en>AnomieBOT: Dating maintenance tags: {{Unreferenced}}

2014-10-27T18:20:16Z

Dating maintenance tags: {{Unreferenced}}

← Older revision		Revision as of 20:20, 27 October 2014
Line 1:		Line 1:
	~~The '''Patterson function'''~~ is ~~used~~ to solve the [[phase problem]] in [[X-ray crystallography]]. It was introduced in 1935 by [[Arthur Lindo Patterson]] (1902–1966) while he was a visiting researcher in the laboratory of [[Bertram Eugene Warren]] (1902–1991) at MIT.<ref>A. L. Patterson ''Z. ~~Krist~~'~~'. '''A90''', 517 (1935)~~.~~</ref>~~		Alyson is what my husband enjoys to contact me but I don't like when individuals use my complete title. My day job is an invoicing officer but I've already applied for an additional one. She is really fond of caving but she doesn't have the time recently. My wife and I live in Mississippi but now I'm contemplating other choices.<br><br>My web blog :: [http://www.youronlinepublishers.com/authWiki/AdolphvhBladenqq online psychic readings]

	~~The Patterson function~~ is ~~defined as~~

	~~:<math>P(u,v,w) = \sum\limits_{h k l} \left\|F_{h k l}\right\|^2 \;e^{-2\pi i(hu + kv + lw)}.</math>~~

	It is essentially the [[Fourier transform]] of the intensities rather than the [[structure factor]]s. The Patterson function is also equivalent to the [[electron density]] [[convolution\|convolved]] with its inverse:

	~~:<math>P(\vec{u}) = \rho(\vec{r}) * \rho(-\vec{r}).</math>~~

	~~Furthermore, a Patterson map~~ of '~~'N'' points will~~ have ~~''N(N−1)'' peaks, excluding~~ the ~~central peak~~ and ~~any overlap.~~

	~~The peaks~~ in ~~the Patterson function are the interatomic distance vectors weighted by the product of the number of electrons in the atoms concerned.~~

	~~Because for each vector between atoms i and j there is an oppositely oriented vector of the same length (between atoms j and i), the Patterson function always has [[centrosymmetry]]~~.

	~~==One-dimensional example==~~
	~~Consider the series of [[Dirac delta function\|delta function]]s given by~~

	:<~~math~~>~~f(x) = \delta(x) + 3 \delta(x-2) + \delta(x-5) + 3 \delta(x-8) + 5 \delta(x-10). \,~~<~~/math~~>

	~~Then the Patterson function is~~

	:~~<math>P(u) = 5 \delta(u+10) + 18 \delta(u+8) + 9 \delta(u+6) + 6 \delta(u+5) + 6 \delta(u+3) + 18 \delta(u+2) + 45 \delta(u) \, </math>~~
	::~~::<math> {} + 18 \delta(u-2) + 6 \delta(u-3) + 6 \delta(u-5) + 9 \delta(u-6) + 18 \delta(u-8) + 5 \delta(u-10)~~. ~~\, <~~/~~math>~~

	~~==References==~~
	~~{{reflist}}~~

	~~{{DEFAULTSORT:Patterson Function}}~~
	~~[[Category:Crystallography]~~]

en>CBM: Article already marked as stub

2009-08-17T00:20:25Z

Article already marked as stub

New page

The '''Patterson function''' is used to solve the [[phase problem]] in [[X-ray crystallography]]. It was introduced in 1935 by [[Arthur Lindo Patterson]] (1902–1966) while he was a visiting researcher in the laboratory of [[Bertram Eugene Warren]] (1902–1991) at MIT.<ref>A. L. Patterson ''Z. Krist''. '''A90''', 517 (1935).</ref>

The Patterson function is defined as

:<math>P(u,v,w) = \sum\limits_{h k l} \left|F_{h k l}\right|^2 \;e^{-2\pi i(hu + kv + lw)}.</math>

It is essentially the [[Fourier transform]] of the intensities rather than the [[structure factor]]s. The Patterson function is also equivalent to the [[electron density]] [[convolution|convolved]] with its inverse:

:<math>P(\vec{u}) = \rho(\vec{r}) * \rho(-\vec{r}).</math>

Furthermore, a Patterson map of ''N'' points will have ''N(N−1)'' peaks, excluding the central peak and any overlap.

The peaks in the Patterson function are the interatomic distance vectors weighted by the product of the number of electrons in the atoms concerned.

Because for each vector between atoms i and j there is an oppositely oriented vector of the same length (between atoms j and i), the Patterson function always has [[centrosymmetry]].

==One-dimensional example==
Consider the series of [[Dirac delta function|delta function]]s given by

:<math>f(x) = \delta(x) + 3 \delta(x-2) + \delta(x-5) + 3 \delta(x-8) + 5 \delta(x-10). \,</math>

Then the Patterson function is

:<math>P(u) = 5 \delta(u+10) + 18 \delta(u+8) + 9 \delta(u+6) + 6 \delta(u+5) + 6 \delta(u+3) + 18 \delta(u+2) + 45 \delta(u) \, </math>
::::<math> {} + 18 \delta(u-2) + 6 \delta(u-3) + 6 \delta(u-5) + 9 \delta(u-6) + 18 \delta(u-8) + 5 \delta(u-10). \, </math>

==References==
{{reflist}}

{{DEFAULTSORT:Patterson Function}}
[[Category:Crystallography]]

Lightface analytic game - Revision history

en>AnomieBOT: Dating maintenance tags: {{Unreferenced}}

en>CBM: Article already marked as stub