VLD - Revision history

BrianMcMahon: Style edits to align with printed edition

2017-05-17T18:10:06Z

Style edits to align with printed edition

MassimoNespolo: cat

2015-02-26T07:58:15Z

cat

BrianMcMahon at 12:51, 19 May 2014

2014-05-19T12:51:03Z

GervaisChapuis at 18:09, 20 September 2013

2013-09-20T18:09:33Z

GervaisChapuis at 13:17, 20 September 2013

2013-09-20T13:17:37Z

GervaisChapuis at 12:57, 20 September 2013

2013-09-20T12:57:28Z

GervaisChapuis at 12:52, 20 September 2013

2013-09-20T12:52:34Z

GervaisChapuis at 12:26, 20 September 2013

2013-09-20T12:26:48Z

GervaisChapuis at 12:26, 20 September 2013

2013-09-20T12:26:10Z

GervaisChapuis: Created page with "VLD (Vive la Différence) is a phasing approach based on the properties of the Fourier transforms. Probabilistic techniques lead to the difference electron density with Fourier..."

2013-09-20T12:07:32Z

Created page with "VLD (Vive la Différence) is a phasing approach based on the properties of the Fourier transforms. Probabilistic techniques lead to the difference electron density with Fourier..."

New page

VLD (Vive la Différence) is a phasing approach based on the properties of the Fourier transforms. Probabilistic techniques lead to the difference electron density with Fourier coefficients

<math>F_q\approx \bigg[(m|F|-D|F_p|)-|F_p|(1-D) \bigg( \frac{e-\sigma^2_A}{1-\sigma^2_A} \bigg) \bigg]exp(\textrm{i}\varphi_p)~~~~~(1)</math>

<math>|F|</math>and <math>|F_p|</math>are the target and the model structure factor amplitudes, respectively, <math>\varphi</math> and <math>\varphi_p</math> the associated phases, <math>\textit{e}</math> is related to the experimental error,

<math>\sigma_A=\Bigg(\frac{\sum_p}{\sum_N}\Bigg)^\frac{1}{2}D</math>

<math>\sum N</math> and <math>\sum p</math> are the scattering powers of the target and of the model structure respectively. <math>D</math> is related to the misfit between model and target structure via the relation <math>D=\langle\cos(2\pi \mathbf{h}\Delta \mathbf{r})\rangle</math>

The difference electron density calculated via coefficients (1) is well correlated with the true difference density even when the model is uncorrelated with the target, and suggests the following cyclic algorithm :

a) Assign random phases to the target structure factors and calculate the corresponding target electron density map;

b) Select a model electron density and calculate the difference electron density via the coefficients (1). Once modified and Fourier inverted it will provide <math>F_q</math> coefficients;

c) A new electron density map may be obtained by summing model and difference electron densities via the tangent formula

<math>\tan\varphi=\frac{R_p\sin\varphi_p+w_qR_q\sin\varphi_q}{R_p\cos\varphi_p+w_qR_q\cos\varphi_q}~~~~~(2)</math>

where <math>w_q=\sqrt{2(1-\sigma_A)}</math>.

d) Calculate the new electron density map for the target by using phases given by (2) and return to b).
Repeated cycles of the above algorithms lead from random phases to the correct values.
The method may be generalized by replacing the difference electron density by hybrid electron densities. Furthermore , VLD may be used for extending and refining models provided by non ab initio approaches.

