Hi Lijun,
I take your point, and you're right I've confused someone else already! I made the NCS exact because a) I was using Eleanor's example (exactly) and was too lazy to make it inexact, and b) making it exact makes the point equally well as making it inexact (actually IMO better because it makes it very easy to distinguish pseudo-absences from accidentally weak reflections) - as long as you don't over-interpret the results!
So for anyone who's confused, my apologies, just imagine that the NCS translation isn't exact, and consequently the 'absences' won't be exactly zero. The point I was making is that NCS translations do not necessarily produce the same systematic absences (or pseudo-absences) as crystallographic translations.
Cheers
-- IAn
> -----Original Message-----
> From: Lijun Liu [mailto:[log in to unmask]]
> Sent: 15 December 2008 18:10
> To: Ian Tickle
> Cc: [log in to unmask]
> Subject: Re: [ccp4bb] About system absence in P4222?
>
> Ian,
>
> Your examples may cause more confusion, especially for those
> beginners with symmetry.
> In your P222 and P3 cases, an exact "NCS" (0, 0, 1/2) turns
> to be an exact crystallographic
> translation, which reduces the unit cell to a half while the
> reciprocal unit cell gets doubled. A
> half of reflection were absent, including those listed as (0,
> 0, 2n+1). This rule applies generally
> to all non-centrosymmetric space groups (P1, P2, P3, P4, and
> P6) with P-lattice when only having
> one rotational symmetric element other than P1, and some
> other space groups like P222.
>
> (Pseudo) translational NCS' role in systematic
> absences(weakness) is complicated. However,
> to do the math with
> --------------
>
> Plug the coordinates (x,y,z) and x+tx, Y+ty,
> z+tz) into the
>
>
> SF equation.
>
> --------------
> is exactly the only way to test it.
>
> Lijun
>
>
> On Dec 15, 2008, at 5:04 AM, Ian Tickle wrote:
>
>
>
> But that only means that the SF contribution from that
> pair of molecules in the unit cell is zero for (00l) l=odd
> reflections. Depending on the crystallographic symmetry
> (e.g. if it were 3-fold or higher order) there may be other
> pairs for which the SF contribution is non-zero for all (00l)
> (but zero for the the odd orders in some other line that is
> symmetry-equivalent to (00l)).
>
> So for example I did a test with 2 mols in the a.u.
> related by an exact (0,0,1/2) NCS translation in P222:
>
> h k l Fcalc phicalc
> 0 0 1 0.00 180.00
> 0 0 2 5120.88 180.00
> 0 0 3 0.00 180.00
> 0 0 4 1273.09 0.00
> 0 0 5 0.01 0.00
> 0 0 6 260.21 180.00
> 0 0 7 0.00 180.00
> 0 0 8 39.42 180.00
> 0 0 9 0.01 0.00
> 0 0 10 43.19 0.00
> 0 0 11 0.00 180.00
> 0 0 12 118.59 180.00
> 0 0 13 0.01 0.00
> 0 0 14 120.89 180.00
> 0 0 15 0.01 0.00
>
> (00l) l odd are definitely absent here! - because none
> of the crystallographic 2-folds affect the (0,0,1/2) translation.
>
> Then I generated 2 mols in the a.u. related by the
> (1/2,0,0) NCS translation in P4 to get the (h00) line (note
> that the 4-fold along c would not affect a c-axis translation):
>
> 1 0 0 25189.10 0.00
> 2 0 0 200.09 0.00
> 3 0 0 14404.46 180.00
> 4 0 0 12608.60 180.00
> 5 0 0 4669.64 180.00
> 6 0 0 748.81 0.00
> 7 0 0 3184.06 0.00
> 8 0 0 3858.87 0.00
> 9 0 0 2578.38 0.00
> 10 0 0 382.61 0.00
> 11 0 0 683.43 180.00
> 12 0 0 444.89 180.00
> 13 0 0 236.65 180.00
> 14 0 0 352.46 180.00
> 15 0 0 5.62 0.00
>
> No absences! The 4-fold generates a pair of molecules
> related by the (0,1/2,0), not the (1/2,0,0) translation. So
> Eleanor is right only in specific cases, Ronald is right in
> the general case.
>
> As an aside, while I was verifying this, I think I
> found a problem with the P3 specific SF calculation in SFALL.
