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: owner-ccp...@jiscmail.ac.uk
[mailto:owner-ccp...@jiscmail.ac.uk] On Behalf Of Eleanor Dodson
Sent: 15 December 2008 09:56
To: Ronald E Stenkamp
Cc: CCP4BB@jiscmail.ac.uk
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:ccp...@jiscmail.ac.uk]
On Behalf Of
Eleanor Dodson
Sent: 11 December 2008 09:41
To: CCP4BB@JISCMAIL.AC.UK
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
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