@@ Line 4: / Line 4: @@
 <center>
-<math>F_q\approx \bigg[(m|F|-D|F_p|)-|F_p|(1-D) \bigg(  \frac{e-\sigma^2_A}{1-\sigma^2_A} \bigg) \bigg]exp(\textrm{i}\varphi_p)~~~~~(1)</math>
+<math>F_q\approx \bigg[(m|F|-D|F_p|)-|F_p|(1-D) \bigg(  \frac{e-\sigma^2_A}{1-\sigma^2_A} \bigg) \bigg]\exp(\textrm{i}\varphi_p).~~~~~(1)</math>
 </center>
@@ Line 10: / Line 10: @@
 <center>
-<math>\sigma_A=\Bigg(\frac{\sum_p}{\sum_N}\Bigg)^\frac{1}{2}D</math>
+<math>\sigma_A=\Bigg(\frac{\sum_p}{\sum_N}\Bigg)^{1/2}D,</math>
 </center>
-<math>\sum</math><sub>''N'' </sub>  and  <math>\sum</math><sub>''p'' </sub>  are  the scattering powers of the target and of the model structure respectively. <math>D</math>  is related to the misfit between model and target structure  via the relation  <math>D=\langle\cos(2\pi \mathbf{h}\Delta \mathbf{r})\rangle</math>
+<math>\sum</math><sub>''N'' </sub>  and  <math>\sum</math><sub>''p'' </sub>  are  the scattering powers of the target and of the model structure respectively. <math>D</math>  is related to the misfit between model and target structure ''via'' the relation  <math>D=\langle\cos(2\pi \mathbf{h}\Delta \mathbf{r})\rangle</math>.
-The difference electron density calculated via coefficients (1)  is well correlated with  the true difference density even when the model is uncorrelated with the target, and suggests the following cyclic algorithm:
+The difference electron density calculated ''via'' coefficients (1)  is well correlated with  the true difference density even when the model is uncorrelated with the target, and suggests the following cyclic algorithm:
-a) Assign random phases to  the target structure factors and calculate the  corresponding target  electron density  map;
+(''a'') Assign random phases to  the target structure factors and calculate the  corresponding target  electron density  map.
-b) Select  a model electron density and calculate the difference electron density  via the coefficients (1). Once modified and  Fourier inverted  it will provide <math>F_q</math> coefficients;
+(''b'') Select  a model electron density and calculate the difference electron density ''via'' the coefficients (1). Once modified and  Fourier inverted it will provide <math>F_q</math> coefficients.
-c) A new electron density map may be obtained by  summing model and difference electron densities via the tangent formula
+(''c'') A new electron density map may be obtained by summing model and difference electron densities ''via'' the tangent formula
 <center>
 <math>\tan\varphi=\frac{R_p\sin\varphi_p+w_qR_q\sin\varphi_q}{R_p\cos\varphi_p+w_qR_q\cos\varphi_q}~~~~~(2)</math></center><br>
 where <math>w_q=\sqrt{2(1-\sigma_A)}</math>.
-d) Calculate the new electron density map for the target  by using phases given by (2) and return to b).
+(''d'') Calculate the new electron density map for the target  by using phases given by (2) and return to (''b'').
 Repeated cycles of the above algorithms lead from random phases to the correct values.
-The method may be generalized by replacing the difference electron density by hybrid electron densities.  Furthermore , VLD may be used for extending and refining models provided by non ab initio approaches.
+The method may be generalized by replacing the difference electron density by hybrid electron densities. Furthermore, VLD may be used for extending and refining models provided by non ab initio approaches.
 == References ==
-*Burla, M.C., Caliandro, C. ''et al.'' (2010). ''The difference electron density: a probabilistic reformulation'', "Acta Cryst." A'''66''', 347-361.
+*Burla, M. C., Caliandro, C. ''et al.'' (2010).  ''Acta Cryst.'' A'''66''', 347-361. ''The difference electron density: a probabilistic reformulation''.
-*Burla, M.C., Carrozzini, B. ''et al.'' (2012) . ''VLD algorithm and hybrid Fourier syntheses'', "J. Appl. Cryst." '''45''', 1287-1294.
+*Burla, M. C., Carrozzini, B. ''et al.'' (2012). ''J. Appl. Cryst.'' '''45''', 1287-1294. ''VLD algorithm and hybrid Fourier syntheses''.
 [[Category: Structure determination]]

← Older revision		Revision as of 07:58, 26 February 2015
Line 37:		Line 37:
	*Burla, M.C., Caliandro, C. ''et al.'' (2010). ''The difference electron density: a probabilistic reformulation'', "Acta Cryst." A'''66''', 347-361.		*Burla, M.C., Caliandro, C. ''et al.'' (2010). ''The difference electron density: a probabilistic reformulation'', "Acta Cryst." A'''66''', 347-361.
	*Burla, M.C., Carrozzini, B. ''et al.'' (2012) . ''VLD algorithm and hybrid Fourier syntheses'', "J. Appl. Cryst." '''45''', 1287-1294.		*Burla, M.C., Carrozzini, B. ''et al.'' (2012) . ''VLD algorithm and hybrid Fourier syntheses'', "J. Appl. Cryst." '''45''', 1287-1294.
		+
		+	[[Category: Structure determination]]

