Crystallography World Wide Crystallography World WideFrom cmgc055@utxvms.cc.utexas.edu (Vince Lynch) Newsgroups: sci.techniques.xtallography Subject: False positive for Flack 'x' parameter (?) Date: Fri Jul 07 16:54:45 MET DST 1995 Organization: The University of Texas at AustinI recently collected data on a crystal containing a chiral auxillary of known absolute configuration. This was an excellent crystal and, because I had the instrument time, I collected two equivalent sets of data out to 65 deg in two-theta. I was using a Moly tube. I was curious to see if I could determine the absolute stereochemistry from the X-ray results. The molecule contained one S atom and had a mu of 0.198. Refining on F-squared using SHELXL93 proceeded without a glitch. The Flack x parameter for the correct configuration was 0.24(10) and -0.04(10) for the inverted configuration. A colleague had a similar experience. In his structure, mu = 0.464 for a sample with three S atoms. Again, the crystals diffracted beautifully and he collected two+ equivalents out to 75 degrees in two-theta. He did not know the absolute configuration beforehand. One configuration yielded an x parameter of 0.11(4) while the other produced one of 0.09(4). This structure was corrected for absorption by the face-indexing method. The Rint's for both data sets were quite good 2.3% and 2.4%, respectively, on F-squared.
I have seen articles in our beloved Acta Cryst. stating that the absolute configuration was determined by reference to the Flack x parameter but I rarely see the Flack parameter listed for the inverted structure. Shouldn't this be mentioned as a matter of course?
Vince Lynch, UT-Austin
From Howard.Flack@cryst.unige.ch (Howard Flack) Newsgroups: sci.techniques.xtallography Subject: Re: False positive for Flack 'x' parameter (?) Organization: University of Geneva, Switzerland Date: Mon Jul 10 12:41:39 MET DST 1995I must admit that using x we never had results quite like this. The following points spring to my mind:
> I have seen articles in our beloved Acta Cryst. stating that the >absolute configuration was determined by reference to the Flack x parameter >but I rarely see the Flack parameter listed for the inverted structure. >Shouldn't this be mentioned as a matter of course?According to me, no. You don't report incorrect atomic positional and displacement parameters do you! Howard Flack
From Hakon Hope <hhope@ucdavis.edu> Newsgroups: sci.techniques.xtallography Subject: Re: False positive for Flack 'x' parameter (?) Date: Tue Jul 11 03:12:37 MET DST 1995 Organization: University of California, Davis cmgc055@utxvms.cc.utexas.edu (Vince Lynch) wrote: > > I recently collected data on a crystal containing a chiral > auxillary of known absolute configuration.The situation seems to be covered in Sheldrick's SHELXL-93 manual. The wrong absolute structure in a polar space group can give results like the ones you describe.
It is not really a problem with the Flack parameter.
Some time ago I wrote the following in correspondence with George Sheldrick:
Hakon Hope
X-Sender: vmlynch@mail.utexas.edu X-Envelope-to: Howard.Flack@cryst.unige.ch X-Mailer: <PC Eudora Version 1.4>Thank you for responding to my newsgroup submission concerning my experiences using your method for determining absolute stereochemistry. In my comments to the newsgroup, I meant to say that only the x parameter for the inverted structure be listed and not the entire refined structure which would be somewhat mind-numbing. This practice would be analogous to listing the wR for the inverted structure when applying Hamilton's test. A practice that was routinely followed in the 'olden days'.
For your information, in the second structure mentioned, in addition to the two symmetry equivalent data sets, a few hundred additional reflections were collected corresponding to Friedel relatives. That is to say, in space group, P21, +/- h, -2 to +k, +/- l reflections were collected.
Such care was not taken in the first case as the stereochemistry was already known. I have used the method when dealing with chiral di-Rhodium complexes, refining using SHELXL93, and the results are as expected. I get a value around 0.0 with a small esd for one enantiomer and a value around 1.0 with the same esd for the inverted structure. I always refine the entire structure and inverting.
