Re: [ccp4bb] Friedel vs Bijvoet
Hi James, Derek Logan wrote: - When Rontgen discovered a new kind of light, he called it x-rays. Now only the Germans call them Rontgen rays. Thanks for a great essay! Since I have nothing of real value contribute here, I won't pass over the opportunity to be a besserwisser (as the Swedes say, using a borrowed word...) the Röntgen moniker has stuck here in northern Europe too: in Swedish: Röntgenstrålning, in Danish and Norwegian: Røntgenstråling, in Dutch: Röntgenstraling. Also thanks to Wikipedia, I can inform you that it's called Röntgengeislun in Icelandic and Röntgensäteily in Finnish. Eastern Europe seems to have adopted various forms based on Rentgen, but I won't pretend I knew that before 5 minutes ago ;-) Interestingly enough, even though the Dutch say Röntgenstralen, the Flemish (100 miles more to the south) say X-stralen. Bram -- *Bram Schierbeek* Application Scientist Structural Biology Solutions Bruker AXS BV Oostsingel 209,P.O.Box 811 2600 AV Delft, the Netherlands T: +31 (0)152 152 508 F: +31 (0)152 152 599 E: [EMAIL PROTECTED] W: www.bruker-axs.com
Re: [ccp4bb] Friedel vs Bijvoet
- When Rontgen discovered a new kind of light, he called it x- rays. Now only the Germans call them Rontgen rays. Thanks for a great essay! Since I have nothing of real value contribute here, I won't pass over the opportunity to be a besserwisser (as the Swedes say, using a borrowed word...) the Röntgen moniker has stuck here in northern Europe too: in Swedish: Röntgenstrålning, in Danish and Norwegian: Røntgenstråling, in Dutch: Röntgenstraling. Also thanks to Wikipedia, I can inform you that it's called Röntgengeislun in Icelandic and Röntgensäteily in Finnish. Eastern Europe seems to have adopted various forms based on Rentgen, but I won't pretend I knew that before 5 minutes ago ;-) Derek - When the largest protein ever was discovered, it was called connectin, but a subsequent paper called it titin and the second name has stuck. I actually can't remember who the connectin guy was ... - When Joseph Fourier discovered that heat radiated from the earth could be reflected back by gasses in the atmosphere, he simply named it by describing it (in French). Now this is (incorrectly) called the greenhouse effect. Why not the Fourier effect? Fortunately for Fourier, a mathematical series was named after him, although he neither discovered it (Budan did that), nor implemented it (Navier did that). All Fourier did was present a theorem based on a flawed premise that turned out to be right anyway. So, I decided to look up Friedel and Bijvoet in the Undisputed Source of All Human Knowledge (wikipedia) and found that Friedel's Law ... is a property of Fourier transforms http://en.wikipedia.org/wiki/Fourier_transform of real functions. I am willing to believe that. And considering this origin I would think it appropriate to call (hkl) and (-h-k-l) a Friedel pair (or Friedel's pair as it is described in the USAHK). G. Friedel was indeed a crystallographer, but I doubt he considered more than this simple centrosymmetric property. Who would care in 1913 which is F+ and F-? The atomic scattering factors had not yet been worked out at that time. Ewald may have predicted it, but anomalous scattering was not shown to exist until the classic work of Koster, Knol and Prins (1930). I guess that goes to show that if you want something named after you... keep it at one or two authors. Perhaps it has to do with the original paper getting old enough that it gets too hard to find. I'm sure in G. Friedel's paper in 1913 he cited Joseph Fourier's Paper from 1822. Or did he? I wonder if they were already calling it a Fourier Transform at that time? Okay, so what, exactly did Bijvoet do? Everyone cites his Nature paper (1951), but one thing that I was NOT KIDDING about in my April Fool's joke was that this paper (like so many other high-profile papers) contains almost no information about how to reproduce the results. I was also not kidding that boring little details like the reasoning behind the conclusion (the hand of the microworld) were relegated to a more obscure journal (the one in the Proc. Royal. Soc. Amsterdam). I WAS kidding about having found and read that paper. I have never seen it. Still, Bijvoet did the first experiment to elucidate the absolute configuration, and he definitely deserves credit for that. So, particularly in that light, I would agree that any pair of reflections that would be equivalent if not for anomalous scattering effects could be called a Bijvoet pair. This is because they contain the information needed to apply Bijvoet's technique. Something that has always eluded me is who decided which is F+ and F-? After all, the reciprocal lattice is very very nearly centrosymmetric. You cannot tell by looking at a single diffraction image whether that spot at a given X,Y pixel coordinate is F+ or F-, you need to know the axis convention of the camera. At some point in writing the CCP4 libraries with their asymmetric unit definitions, someone must have established a convention. What is it? To me, the reasoning behind these assignments is, in fact, they key to assigning the absolute configuration, not the anomalous scattering effect itself. So, who worked this out? Should we really be calling them Dodson pairs? -James Holton MAD Scientist
