Re: [ccp4bb] (EXTERNAL) RE: [ccp4bb] Confused about centric reflections
On 03/02/2019 09:59 PM, Ronald E. Stenkamp wrote: I was taught about centric reflections using different words from those in the wiki. If you look at your crystal structure in projection and the planar view looks centrosymmetric, the zone of reflections corresponding to that projection will have centric phases, i.e., their phases will be restricted to one of two values. Sometimes those phases are restricted to 0 and 180 degrees, other times, depending on the location of the pseudo-inversion center, the phases might be 90 or 270 degrees. So if you look down the two-fold axis in P2, the coordinates of equivalent positions become x,0,z and (-x,0,-z). The zone perpendicular to the two-fold contains the h0l reflections, and they end up with restricted phases. For orthorhombic structures, all three zones (h0l, hk0, 0kl) are centric. And if you look at trigonal structures, as in P3(1), there are no centric reflections. (In P3(1)21, there are centric zones, but they aren't the hk0 reflections. Ron Stenkamp Thanks, I think I see that. Any time you have a two-fold axis, proper or screw, the projection of density onto a plane perpendicular to that axis and passing through the origin will be 2-fold symmetric. Any reflection whose scattering vector lies within that plane will be taken to its Friedel mate by the reciprocal space version of the operator, and that reflection's scattering vector will lie along the same line but in the opposite direction. The further projection of the density onto one of those scattering vectors will obey the 2-fold and be centrosymetric. Centrosymmetry in one-dimension is also called "even function" (vs odd function). The fourier components of even functions are non-zero only for the cos terms (sin is an odd function), taking zero at the point of centrosymmetry. If the center of symmetry is offset from the origin then there is a phase shift equal to 2pi times the fractional distance from origin to center along the scattering vector. If we don't like negative am p litudes, we make them positive and add pi to the phase. So we get 2 possible phases, separated by 180*. (Or something like that.) -Original Message- From: CCP4 bulletin board On Behalf Of Edward A. Berry Sent: Saturday, March 2, 2019 2:00 PM To: CCP4BB@JISCMAIL.AC.UK Subject: [ccp4bb] Confused about centric reflections The wiki: https://strucbio.biologie.uni-konstanz.de/ccp4wiki/index.php/Centric_and_acentric_reflections says: "A reflection is centric if there is a reciprocal space symmetry operator which maps it onto itself (or rather its Friedel mate). . . . Centric reflections in space group P2 and P21 are thus those with 0,k,0." The operator -h,k,-l does NOT take 0,k,0 to its Friedel mate. it takes h,0,k to their Friedel mates. In other words the plane perpendicular to the 2-fold axis, at 0 along the axis Or am I missing something? eab To unsubscribe from the CCP4BB list, click the following link: https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB&A=1 To unsubscribe from the CCP4BB list, click the following link: https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB&A=1
Re: [ccp4bb] Confused about centric reflections
Thaks! typo- h,0,l not h,0,k I have not registered for editing on that wiki, so I was hoping someone else would take care of it. But it seems all that's needed is to confirm your account, so I'll register and give it a try. Hope I don't make things worse! (what is this urldefense.proofpoint? did my institution add that, or JISCMAIL?) On 03/02/2019 05:28 PM, Dale Tronrud wrote: You are correct, other than your typo. The centric zone in a monoclinic space group (B setting) is h0l. This web site is a wiki so you should be able to correct it yourself. Dale Tronrud On 3/2/2019 2:00 PM, Edward A. Berry wrote: The wiki: https://urldefense.proofpoint.com/v2/url?u=https-3A__strucbio.biologie.uni-2Dkonstanz.de_ccp4wiki_index.php_Centric-5Fand-5Facentric-5Freflections&d=DwICaQ&c=ogn2iPkgF7TkVSicOVBfKg&r=cFgyH4s-peZ6Pfyh0zB379rxK2XG5oHu7VblrALfYPA&m=HENAQrgItEIhnnUZhWe8GMKW5sRX2v7V-rsby0AB7LQ&s=8D9Gvr-8AQeITEdUbf2xeIBDNzdTzUTnE78AI70O1J0&e= says: "A reflection is centric if there is a reciprocal space symmetry operator which maps it onto itself (or rather its Friedel mate). . . . Centric reflections in space group P2 and P21 are thus those with 0,k,0." The operator -h,k,-l does NOT take 0,k,0 to its Friedel mate. it takes h,0,k to their Friedel mates. In other words the plane perpendicular to the 2-fold axis, at 0 along the axis Or am I missing something? eab To unsubscribe from the CCP4BB list, click the following link: https://urldefense.proofpoint.com/v2/url?u=https-3A__www.jiscmail.ac.uk_cgi-2Dbin_webadmin-3FSUBED1-3DCCP4BB-26A-3D1&d=DwICaQ&c=ogn2iPkgF7TkVSicOVBfKg&r=cFgyH4s-peZ6Pfyh0zB379rxK2XG5oHu7VblrALfYPA&m=HENAQrgItEIhnnUZhWe8GMKW5sRX2v7V-rsby0AB7LQ&s=3wVLGfTBHIP0cGn10BGQ_4UFrEQh9_uJ8GdR1Yd6i-c&e= To unsubscribe from the CCP4BB list, click the following link: https://urldefense.proofpoint.com/v2/url?u=https-3A__www.jiscmail.ac.uk_cgi-2Dbin_webadmin-3FSUBED1-3DCCP4BB-26A-3D1&d=DwICaQ&c=ogn2iPkgF7TkVSicOVBfKg&r=cFgyH4s-peZ6Pfyh0zB379rxK2XG5oHu7VblrALfYPA&m=HENAQrgItEIhnnUZhWe8GMKW5sRX2v7V-rsby0AB7LQ&s=3wVLGfTBHIP0cGn10BGQ_4UFrEQh9_uJ8GdR1Yd6i-c&e= To unsubscribe from the CCP4BB list, click the following link: https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB&A=1
Re: [ccp4bb] Confused about centric reflections
You are correct, other than your typo. The centric zone in a monoclinic space group (B setting) is h0l. This web site is a wiki so you should be able to correct it yourself. Dale Tronrud On 3/2/2019 2:00 PM, Edward A. Berry wrote: > The wiki: > > https://strucbio.biologie.uni-konstanz.de/ccp4wiki/index.php/Centric_and_acentric_reflections > > > says: > "A reflection is centric if there is a reciprocal space symmetry > operator which maps it onto itself (or rather its Friedel mate). > . . . > Centric reflections in space group P2 and P21 are thus those with 0,k,0." > > The operator -h,k,-l does NOT take 0,k,0 to its Friedel mate. > it takes h,0,k to their Friedel mates. In other words the plane > perpendicular to the 2-fold axis, at 0 along the axis > > Or am I missing something? > eab > > > > To unsubscribe from the CCP4BB list, click the following link: > https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB&A=1 > To unsubscribe from the CCP4BB list, click the following link: https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB&A=1
[ccp4bb] Confused about centric reflections
The wiki: https://strucbio.biologie.uni-konstanz.de/ccp4wiki/index.php/Centric_and_acentric_reflections says: "A reflection is centric if there is a reciprocal space symmetry operator which maps it onto itself (or rather its Friedel mate). . . . Centric reflections in space group P2 and P21 are thus those with 0,k,0." The operator -h,k,-l does NOT take 0,k,0 to its Friedel mate. it takes h,0,k to their Friedel mates. In other words the plane perpendicular to the 2-fold axis, at 0 along the axis Or am I missing something? eab To unsubscribe from the CCP4BB list, click the following link: https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB&A=1