Vince Lynch
From Howard.Flack@cryst.unige.ch (Howard Flack) Newsgroups: sci.techniques.xtallography Subject: Re: False positive for Flack 'x' parameter (?) Organization: University of Geneva, Switzerland Date: Tue Jul 11 16:22:34 MET DST 1995The 'polar dispersion error' (pde) was first shown to exist by the Templetons and arises if a structure:
In all of our own uses of the x parameter, either in X-RAY, Xtal or a programme called GMLX (I think) that I hacked for use at the IUCr computing school in Mülheim, Germany in 1984, x was always refined simultaneously in a full normal-equations matrix with the other atomic and crystal parameters. With an implementation such as this, the possibility of a pde disappears because the atomic coordinates and x can vary together - x always moving towards the 'best' value. For example if you have a refined structure giving a value of x near to 0.0 and you 'invert' the coordinates (and perhaps the space group), on further refinement x steps straightaway to a value near to 1.0. I do not remember ever having tried myself to see what happens to x when you are in a situation where a pde could occur when one inverts the coordinates and then just refines the scale factor and x. It seems to me to be asking for trouble! The Lynch and Hope refinements correspond to the trial I never attempted myself and they seem to have found the trouble.
Our own and other people's experience with x has shown that in practice it is an extraordinarily stable parameter during least-squares refinement. This means that one can let it vary with the other parameters during the whole course of a refinement with no difficulty.
Now with all of that said, there is nevertheless something fishy with the results from Lynch's first crystal (2 asymmetric regions of reciprocal space measured without Friedel opposites, 2-theta max 65 deg, MoKalpha, molecule has on S - [[but what is the space group Vince?]]) because he says he gets x = 0.24 for the CORRECT configuration and -0.04 for the INVERTED configuration - i.e. he seems to be getting a sensible x for the wrong configuration and a wonky value for the correct configuration where I would expect the contrary. (Maybe the space group itself needs inverting to take P31 instead of P32 for example but let me out of my agony and tell me what the space group really is).
Lynch's second crystal (more correctly that of his colleague) corresponds to a case where a pde could occur (two asymetric regions + some Freidel opposites measured, 2-theta max 75 degrees, molecule contains 3 S atoms, space group P21,) x value for one configuration (the wrong one, I suppose) of 0.11, and 0.09 for the other (the correct one, I suppose). In this case there is, of course, no problem with inverting the space group. Further rather than the pde showing itself up as coordinate shifts along the polar axis (where you need Templeton's care and genius to spot it), the wrongness of the structure description appears in a wonky value of x which happily is a bit easier to spot. Clearly Hope's refinements correspond to the same situation with the added complication of an 'invertable' space group.
I do not at all understand why the refinement of x has been implemented into SHELXL93 in the manner of a post-cycle calculation refining only the scale factor and x. All of the values that are needed to calculate F2 and derivatives for reflection h k l are the same (with a few signs changed) for -h -k -l. A little organisation and the calculation is done for free. It hence seems perfectly natural to implement x refinement as an ordinary parameter alongside the scale, coordinate, displacement and other things. I see no reason or advantage in doing otherwise. It is disappointing to see that the choice of the post-cycle strategy has clouded an issue that had become, at least for me, particularly clear. Further, experience leads me to be very sceptical concerning the effectiveness of writing warning messages into a programme's documentation or output.
Howard Flack
From chem91@Elroy.UH.EDU ("Bill Harrison (713)-743-2789")
Newsgroups: sci.techniques.xtallography
Subject: Re: False positive for Flack 'x' parameter (?)
Date: Tue Jul 11 16:52:54 MET DST 1995
Organization: University of Houston
CRYSTALS does a "proper" least-squares treatment of x... For the inorganic
systems I've worked on, x often refines to an "intermediate" value between
0 and 1, but not necessarily 0.5. Whether it's due to not enough data
(I don't usually collect Friedel equivalences) or some kind of twinning,
I don't know... These are systems where there's no reason to suspect
that one chirality will predominate.