Re: [ccp4bb] Friedel vs Bijvoet
Thanks very much for this interesting discussion. We should have that more often. Marius -BEGIN PGP SIGNED MESSAGE- Hash: SHA1 Le 26 juin 08 à 18:49, Ethan Merritt a écrit : On Thursday 26 June 2008 09:36:16 am Serge Cohen wrote: Please some one tells me if I'm wrong ... but I though that indeed one is NOT supposed to measure anomalous difference from reflections h and h' if those are related by one of the symmetry operator of the point group... This statement is logically equivalent to what Patrick writes below. You are agreeing with each other. Indeed I was thinking of Bernie Santarsiero mail when sending this mail. Bernie's mail was confusing my understanding. To quote the part I was referring to : Friedel pair is strictly F(hkl) and F(-h,-k,-l). Bijvoet pair is F(h) and any mate that is symmetry-related to F(- h), e.g., F(hkl) and F(-h,k,-l) in monoclinic. That is in monoclinic (P 1 2 1, more precisely) , (h, k, l) and (-h, k, -l) should have the same F ... (in a determinist's world) Yes, but that is not an example of h and h'. You mean that in P 1 2 1, h,k,l and -h,k-l are not strictly equivalent? In the context of my message h and h' were defined as : reflections h and h' if those are related by one of the symmetry operator of the point group To come back to the initial mail : b) A Friedel pair is any reflection h = -h including hR = -h, i.e. including centric reflections. I find this notation confusing since (I guess) the '=' does not mean the same thing in both cases : In the first case it means the pair (h, -h) (or more precisely what I understand it means) While the second really means There is a R operator of the PG such that -h = Rh (if the first case had to be understood this way, the only Friedel pair would be (0,0,0) ). So if I try to put this definitions of terms as I understand them: Friedel pair : (h, g) There is a operator R of the P.G. such that -Rh = g Bijvoet pair : (h, g) There is a operator R of the P.G. such that -Rh = g AND : For all operator R of the P.G. : Rh != g Hope I'm getting it right ... and I'm not adding to the overall confusion ;-) Serge. *** Dr. Serge COHEN GPG Key ID: 0B5CDAEC N.K.I. Department of Molecular Carcinogenesis (B8) Plesmanlaan 121 1066 CX Amsterdam; NL E-Mail: [EMAIL PROTECTED] Tel : +31 20 512 2053 *** -BEGIN PGP SIGNATURE- Version: GnuPG v1.4.8 (Darwin) iEYEARECAAYFAkhj+MEACgkQlz6UVQtc2uw7FACguUgF1+XrN9xdRTcLLdShA/Eu A2UAniYPecEAz5BJ/ljrQYymnGRK7Mor =SItL -END PGP SIGNATURE- Dr.habil. Marius Schmidt Asst. Professor University of Wisconsin-Milwaukee Department of Physics Room 454 1900 E. Kenwood Blvd. Milwaukee, WI 53211 phone: +1-414-229-4338 email: [EMAIL PROTECTED] http://users.physik.tu-muenchen.de/marius/
Re: [ccp4bb] Friedel vs Bijvoet
Ahh. The history of science. I've always wondered how these naming conventions get decided. Who is the authority on what gets named after who? Historically, it seems to vary a lot. - When Patterson published his incredibly useful map he called it the F-square synthesis. Does anyone NOT call it a Patterson map? - When Rontgen discovered a new kind of light, he called it x-rays. Now only the Germans call them Rontgen rays. - When the largest protein ever was discovered, it was called connectin, but a subsequent paper called it titin and the second name has stuck. I actually can't remember who the connectin guy was ... - When Joseph Fourier discovered that heat radiated from the earth could be reflected back by gasses in the atmosphere, he simply named it by describing it (in French). Now this is (incorrectly) called the greenhouse effect. Why not the Fourier effect? Fortunately for Fourier, a mathematical series was named after him, although he neither discovered it (Budan did that), nor implemented it (Navier did that). All Fourier did was present a theorem based on a flawed premise that turned out to be right anyway. So, I decided to look up Friedel and Bijvoet in the Undisputed Source of All Human Knowledge (wikipedia) and found that Friedel's Law ... is a property of Fourier transforms http://en.wikipedia.org/wiki/Fourier_transform of real functions. I am willing to believe that. And considering this origin I would think it appropriate to call (hkl) and (-h-k-l) a Friedel pair (or Friedel's pair as it is described in the USAHK). G. Friedel was indeed a crystallographer, but I doubt he considered more than this simple centrosymmetric property. Who would care in 1913 which is F+ and F-? The atomic scattering factors had not yet been worked out at that time. Ewald may have predicted it, but anomalous scattering was not shown to exist until the classic work of Koster, Knol and Prins (1930). I guess that goes to show that if you want something named after you... keep it at one or two authors. Perhaps it has to do with the original paper getting old enough that it gets too hard to find. I'm sure in G. Friedel's paper in 1913 he cited Joseph Fourier's Paper from 1822. Or did he? I wonder if they were already calling it a Fourier Transform at