Editing Electron density (section)

==Overview==
In [[molecule]]s, regions of large electron density are usually found around the [[atom]], and its bonds. In de-localised or [[conjugated system]]s, such as [[phenol]], [[benzene]] and compounds such as [[hemoglobin]] and [[chlorophyll]], the electron density is significant in an entire region, i.e., in benzene they are found above and below the planar ring. This is sometimes shown diagrammatically as a series of alternating single and double bonds. In the case of phenol and benzene, a circle inside a [[hexagon]] shows the delocalised nature of the compound. This is shown below:

[[File:Phenol mesomeric structures.png|503px|center|Mesomeric structures of phenol]]

In compounds with multiple ring systems which are interconnected, this is no longer accurate, so alternating single and double bonds are used. In compounds such as chlorophyll and phenol, some diagrams show a dotted or dashed line to represent the delocalization of areas where the electron density is higher next to the single bonds.<ref>e.g., the white line in the diagram on [http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/C/Chlorophyll.html Chlorophylls and Carotenoids] {{Webarchive|url=https://web.archive.org/web/20170809120412/http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/C/Chlorophyll.html |date=2017-08-09 }}</ref> Conjugated systems can sometimes represent regions where [[electromagnetic radiation]] is absorbed at different wavelengths resulting in compounds appearing coloured. In [[polymer]]s, these areas are known as chromophores.

In [[Quantum chemistry|quantum chemical calculations]], the electron density, ρ('''r'''), is a function of the coordinates '''r''', defined so ρ('''r''')d'''r''' is the number of electrons in a small volume d'''r'''.  For [[Open shell|closed-shell]] molecules, <math> \rho(\mathbf{r}) </math> can be written in terms of a sum of products of basis functions, φ:
:<math> \rho(\mathbf{r}) = \sum_\mu \sum_\nu P_{\mu \nu} \phi_\mu(\mathbf{r}) \phi_\nu(\mathbf{r}) </math>
[[File:ElectronDensityAniline.PNG|300px|thumb|right|Electron density calculated for [[aniline]], high density values indicate atom positions, intermediate density values emphasize [[Chemical bond|bonding]], low values provide information on a molecule's shape and size.]]

where P is the [[density matrix]]. Electron densities are often rendered in terms of an isosurface (an isodensity surface) with the size and shape of the surface determined by the value of the density chosen, or in terms of a percentage of total electrons enclosed.

[[List of quantum chemistry and solid state physics software|Molecular modeling software]] often provides graphical images of electron density. For example, in [[aniline]] (see image at right). Graphical models, including electron density are a commonly employed tool in chemistry education.<ref>{{cite journal | title = Teaching Chemistry with Electron Density Models |author1=Alan J. Shusterman |author2=Gwendolyn P. Shusterman | journal = The Journal of Chemical Education | volume = 74 |issue=7 | pages = 771–775 | year = 1997 | doi = 10.1021/ed074p771|bibcode = 1997JChEd..74..771S}}</ref> Note in the left-most image of aniline, high electron densities are associated with the [[carbon]]s and [[nitrogen]], but the [[hydrogen]]s with only one proton in their nuclei, are not visible. This is the reason that [[X-ray crystallography|X-ray diffraction]] has a difficult time locating hydrogen positions.

Most molecular modeling software packages allow the user to choose a value for the electron density, often called the isovalue. Some software<ref>[http://www.wavefun.com/products/Sp_Comp.pdf or example, the Spartan program from Wavefunction, Inc.]</ref> also allows for specification of the electron density in terms of percentage of total electrons enclosed. Depending on the isovalue (typical units are electrons per cubic [[Bohr radius|bohr]]), or the percentage of total electrons enclosed, the electron density surface can be used to locate atoms, emphasize electron densities associated with [[chemical bond]]s , or to indicate overall molecular size and shape.<ref>{{cite book |author=Warren J. Hehre |author2=Alan J. Shusterman |author3=Janet E. Nelson | title = The Molecular Modeling Workbook for Organic Chemistry | publisher = Wavefunction | year = 1998 | location = Irvine, California | pages = 61–86 | isbn = 978-1-890661-18-2}}</ref>

Graphically, the electron density surface also serves as a canvas upon which other electronic properties can be displayed. The electrostatic potential map (the property of [[electrostatic potential]] mapped upon the electron density) provides an indicator for charge distribution in a molecule. The local ionisation potential map (the property of [[Ionization energy|local ionisation potential]] mapped upon the electron density) provides an indicator of electrophilicity. And the LUMO map ([[LUMO|lowest unoccupied molecular orbital]] mapped upon the electron density) can provide an indicatory for nucleophilicity.<ref>{{cite book | last = Hehre | first = Warren J. | title = A Guide to Molecular Mechanics and Quantum Chemical Calculations | publisher = Wavefunction, Inc. | year = 2003 | location = Irvine, California | pages = 85–100 | isbn = 978-1-890661-06-9}}</ref>