@@ Line 1: / Line 1: @@
 ==Definition==
-VLD (Vive la Différence) is a phasing approach based on the properties of the Fourier transforms.  Probabilistic techniques  lead to the difference electron density with Fourier coefficients
+VLD ("Vive la Différence") is a phasing approach based on the properties of the Fourier transforms.  Probabilistic techniques  lead to the difference electron density with Fourier coefficients
 <center>
@@ Line 16: / Line 16: @@
-The difference electron density calculated via coefficients (1)  is well correlated with  the true difference density even when the model is uncorrelated with the target, and suggests the following cyclic algorithm :
+The difference electron density calculated via coefficients (1)  is well correlated with  the true difference density even when the model is uncorrelated with the target, and suggests the following cyclic algorithm:
@@ Line 35: / Line 35: @@
-*Burla, M.C., Caliandro, C. ''et al.'' (2010). ''The difference electron density: a probabilistic reformulation'', Acta Cryst. '''A66''', 347-361.
+*Burla, M.C., Caliandro, C. ''et al.'' (2010). ''The difference electron density: a probabilistic reformulation'', "Acta Cryst." A'''66''', 347-361.
-*Burla, M.C., Carrozzini, B. ''et al.'' (2012) . ''VLD algorithm and hybrid Fourier syntheses''. J.Appl. Cryst. '''45''', 1287-1294.
+*Burla, M.C., Carrozzini, B. ''et al.'' (2012) . ''VLD algorithm and hybrid Fourier syntheses'', "J. Appl. Cryst." '''45''', 1287-1294.

← Older revision		Revision as of 18:09, 20 September 2013
Line 36:		Line 36:

	*Burla, M.C., Caliandro, C. ''et al.'' (2010). ''The difference electron density: a probabilistic reformulation'', Acta Cryst. '''A66''', 347-361.		*Burla, M.C., Caliandro, C. ''et al.'' (2010). ''The difference electron density: a probabilistic reformulation'', Acta Cryst. '''A66''', 347-361.
−	*Burla, M.C., ~~Giacovazzo~~, C. ''et al.'' (~~2010~~). ''~~The~~ VLD algorithm''. J. Appl. Cryst~~. (2010)~~. '''43''', ~~825–836~~.	+	*Burla, M.C., Carrozzini, B. ''et al.'' (2012) . ''VLD algorithm and hybrid Fourier syntheses''. J.Appl. Cryst. '''45''', 1287-1294.

← Older revision		Revision as of 13:17, 20 September 2013
Line 13:		Line 13:
	</center>		</center>

−	<math>\sum N</~~math~~> and <math>\sum p</~~math~~> are the scattering powers of the target and of the model structure respectively. <math>D</math> is related to the misfit between model and target structure via the relation <math>D=\langle\cos(2\pi \mathbf{h}\Delta \mathbf{r})\rangle</math>	+	<math>\sum</math><sub>''N'' </sub> and <math>\sum</math><sub>''p'' </sub> are the scattering powers of the target and of the model structure respectively. <math>D</math> is related to the misfit between model and target structure via the relation <math>D=\langle\cos(2\pi \mathbf{h}\Delta \mathbf{r})\rangle</math>

← Older revision		Revision as of 12:52, 20 September 2013
Line 27:		Line 27:
	Repeated cycles of the above algorithms lead from random phases to the correct values.		Repeated cycles of the above algorithms lead from random phases to the correct values.
	The method may be generalized by replacing the difference electron density by hybrid electron densities. Furthermore , VLD may be used for extending and refining models provided by non ab initio approaches.		The method may be generalized by replacing the difference electron density by hybrid electron densities. Furthermore , VLD may be used for extending and refining models provided by non ab initio approaches.
		+
		+	== References ==
		+
		+
		+	*Burla, M.C., Caliandro, C. ''et al.'' (2010). ''The difference electron density: a probabilistic reformulation'', Acta Cryst. '''A66''', 347-361.
		+	*Burla, M.C., Giacovazzo, C. ''et al.'' (2010). ''The VLD algorithm''. J. Appl. Cryst. (2010). '''43''', 825–836.

← Older revision		Revision as of 12:26, 20 September 2013
Line 1:		Line 1:
		+	==Definition==
		+
	VLD (Vive la Différence) is a phasing approach based on the properties of the Fourier transforms. Probabilistic techniques lead to the difference electron density with Fourier coefficients		VLD (Vive la Différence) is a phasing approach based on the properties of the Fourier transforms. Probabilistic techniques lead to the difference electron density with Fourier coefficients