that time? Okay, so what, exactly did Bijvoet do? Everyone cites his Nature paper (1951), but one thing that I was NOT KIDDING about in my April Fool's joke was that this paper (like so many other high-profile papers) contains almost no information about how to reproduce the results. I was also not kidding that boring little details like the reasoning behind the conclusion (the hand of the microworld) were relegated to a more obscure journal (the one in the Proc. Royal. Soc. Amsterdam). I WAS kidding about having found and read that paper. I have never seen it. Still, Bijvoet did the first experiment to elucidate the absolute configuration, and he definitely deserves credit for that. So, particularly in that light, I would agree that any pair of reflections that would be equivalent if not for anomalous scattering effects could be called a Bijvoet pair. This is because they contain the information needed to apply Bijvoet's technique. Something that has always eluded me is who decided which is F+ and F-? After all, the reciprocal lattice is very very nearly centrosymmetric. You cannot tell by looking at a single diffraction image whether that spot at a given X,Y pixel coordinate is F+ or F-, you need to know the axis convention of the camera. At some point in writing the CCP4 libraries with their asymmetric unit definitions, someone must have established a convention. What is it? To me, the reasoning behind these assignments is, in fact, they key to assigning the absolute configuration, not the anomalous scattering effect itself. So, who worked this out? Should we really be calling them Dodson pairs? -James Holton MAD Scientist
[ccp4bb] Friedel vs Bijvoet
Dear All, I wonder about the conventions using Friedel vs Bijvoet pair. a) there are no differences. As long as h = -h, it's a Friedel or a Bijvoet pair. They are the same. b) A Friedel pair is any reflection h = -h including hR = -h, i.e. including centric reflections. A Bijvoet pair is an acentric Friedel pair, it can carry anomalous amplitude differences, whereas centric Friedel pairs invariably cannot. Actually, Bijvoet pairs (acentric Friedel pairs) invariably do carry anomalous amplitude differences. There is no such thing as no anomalous scattering. We may elect to ignore it, only. c) of course, this all assumes absence of anisotropic AS. def b) seems to be helpful in discussions and make sense given that absolute configuration that needs AS signal is somehow associated with Bijvoet's work. Are any authoritative answers/conventions/opinions available on that ? Thx, BR - Bernhard Rupp 001 (925) 209-7429 +43 (676) 571-0536 [EMAIL PROTECTED] [EMAIL PROTECTED] http://www.ruppweb.org/ - The hard part about playing chicken is to know when to flinch -
Re: [ccp4bb] Friedel vs Bijvoet
Friedel pair is strictly F(hkl) and F(-h,-k,-l). Bijvoet pair is F(h) and any mate that is symmetry-related to F(-h), e.g., F(hkl) and F(-h,k,-l) in monoclinic. There are always anomalous differences, though they can be unmeasurably small. Bernie Santarsiero On Thu, June 26, 2008 10:55 am, Bernhard Rupp wrote: Dear All, I wonder about the conventions using Friedel vs Bijvoet pair. a) there are no differences. As long as h = -h, it's a Friedel or a Bijvoet pair. They are the same. b) A Friedel pair is any reflection h = -h including hR = -h, i.e. including centric reflections. A Bijvoet pair is an acentric Friedel pair, it can carry anomalous amplitude differences, whereas centric Friedel pairs invariably cannot. Actually, Bijvoet pairs (acentric Friedel pairs) invariably do carry anomalous amplitude differences. There is no such thing as no anomalous scattering. We may elect to ignore it, only. c) of course, this all assumes absence of anisotropic AS. def b) seems to be helpful in discussions and make sense given that absolute configuration that needs AS signal is somehow associated with Bijvoet's work. Are any authoritative answers/conventions/opinions available on that ? Thx, BR - Bernhard Rupp 001 (925) 209-7429 +43 (676) 571-0536 [EMAIL PROTECTED] [EMAIL PROTECTED] http://www.ruppweb.org/ - The hard part about playing chicken is to know when to flinch -
Re: [ccp4bb] Friedel vs Bijvoet
I've always thought that a Bijvoet pair is any pair for which an anomalous difference could be observed. This includes Friedel pairs (h h-bar), but it also includes pairs of the form h h', where h' is symmetry-related to h-bar. Thus Friedel pairs are a subset of all possible Bijvoet pairs. This is what Ed and I say in our book, at least (shameless plug); and you can buy it from Amazon, so it must be right, yes? Pat On 26 Jun 2008, at 11:55 AM, Bernhard Rupp wrote: Dear All, I wonder about the conventions using Friedel vs Bijvoet pair. a) there are no differences. As long as h = -h, it's a Friedel or a Bijvoet pair. They are the same. b) A Friedel pair is any reflection h = -h including hR = -h, i.e. including centric reflections. A Bijvoet pair is an acentric Friedel pair, it can carry anomalous amplitude differences, whereas centric Friedel pairs invariably cannot. Actually, Bijvoet pairs (acentric Friedel pairs) invariably do carry anomalous amplitude differences. There is no such thing as