Bill Harrison
From spea@faculty.chem.ruu.nl (Ton Spek) Newsgroups: sci.techniques.xtallography Subject: Re: False positive for Flack 'x' parameter (?) Organization: Physics and Astronomy, University of Utrecht, The Netherlands Date: Thu Jul 13 09:23:07 MET DST 1995As was already remarked by Howard: People do not seem to read the documentation. As far as the Flack parameter x is concerned as available in SHELXL93: (page 46 in the manual) you should use the two instruction lines
This issue was addressed last year with a poster by Curt Haltiwanger at the ACA-meeting in Atlanta. I suspect that the matter will be clearified in the coming updated version of SHELXL.
Ton Spek
From: gsheldr@shelx.uni-ac.gwdg.de <gsheldr@shelx.uni-ac.gwdg.de> Date: Thu Jul 13, 17:03 To: vmlynch@mail.utexas.edu Cc: /home/gsheldr/Flack Subject: Flack x parameterHoward Flack has sent me a copy of your discussion. Our internet connection here is so slow that I don't have time take part in such network debates myself.
After the last refinement cycle of a non-centrosymmetric structure SHELXL-93 performs a final structure factor calculation to obtain final R-factors and phases for Fouriers etc. Since there are many cases in the literature of people forgetting to check the 'absolute structure', thereby introducing errors in the coordinates if it happens to be wrong, I had the bright idea (which I am now regretting) of getting the program to make a crude estimate of the Flack parameter so that it could print a warning when further action might be necessary. This estimate ignores correlation between the Flack parameter and all other parameters (except the overall scale) and may therefore give an underestimate of x when the absolute structure is wrong (especially in polar space groups such as P21). If I had realized how strong this correlation can be in certain cases I would probably have dropped the idea.
As explained in the manual and also more eloquently in your communications from Howard and Hakon, if there is any doubt it is ESSENTIAL to refine the Flack parameter with all the other parameters in the same full matrix. In SHELXL this is performed by adding the instruction 'TWIN' (no further parameters needed, since the matrix for racemic twinning is the default) and the instruction 'BASF' (batch scale factors) followed by one number, the starting value for the Flack parameter. We usually start at 0.5, but to be more thorough you can run two jobs starting from 0.0 and 1.0 respectively; I am confident that they would converge to the same answer. A comparison of the resulting value with its esd (oops - I mean standard uncertaintly) will give a reasonable indication of the reliability of the absolute structure assignment, or whether racemic twinning is really present. However you should note that such esds assume that only random erros remain, and in practice may be underestimated (by say a factor of up to two). By measuring the reflection h k l and -h -k -l in such a way (+/- 2theta, same chi and phi, omegas differ by 2theta) that absorption errors are substantially cancelled, and making these measurements close in time (and/or cooling to reduce crystal decay), you can reduce the systematic errors and so improve the reliability of the determination. If only CHNO are present it is essential to cool and measure to higher 2theta (the ratio f"/f increases with sin theta/lambda).
If you have problems with my programs in future it may be a good idea to email me directly, or at least email me a copy of anything you post for discussion; I try to respond to all emails reasonably promptly. I shall also be at the Montreal ACA, and it is precisely such problems that the SHELX Workshop there is designed to cover !
(It might be a good idea to post this onto your network discussion, if you have no objections).
George Sheldrick
From: Vince Lynch <vmlynch@mail.utexas.edu> Date: Sat Jul 15, 13:02 To: Howard Flack <Howard.Flack@cryst.unige.ch> Cc: Subject: Re: Flack 'x' parameter > What is the space group of your first crystal?The space group for both samples is monoclinic, P21. In the meantime, I have received some e-mail from George Sheldrick on the subject along the lines of the post by Ton Spek in the newsgroup. I will take their advice and try it out on these data sets and relay the information to you. It appears from this that I probably misused the method as it was intended by George Sheldrick.
My original post was never meant to be a criticism of your method of determining absolute structure or of SHELXL93. I was simply baffled at my experiences with these two structures. Prior to this, results fell into one of two categories. Either I found that the Flack parameter had some non-zero value with a high esd (.3 - .4) which told me I could not determine absolute structure from the X-ray data (and in light of Ton Spek's comments I will re-evaluate) or I got values near 0 or 1 with a small esd.
Vince Lynch