed|date=June 2015}} 
Also referred to as a ''van der Waals envelope,'' the van der Waals surface is named for [[Johannes Diderik van der Waals]], a Dutch theoretical physicist and thermodynamicist who developed theory to provide a [[Van der Waals equation|liquid-gas equation of state]] that accounted for the non-zero volume of atoms and molecules, and on their exhibiting an [[Van der Waals force|attractive force]] 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]] software. 
Practically speaking, [[space-filling model|CPK model]]s, developed by and named for [[Robert Corey]], [[Linus Pauling]], and [[Walter Koltun]],<ref name="corpau">Robert B. Corey & Linus Pauling, 1953, "Molecular models of amino acids, peptides, and proteins," ''[[Review of Scientific Instruments|Rev. Sci. Instrum.]],'' '''24'''(8), pp. 621–627, DOI 10.1063/1.1770803, see [http://profiles.nlm.nih.gov/ps/access/MMBBHN.pdf], accessed 23 June 2015.</ref> 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 ==

[[File:3D methane.PNG|thumb|right|200 px|Methane, CH<sub>4</sub>, space-filling, van der Waals-based representation, carbon (C ) in black, hydrogen (H) in white. In [[chemistry]], a ''space-filling model'' is a type of [[three dimensional space|three-dimensional]] (3D) [[molecular model]] where the [[atom]]s are represented by spheres whose radii are, either as [[van der Waals radii]] or otherwise, proportional to the [[atomic radii|radii of the atoms]]. Center-to-center distances of the atoms are proportional to the distances between the [[atomic nucleus|atomic nuclei]], all in the same scale. Atoms of different [[chemical element]]s are usually represented by spheres of different colors, see below.]]

Related to the title concept are the ideas of a ''van der Waals volume'', V<sub>w</sub>, and a ''van der Waals surface area,'' abbreviated variously as A<sub>w</sub>, vdWSA, VSA, and WSA.{{citation needed|date=June 2015}} 
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:

{{center|1=<math>A_{\rm w} = 4\pi r_{\rm w}^2</math> .}}

The ''van der Waals volume'', a type of ''atomic'' or ''molecular volume,'' is a property directly related to the [[van der Waals radius]], 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, V<sub>w</sub> is simply the computed volume of a sphere of radius equal to the van der Waals radius of the gaseous atom:

{{center|1=<math>V_{\rm w} = {4\over 3}\pi r_{\rm w}^3</math> .}}

For a molecule, V<sub>w</sub> is the volume enclosed by the ''van der Waals surface''; hence, computation of  V<sub>w</sub> 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]] 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]]), from the [[critical point (thermodynamics)|critical point]] (e.g., of a fluid), from [[crystallography|crystallographic]] measurements of the spacing between pairs of unbonded atoms in crystals, or from measurements of electrical or optical properties (i.e., [[polarizability]] or [[molar refractivity]]). 
In all cases, measurements are made on macroscopic samples and results are expressed as [[mole (unit)|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 various methods give radius values which are similar, but not identical—generally within 1–2&nbsp;[[angstrom|Å]] (100–200&nbsp;[[picometre|pm]]). 
Useful tabulated values of van der Waals radii are obtained by taking a [[weighted mean]] 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.<ref name="Bondi1964"/>

== Gallery ==
<gallery>
File:3D ammoniac.PNG|alt=Ammonia, van-der-Waals-based model|Ammonia, NH<sub>3</sub>, 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, PH<sub>3</sub>, 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 [[octane|''n''-octane]], the straight chain (normal) [[hydrocarbon]] composed of 8 carbons and 18 hydrogens, formulae: CH<sub>3</sub>CH<sub>2</sub>(CH<sub>2</sub>)<sub>4</sub>CH<sub>2</sub>CH<sub>3</sub> ''or'' {{chem|C|8|H|18}}. Note, the representative shown is of a ''single [[Conformational isomerism|conformational]] "pose"'' of a population of molecules, which, because of low [[Gibbs free energy|Gibbs energy]] 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, [[tetrahydrocannabinol|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, H<sub>2</sub>S, 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|electrostatic potential surface]], (computed for the molecule in unknown fashion), using [[computational chemistry]] tools. It is shaded from blue for [[electropositivity|electropositive]] areas to red for [[electronegativity|electronegative]] areas.  
</gallery>

== See also ==
* [[Molecular surface (disambiguation)]]
* [[van der Waals force]]
* [[van der Waals molecule]]
* [[van der Waals radius]]
* [[van der Waals strain]]

== References and notes ==

{{reflist}}

== Further reading ==

*DC Whitley, [http://www.ingentaconnect.com/content/klu/jomc/1998/00000023/F0020003/00328856 van der Waals surface graphs and molecular shape], ''Journal of Mathematical Chemistry'', Volume 23, Numbers 3-4, 1998, pp.&nbsp;377–397(21).
*M. Petitjean, [https://archive.today/20121217195529/http://www3.interscience.wiley.com/cgi-bin/jtoc/109572744/ On the Analytical Calculation of van der Waals Surfaces and Volumes: Some Numerical Aspects], ''Journal of Computational Chemistry'', Volume 15, Number 5, 1994, pp.&nbsp;507–523.

== External links ==

* [http://demonstrations.wolfram.com/VanDerWaalsSurface/ VSAs for various molecules] by Anton Antonov, [[The Wolfram Demonstrations Project]], 2007.
* [http://www.imb-jena.de/ImgLibDoc/glossary/IMAGE_VDWR.html van der Waals radii], Structural Biology Glossary, Image Library of Biological Macromolecules.
* [http://petitjeanmichel.free.fr/itoweb.petitjean.spheres.html Analytical calculation] of van der Waals surfaces and volumes.

[[Category:Intermolecular forces]]
[[Category:Physical chemistry]]
[[Category:Johannes Diderik van der Waals|Surface]]