no anomalous scattering. We may elect to ignore it, only. c) of course, this all assumes absence of anisotropic AS. def b) seems to be helpful in discussions and make sense given that absolute configuration that needs AS signal is somehow associated with Bijvoet's work. Are any authoritative answers/conventions/opinions available on that ? Thx, BR - Bernhard Rupp 001 (925) 209-7429 +43 (676) 571-0536 [EMAIL PROTECTED] [EMAIL PROTECTED] http://www.ruppweb.org/ - The hard part about playing chicken is to know when to flinch - --- Patrick J. Loll, Ph. D. Professor of Biochemistry Molecular Biology Director, Biochemistry Graduate Program Drexel University College of Medicine Room 10-102 New College Building 245 N. 15th St., Mailstop 497 Philadelphia, PA 19102-1192 USA (215) 762-7706 [EMAIL PROTECTED] http://www.amazon.com/Protein-Crystallography-Eaton-E-Lattman/dp/ 0801888085/ref=sr_1_10?ie=UTF8s=booksqid=1214496225sr=1-10
Re: [ccp4bb] Friedel vs Bijvoet
On Thursday 26 June 2008 09:36:16 am Serge Cohen wrote: Please some one tells me if I'm wrong ... but I though that indeed one is NOT supposed to measure anomalous difference from reflections h and h' if those are related by one of the symmetry operator of the point group... This statement is logically equivalent to what Patrick writes below. You are agreeing with each other. That is in monoclinic (P 1 2 1, more precisely) , (h, k, l) and (-h, k, -l) should have the same F ... (in a determinist's world) Yes, but that is not an example of h and h'. Though (h, k, l) and (-h, -k, -l) are likely to be different, and hence (h, k, l) and (h, -k, l) would show the same difference. Serge. Le 26 juin 08 à 18:07, Patrick Loll a écrit : I've always thought that a Bijvoet pair is any pair for which an anomalous difference could be observed. This includes Friedel pairs (h h-bar), but it also includes pairs of the form h h', where h' is symmetry-related to h-bar. Thus Friedel pairs are a subset of all possible Bijvoet pairs. This is what Ed and I say in our book, at least (shameless plug); and you can buy it from Amazon, so it must be right, yes? Pat On 26 Jun 2008, at 11:55 AM, Bernhard Rupp wrote: Dear All, I wonder about the conventions using Friedel vs Bijvoet pair. a) there are no differences. As long as h = -h, it's a Friedel or a Bijvoet pair. They are the same. b) A Friedel pair is any reflection h = -h including hR = -h, i.e. including centric reflections. A Bijvoet pair is an acentric Friedel pair, it can carry anomalous amplitude differences, whereas centric Friedel pairs invariably cannot. Actually, Bijvoet pairs (acentric Friedel pairs) invariably do carry anomalous amplitude differences. There is no such thing as no anomalous scattering. We may elect to ignore it, only. c) of course, this all assumes absence of anisotropic AS. def b) seems to be helpful in discussions and make sense given that absolute configuration that needs AS signal is somehow associated with Bijvoet's work. Are any authoritative answers/conventions/opinions available on that ? Thx, BR *** Dr. Serge COHEN GPG Key ID: 0B5CDAEC N.K.I. Department of Molecular Carcinogenesis (B8) Plesmanlaan 121 1066 CX Amsterdam; NL E-Mail: [EMAIL PROTECTED] Tel : +31 20 512 2053 *** -- Ethan A Merritt Biomolecular Structure Center University of Washington, Seattle 98195-7742
Re: [ccp4bb] Friedel vs Bijvoet
Let's try this again, with definitions, and pls scream if I am wrong: a) Any reflection pair hR = h forms a symmetry related pair. R is any one of G point group operators of the SG. This is a set of reflections (S). Their amplitudes are invariably the same. They do not even show up as individual pairs in the asymmetric unit of the reciprocal space. NB: their phases are restricted but not the same. b) a set h=-h (set F) exist where reflections may or may not carry anomalous signal. They form the centrosymmetrically related wedge of the asymmetric unit of reciprocal space. c) a centric reflection (set C) is defined as hR=-h and cannot carry anomalous signal. Example zone h0l in PG 2. As Ian Tickle pointed out, the CCP4 wiki is wrong: Centric reflections in space group P2 and P21 are thus those with 0,k,0. Not so; an example listing is attached at the end. d) therefore, some e:F exist that carry AS (F.ne.C) and some that do not carry AS (F.el.C). I hope we can agree on those facts. Now for the name calling: (S) is simply the set of symmetry related reflections, defined as hR=h. (F) is the set of Friedel pairs, defined as h=-h. (C) are centric reflections, defined as hR=-h. Thus, only if (F.ne.C), anomalous signal. I thought those are Bijvoet pairs. They are, but it may not be the definition of a Bijvoet pair. Try 1: Bijvoet pair is F(h) and any mate that is symmetry-related to F(-h), e.g., F(hkl) and F(-h,k,-l) in monoclinic. hkl is not related to -hk-l via h = -h. Only h0l is, and those are (e:C). So, I cannot quote follow that, probably try 1 is not a good definition. Try 2: I've always thought that a Bijvoet pair is any pair for which an anomalous difference could be observed. Good start. I subscribe to that. This includes Friedel pairs (h h-bar) Good. That's the definition of F. but it also includes pairs