> Here's what I get for 2 mols in the a.u. related by an exact
> (0,0,1/2) NCS translation in P3 using the default P3 specific routine:
>
> 0 0 1 8.24 -175.63
> 0 0 2 7339.05 121.46
> 0 0 3 27.32 125.92
> 0 0 4 949.76 -10.37
> 0 0 5 39.10 -103.39
> 0 0 6 461.79 -115.99
> 0 0 7 19.18 61.53
> 0 0 8 219.72 -96.80
> 0 0 9 66.51 -174.45
> 0 0 10 288.25 -86.65
>
> Now if I use the P1 routine (SFSG 1):
>
> 0 0 1 0.00 165.96
> 0 0 2 7343.28 121.51
> 0 0 3 0.00 -24.58
> 0 0 4 974.19 -13.35
> 0 0 5 0.00 -155.29
> 0 0 6 438.79 -115.60
> 0 0 7 0.01 133.49
> 0 0 8 226.07 -97.44
> 0 0 9 0.01 -101.82
> 0 0 10 291.15 -83.96
>
> The 3-fold along c should not generate any pairs not
> related by the (0,0,1/2) NCS translation, so there should be
> (00l) l odd absences in this case. So something wrong here!
> Personally I always use the P1 routines, why take a chance
> just to shave a few secs off the run time? (note that ccp4i
> uses the default, i.e. the space-group specific routines).
>
> Cheers
>
> -- Ian
>
>
>
> -----Original Message-----
>
>
> From: [log in to unmask]
>
>
> [mailto:[log in to unmask]] On Behalf
> Of Eleanor Dodson
>
>
> Sent: 15 December 2008 09:56
>
>
> To: Ronald E Stenkamp
>
>
> Cc: [log in to unmask]
>
>
> Subject: Re: [ccp4bb] About system absence in P4222?
>
>
>
> Plug the coordinates (x,y,z) and x+tx, Y+ty,
> z+tz) into the
>
>
> SF equation.
>
>
> If the translation component along c is 0.5
> say, then all the 00l
>
>
> reflections for l=2n+1 will be absent.
>
>
>
> Eleanor
>
>
>
>
> Ronald E Stenkamp wrote:
>
>
> Hi.
>
>
>
> Non-crystallographic symmetry (NCS)
> doesn't apply to the entire
>
>
> crystal, so how can it give rise to
> systematic absences? I know it
>
>
> can give rise to systematically weak classes of
>
>
> reflections, but they
>
>
> aren't entirely absent.
>
>
>
> Ron
>
>
>
> On Thu, 11 Dec 2008, Winter, G (Graeme) wrote:
>
>
>
> One of the many facilities in
> pointless is to search for
>
>
> absences and
>
>
> provide a list of likely
> spacegroup choices based on the
>
>
> results. It
>
>
> includes adjustments for
> neighbouring spots to address one of
>
>
> Eleanor's concerns. NCS can
> cause reflections to be systematically
>
>
> absent too.
>
>
>
> The program can be found on the
> ccp4 prerelease pages or on the
>
>
> pointless ftp site.
>
>
>
> Cheers,
>
>
>
> Graeme
>
>
>
> -----Original Message-----
>
>
> From: CCP4 bulletin board
> [mailto:[log in to unmask]]
>
>
> On Behalf Of
>
>
> Eleanor Dodson
>
>
> Sent: 11 December 2008 09:41
>
>
> To: [log in to unmask]
>
>
> Subject: Re: [ccp4bb] About
> system absence in P4222?
>
>
>
> 劉家欣(NTHU) wrote:
>
>
> Dear All:
>
>
>
> We have a crystl with P4222 sg.
>
>
> All statistics look fine.
>
>
> However, there is a
> system absense in l axis.
>
>
> Any body have
> experiences on that?
>
>
> Any suggestions would
> be high appreciated.
>
>
>
> jaishin
>
>
>
> can you give more details, eg
> all reflections along the particular
>
>
> axis..
>
>
> Things like ice rings or
> overlapping intensity from a next
>
>
> neighbour
>
>
> getting integrated
> inapropriately can cause anomalies..
>
>
> Eleanor
>
>
>
>
>
>
>
>
>
>
> 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
> [log in to unmask] 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
>
>
>
>
> Lijun Liu, PhD
> Institute of Molecular Biology
> HHMI & Department of Physics
> University of Oregon
> Eugene, OR 97403
> 541-346-5176
> http://www.uoregon.edu/~liulj/
>
>
>
>
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 [log in to unmask] 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
|