of the form h h', where h' is symmetry-related to h-bar. Ooops. That is the definition of a centric reflection. Thus Friedel pairs are a subset of all possible Bijvoet pairs. Cannot see that. I still maintain that Bijvoet pairs are a subset of Friedel pairs (which does include Pat's definition). I fail to see anything else but Friedel pairs in my list of reflections - some of them carry AS (F.ne.C) and some don't (F.el.C). B = F.ne.C. Seems to be a necessary and sufficient condition, in agreement with Pat's definition (though not the explanation). But - isn't that exactly what I said from the beginning? A Bijvoet pair is an acentric Friedel pair... Or - where are any other Bijvoet pairs hiding? Where did I miss them? (NB: Absence of anisotropic AS assumed -let's not go there) See reflection list P2 (hkl |F| fom phi 2theta stol2) last 3 items: centric flag, epsilon, m(h) 0 0 1 993.54 1.00 179.9965.61 0.581 1 1 2 0 0 -1 993.54 1.00 179.9965.61 0.581 1 1 2 1 0 0 1412.58 1.00 0.1438.22 0.0001711 1 1 2 -1 0 0 1412.58 1.00 0.1438.22 0.0001711 1 1 2 0 0 2 3279.49 1.00 180.3132.80 0.0002323 1 1 2 0 0 -2 3279.49 1.00 180.3132.80 0.0002323 1 1 2 1 0 1 379.89 1.00 180.2530.36 0.0002712 1 1 2 -1 0 -1 379.89 1.00 180.2530.36 0.0002712 1 1 2 -1 0 2 1355.06 1.00 0.1327.97 0.0003195 1 1 2 1 0 -2 1355.06 1.00 0.1327.97 0.0003195 1 1 2 0 1 0 2432.85 1.0021.0924.35 0.0004216 0 2 1 0 -1 0 2434.14 1.00 339.6524.35 0.0004216 0 2 1 0 1 1 621.36 1.00 101.6722.83 0.0004797 0 1 2 0 -1 -1 623.27 1.00 258.4922.83 0.0004797 0 1 2 1 0 2 319.68 1.00 359.9822.65 0.0004874 1 1 2 -1 0 -2 319.68 1.00 359.9822.65 0.0004874 1 1 2 0 0 3 426.17 1.00 180.9921.87 0.0005227 1 1 2 0 0 -3 426.17 1.00 180.9921.87 0.0005227 1 1 2 -1 0 3 1581.93 1.00 0.4420.98 0.0005680 1 1 2 1 0 -3 1581.93 1.00 0.4420.98 0.0005680 1 1 2 1 1 0 338.67 1.0046.5220.54 0.0005927 0 1 2 -1 -1 0 341.71 1.00 314.7020.54 0.0005927 0 1 2 -1 1 1 1649.38 1.0080.9320.26 0.0006089 0 1 2 1 -1 -1 1652.55 1.00 279.9020.26 0.0006089 0 1 2 0 1 2 343.14 1.0066.8619.55 0.0006540 0 1 2 0 -1 -2 345.84 1.00 293.4219.55 0.0006540 0 1 2 -2 0 1 171.90 1.00 358.5919.48 0.0006586 1 1 2 2 0 -1 171.90 1.00 358.5919.48 0.0006586 1 1 2 2 0 0 1238.53 1.00 180.2019.11 0.0006844 1 1 2 -2 0 0 1238.53 1.00 180.2019.11 0.0006844 1 1 2 1 1 1 201.11 1.00 349.9319.00
Re: [ccp4bb] Friedel vs Bijvoet
Hi, Bernhard, Check out page 8 http://students.washington.edu/zanghell/TAs/BSTR521/notes/anomalous_scattering.pdf I thought that Friedels are reflections related by pure inversion symmetry, while Bijvoets are reflections related by non-inversion symmetry of the reciprocal lattice. Thanks, Hidong Bernhard Rupp [EMAIL PROTECTED] Sent by: CCP4 bulletin board CCP4BB@JISCMAIL.AC.UK 06/26/2008 11:35 AM Please respond to [EMAIL PROTECTED] To CCP4BB@JISCMAIL.AC.UK cc Subject Re: [ccp4bb] Friedel vs Bijvoet Let's try this again, with definitions, and pls scream if I am wrong: a) Any reflection pair hR = h forms a symmetry related pair. R is any one of G point group operators of the SG. This is a set of reflections (S). Their amplitudes are invariably the same. They do not even show up as individual pairs in the asymmetric unit of the reciprocal space. NB: their phases are restricted but not the same. b) a set h=-h (set F) exist where reflections may or may not carry anomalous signal. They form the centrosymmetrically related wedge of the asymmetric unit of reciprocal space. c) a centric reflection (set C) is defined as hR=-h and cannot carry anomalous signal. Example zone h0l in PG 2. As Ian Tickle pointed out, the CCP4 wiki is wrong: Centric reflections in space group P2 and P21 are thus those with 0,k,0. Not so; an example listing is attached at the end. d) therefore, some e:F exist that carry AS (F.ne.C) and some that do not carry AS (F.el.C). I hope we can agree on those facts. Now for the name calling: (S) is simply the set of symmetry related reflections, defined as hR=h. (F) is the set of Friedel pairs, defined as h=-h. (C) are centric reflections, defined as hR=-h. Thus, only if (F.ne.C), anomalous signal. I thought those are Bijvoet pairs. They are, but it may not be the definition of a Bijvoet pair. Try 1: Bijvoet pair is F(h) and any mate that is symmetry-related to F(-h), e.g., F(hkl) and F(-h,k,-l) in monoclinic. hkl is not related to -hk-l via h = -h. Only h0l is, and those are (e:C). So, I cannot quote follow that, probably try 1 is not a good definition. Try 2: I've always thought that a Bijvoet pair is any pair for which an anomalous difference could be observed. Good start. I subscribe to that. This includes Friedel pairs (h h-bar) Good. That's the definition of F. but it also includes pairs of the form h h', where h' is symmetry-related to h-bar. Ooops. That is the definition of a centric reflection. Thus Friedel pairs are a subset of all possible Bijvoet pairs. Cannot see that. I still maintain that Bijvoet pairs are a subset of Friedel pairs (which does include Pat's definition). I fail to see anything else but Friedel pairs in my list of reflections - some of them carry AS (F.ne.C) and some don't (F.el.C). B = F.ne.C. Seems to be a necessary and sufficient condition, in agreement with Pat's definition (though not the explanation). But - isn't that exactly what I said from the beginning? A Bijvoet pair is an acentric Friedel pair... Or - where are any other Bijvoet pairs hiding? Where did I miss them? (NB: Absence of anisotropic AS assumed -let's not go there) See reflection list P2 (hkl |F| fom phi 2theta stol2) last 3 items: centric flag, epsilon, m(h) 0 0 1 993.54 1.00 179.9965.61 0.581 1 1 2 0 0 -1 993.54 1.00 179.9965.61 0.581 1 1 2 1 0 0 1412.58 1.00 0.1438.22 0.0001711 1 1 2 -1 0 0 1412.58 1.00 0.1438.22 0.0001711 1 1 2 0 0 2 3279.49 1.00 180.3132.80 0.0002323 1 1 2 0 0 -2 3279.49 1.00 180.3132.80 0.0002323 1 1 2 1 0 1 379.89 1.00 180.2530.36 0.0002712 1 1 2 -1 0 -1 379.89 1.00 180.2530.36 0.0002712 1 1 2 -1 0 2 1355.06 1.00 0.1327.97 0.0003195 1 1 2 1 0 -2 1355.06 1.00 0.1327.97 0.0003195 1 1 2 0 1 0 2432.85 1.0021.0924.35 0.0004216 0 2 1 0 -1 0 2434.14 1.00 339.6524.35 0.0004216 0 2 1 0 1 1 621.36 1.00 101.6722.83 0.0004797 0 1 2 0 -1 -1 623.27 1.00 258.4922.83 0.0004797 0 1 2 1 0 2 319.68 1.00 359.9822.65 0.0004874 1 1 2 -1 0 -2 319.68 1.00 359.9822.65 0.0004874 1 1 2 0 0 3 426.17 1.00 180.9921.87 0.0005227 1 1 2 0 0 -3 426.17 1.00 180.9921.87 0.0005227 1 1 2 -1 0 3 1581.93 1.00 0.4420.98 0.0005680 1 1 2 1 0 -3 1581.93 1.00 0.4420.98 0.0005680 1 1 2 1 1 0 338.67 1.0046.5220.54 0.0005927 0 1 2 -1 -1 0 341.71 1.00 314.7020.54 0.0005927 0 1 2 -1 1 1 1649.38 1.0080.9320.26 0.0006089 0 1 2 1 -1 -1
Re: [ccp4bb] Friedel vs Bijvoet
I quote from these pages: Bijvoet pairs are Bragg reflections which are true symmetry equivalents to a Friedel pair. These true symmetry equivalents have *equal amplitudes, even in the presence of anomalous scattering*. Sounds more like centric or perhaps simply symmetry related to me. A few lines below: A Bijvoet difference refers to the difference in measured amplitude for a Bijvoet pair I don't think you can have it both ways ?? BR
Re: [ccp4bb] Friedel vs Bijvoet
There was a mistake in the letter that listed the Bijvoet pairs for a monoclinic space group and that is confusing you. Let me try. The equivalent positions for a B setting monoclinic are h,k,l; -h,k,-l. The Friedel mates for the general position (h,k,l) are (-h,-k,-l). This means that the equivalent positions also have Friedel mates at h,-k,l. The Bijvoet mates of h,k,l are therefore, according to the definitions given in previous letters, -h,-k,-l; and h,-k,l. There are more Bijvoet mates to a reflection then Fridel mates. A centric reflection is a reflection that is BOTH a symmetry equivalent reflection AND a Bijvoet mate to some other reflection. This is a very small subset of all reflections. Every reflection has one Friedel mate and has N Bijvoet mates, where N is the number of equivalent positions. Only a small number of reflections are centric (with the limiting case of only F000). Dale Tronrud Bernhard Rupp wrote: Let's try this again, with definitions, and pls scream if I am wrong: a) Any reflection pair hR = h forms a symmetry related pair. R is any one of G point group operators of the SG. This is a set of reflections (S). Their amplitudes are invariably the same. They do not even show up as individual pairs in the asymmetric unit of the reciprocal space. NB: their phases are restricted but not the same. b) a set h=-h (set F) exist where reflections may or may not carry anomalous signal. They form the centrosymmetrically related wedge of the asymmetric unit of reciprocal space. c) a centric reflection (set C) is defined as hR=-h and cannot carry anomalous signal. Example zone h0l in PG 2. As Ian Tickle pointed out, the CCP4 wiki is wrong: Centric reflections in space group P2 and P21 are thus those with 0,k,0. Not so; an example listing is attached at the end. d) therefore, some e:F exist that carry AS (F.ne.C) and some that do not carry AS (F.el.C). I hope we can agree on those facts. Now for the name calling: (S) is simply the set of symmetry related reflections, defined as hR=h. (F) is the set of Friedel pairs, defined as h=-h. (C) are centric reflections, defined as hR=-h. Thus, only if (F.ne.C), anomalous signal. I thought those are Bijvoet pairs. They are, but it may not be the definition of a Bijvoet pair. Try 1: Bijvoet pair is F(h) and any mate that is symmetry-related to F(-h), e.g., F(hkl) and F(-h,k,-l) in monoclinic. hkl is not related to -hk-l via h = -h. Only h0l is, and those are (e:C). So, I cannot quote follow that, probably try 1 is not a good definition. Try 2: I've always thought that a Bijvoet pair is any pair for which an anomalous difference could be observed. Good start. I subscribe to that. This includes Friedel pairs (h h-bar) Good. That's the definition of F. but it also includes pairs of the form h h', where h' is symmetry-related to h-bar. Ooops. That is the definition of a centric reflection. Thus Friedel pairs are a subset of all possible Bijvoet pairs. Cannot see that. I still maintain that Bijvoet pairs are a subset of Friedel pairs (which does include Pat's definition). I fail to see anything else but Friedel pairs in my list of reflections - some of them carry AS (F.ne.C) and some don't (F.el.C). B = F.ne.C. Seems to be a necessary and sufficient condition, in agreement with Pat's definition (though not the explanation). But - isn't that exactly what I said from the beginning? A Bijvoet pair is an acentric Friedel pair... Or - where are any other Bijvoet pairs hiding? Where did I miss them? (NB: Absence of anisotropic AS assumed -let's not go there) See reflection list P2 (hkl |F| fom phi 2theta stol2) last 3 items: centric flag, epsilon, m(h) 0 0 1 993.54 1.00 179.9965.61 0.581 1 1 2 0 0 -1 993.54 1.00 179.9965.61 0.581 1 1 2 1 0 0 1412.58 1.00 0.1438.22 0.0001711 1 1 2 -1 0 0 1412.58 1.00 0.1438.22 0.0001711 1 1 2 0 0 2 3279.49 1.00 180.3132.80 0.0002323 1 1 2 0 0 -2 3279.49 1.00 180.3132.80 0.0002323 1 1 2 1 0 1 379.89 1.00 180.2530.36 0.0002712 1 1 2 -1 0 -1 379.89 1.00 180.2530.36 0.0002712 1 1 2 -1 0 2 1355.06 1.00 0.1327.97 0.0003195 1 1 2 1 0 -2 1355.06 1.00 0.1327.97 0.0003195 1 1 2 0 1 0 2432.85 1.0021.0924.35 0.0004216 0 2 1 0 -1 0 2434.14 1.00 339.6524.35 0.0004216 0 2 1 0 1 1 621.36 1.00 101.6722.83 0.0004797 0 1 2 0 -1 -1 623.27 1.00 258.4922.83 0.0004797 0 1 2 1 0 2 319.68 1.00 359.9822.65 0.0004874 1 1 2 -1 0 -2 319.68 1.00 359.9822.65 0.0004874 1 1 2 0 0 3 426.17 1.00 180.9921.87 0.0005227 1
Re: [ccp4bb] Friedel vs Bijvoet
Bernhard Rupp wrote: I quote from these pages: Bijvoet pairs are Bragg reflections which are true symmetry equivalents to a Friedel pair. These true symmetry equivalents have *equal amplitudes, even in the presence of anomalous scattering*. This is poorly worded. I would change it to A Bijvoet MATE IS A Bragg reflection which IS A true symmetry equivalent to THE Friedel MATE OF SOME OTHER REFLECTION. These true symmetry equivalents have *equal amplitudes, even in the presence of anomalous scattering*. Note that the Bijvoet mate is symmetry related to the Friedel mate not the original reflection. Dale Tronrud Sounds more like centric or perhaps simply symmetry related to me. A few lines below: A Bijvoet difference refers to the difference in measured amplitude for a Bijvoet pair I don't think you can have it both ways ?? BR
Re: [ccp4bb] Friedel vs Bijvoet
On Thursday 26 June 2008 11:35:31 am Bernhard Rupp wrote: Let's try this again, with definitions, and pls scream if I am wrong: a) Any reflection pair hR = h forms a symmetry related pair. ??? Maybe you meanh' = hR R is any one of G point group operators of the SG. This is a set of reflections (S). Their amplitudes are invariably the same. They do not even show up as individual pairs in the asymmetric unit of the reciprocal space. That last statement means nothing to me. NB: their phases are restricted but not the same. Correct. b) a set h=-h (set F) exist where reflections may or may not carry anomalous signal. They form the centrosymmetrically related wedge of the asymmetric unit of reciprocal space. Makes no sense. h=-h=hR can only be true for h = [000] or for R = I(identity operator) c) a centric reflection (set C) is defined as hR=-h and cannot carry anomalous signal. Example zone h0l in PG 2. I think this is way off base. As Ron Stenkamp just pointed out to me, centric refers to the intensity distribution of a class of reflections. See for example Lipsonn Cochran (1957) page 36. Yes, the h0l zone in P2 is an example. They _do_ carry an anomalous _signal_, but not an anomalous _difference_. That is, the phases are affected but the pairs have equal intensity. But please stay tuned Ethan (channeling Ron) As Ian Tickle pointed out, the CCP4 wiki is wrong: Centric reflections in space group P2 and P21 are thus those with 0,k,0. Not so; an example listing is attached at the end. d) therefore, some e:F exist that carry AS (F.ne.C) and some that do not carry AS (F.el.C). I hope we can agree on those facts. Now for the name calling: (S) is simply the set of symmetry related reflections, defined as hR=h. (F) is the set of Friedel pairs, defined as h=-h. (C) are centric reflections, defined as hR=-h. Thus, only if (F.ne.C), anomalous signal. I thought those are Bijvoet pairs. They are, but it may not be the definition of a Bijvoet pair. Try 1: Bijvoet pair is F(h) and any mate that is symmetry-related to F(-h), e.g., F(hkl) and F(-h,k,-l) in monoclinic. hkl is not related to -hk-l via h = -h. Only h0l is, and those are (e:C). So, I cannot quote follow that, probably try 1 is not a good definition. Try 2: I've always thought that a Bijvoet pair is any pair for which an anomalous difference could be observed. Good start. I subscribe to that. This includes Friedel pairs (h h-bar) Good. That's the definition of F. but it also includes pairs of the form h h', where h' is symmetry-related to h-bar. Ooops. That is the definition of a centric reflection. Thus Friedel pairs are a subset of all possible Bijvoet pairs. Cannot see that. I still maintain that Bijvoet pairs are a subset of Friedel pairs (which does include Pat's definition). I fail to see anything else but Friedel pairs in my list of reflections - some of them carry AS (F.ne.C) and some don't (F.el.C). B = F.ne.C. Seems to be a necessary and sufficient condition, in agreement with Pat's definition (though not the explanation). But - isn't that exactly what I said from the beginning? A Bijvoet pair is an acentric Friedel pair... Or - where are any other Bijvoet pairs hiding? Where did I miss them? (NB: Absence of anisotropic AS assumed -let's not go there) See reflection list P2 (hkl |F| fom phi 2theta stol2) last 3 items: centric flag, epsilon, m(h) 0 0 1 993.54 1.00 179.9965.61 0.581 1 1 2 0 0 -1 993.54 1.00 179.9965.61 0.581 1 1 2 1 0 0 1412.58 1.00 0.1438.22 0.0001711 1 1 2 -1 0 0 1412.58 1.00 0.1438.22 0.0001711 1 1 2 0 0 2 3279.49 1.00 180.3132.80 0.0002323 1 1 2 0 0 -2 3279.49 1.00 180.3132.80 0.0002323 1 1 2 1 0 1 379.89 1.00 180.2530.36 0.0002712 1 1 2 -1 0 -1 379.89 1.00 180.2530.36 0.0002712 1 1 2 -1 0 2 1355.06 1.00 0.1327.97 0.0003195 1 1 2 1 0 -2 1355.06 1.00 0.1327.97 0.0003195 1 1 2 0 1 0 2432.85 1.0021.0924.35 0.0004216 0 2 1 0 -1 0 2434.14 1.00 339.6524.35 0.0004216 0 2 1 0 1 1 621.36 1.00 101.6722.83 0.0004797 0 1 2 0 -1 -1 623.27 1.00 258.4922.83 0.0004797 0 1 2 1 0 2 319.68 1.00 359.9822.65 0.0004874 1 1 2 -1 0 -2 319.68 1.00 359.9822.65 0.0004874 1 1 2 0 0 3 426.17 1.00 180.9921.87 0.0005227 1 1 2 0 0 -3 426.17 1.00 180.9921.87 0.0005227 1 1 2 -1
Re: [ccp4bb] Friedel vs Bijvoet
Also only centric phases are restricted. Yes. *Related* would have been be the proper term for symmetry related reflections. In detail: The phases of symmetry related reflection still are *related* by phi(hR)=phi(h)-2pihT (no restrictions on phi(h)) For centrics phi(h)=pihT or pi(hT+1) the phases are *restricted* to certain phi(h) values. I failed to state the exact phase relations. Sorry for the confusion. Thx, BR -- Ian -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Bernhard Rupp Sent: 26 June 2008 19:54 To: 'Hidong Kim' Cc: CCP4BB@JISCMAIL.AC.UK Subject: RE: [ccp4bb] Friedel vs Bijvoet I quote from these pages: Bijvoet pairs are Bragg reflections which are true symmetry equivalents to a Friedel pair. These true symmetry equivalents have *equal amplitudes, even in the presence of anomalous scattering*. Sounds more like centric or perhaps simply symmetry related to me. A few lines below: A Bijvoet difference refers to the difference in measured amplitude for a Bijvoet pair I don't think you can have it both ways ?? BR Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing [EMAIL PROTECTED] and destroy all copies of the message and any attached documents. Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain. Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused by any virus transmitted by this email. E-mail is susceptible to data corruption, interception, unauthorized amendment, and tampering, Astex Therapeutics Ltd only send and receive e-mails on the basis that the Company is not liable for any such alteration or any consequences thereof. Astex Therapeutics Ltd., Registered in England at 436 Cambridge Science Park, Cambridge CB4 0QA under number 3751674
Re: [ccp4bb] Friedel vs Bijvoet
-BEGIN PGP SIGNED MESSAGE- Hash: SHA1 Le 26 juin 08 à 18:49, Ethan Merritt a écrit : On Thursday 26 June 2008 09:36:16 am Serge Cohen wrote: Please some one tells me if I'm wrong ... but I though that indeed one is NOT supposed to measure anomalous difference from reflections h and h' if those are related by one of the symmetry operator of the point group... This statement is logically equivalent to what Patrick writes below. You are agreeing with each other. Indeed I was thinking of Bernie Santarsiero mail when sending this mail. Bernie's mail was confusing my understanding. To quote the part I was referring to : Friedel pair is strictly F(hkl) and F(-h,-k,-l). Bijvoet pair is F(h) and any mate that is symmetry-related to F(- h), e.g., F(hkl) and F(-h,k,-l) in monoclinic. That is in monoclinic (P 1 2 1, more precisely) , (h, k, l) and (-h, k, -l) should have the same F ... (in a determinist's world) Yes, but that is not an example of h and h'. You mean that in P 1 2 1, h,k,l and -h,k-l are not strictly equivalent? In the context of my message h and h' were defined as : reflections h and h' if those are related by one of the symmetry operator of the point group To come back to the initial mail : b) A Friedel pair is any reflection h = -h including hR = -h, i.e. including centric reflections. I find this notation confusing since (I guess) the '=' does not mean the same thing in both cases : In the first case it means the pair (h, -h) (or more precisely what I understand it means) While the second really means There is a R operator of the PG such that -h = Rh (if the first case had to be understood this way, the only Friedel pair would be (0,0,0) ). So if I try to put this definitions of terms as I understand them: Friedel pair : (h, g) There is a operator R of the P.G. such that -Rh = g Bijvoet pair : (h, g) There is a operator R of the P.G. such that -Rh = g AND : For all operator R of the P.G. : Rh != g Hope I'm getting it right ... and I'm not adding to the overall confusion ;-) Serge. *** Dr. Serge COHEN GPG Key ID: 0B5CDAEC N.K.I. Department of Molecular Carcinogenesis (B8) Plesmanlaan 121 1066 CX Amsterdam; NL E-Mail: [EMAIL PROTECTED] Tel : +31 20 512 2053 *** -BEGIN PGP SIGNATURE- Version: GnuPG v1.4.8 (Darwin) iEYEARECAAYFAkhj+MEACgkQlz6UVQtc2uw7FACguUgF1+XrN9xdRTcLLdShA/Eu A2UAniYPecEAz5BJ/ljrQYymnGRK7Mor =SItL -END PGP SIGNATURE-
