[Ifeffit] bond distance resolution and correlation of parameters in MS analyses?
Peter Lay
p.lay at chem.usyd.edu.au
Mon Jun 18 18:19:05 CDT 2007
Dear All
It is unfortunate that the questions that were asked by Mark appeared to be
phrased is such a way to get the responses that were obtained rather than
discussing the real issues behind the questions, or whether they reflected
the information in the Review. As such, I feel compelled to reply to these
comments as they are not an accurate reflection of what was detailed in my
article in Coordination Chemistry Review. While scientific debate is
welcome, as are corrections to errors, I believe that is important that
these information sites should not be used to give incorrect information as
to the contents of a paper.
1. Nowhere in this Coord Chem Rev article did I state that the SS
resolution equation does not apply to paths involving MS contributions, so
the question was incorrectly phrased, as were the responses that claim the
paper was incorrect in saying this. What I did say was that MS analyses
can distinguish metal-ligand bond lengths that differ by less than the
resolution imposed by this equation if the MS pathways from the different
ligands are sufficiently different (within the inherent Fourier transform
resolution) to get around this problem. There are numerous examples in the
literature where metal-ligand bond lengths that differ by less than the SS
resolution have been distinguished in this manner and have been verified by
comparing crystal structure information with those obtained from MS analyses.
Here is a direct copy of the relevant section from the paper, so I am
uncertain as to how the contributors to the e-mails can come to the
conclusion that I stated that the equation does not apply to resolution in
MS paths. Clearly, I have stated that it is only when this resolution is
sufficiently different in other atoms of the restrained ligands that
metal-ligand bond lengths that have differences less than the SS resolution
of bond lengths can be distinguished (the article only talked about ligands
treated as restrained entities).
This limit on the resolution of distances arises because the larger the k
range, the greater the separation of the individual oscillations at the end
of the k range. While this equation is often quoted, the resolution of the
peaks in the FT corresponding to different shells improves as the
temperature is lowered due to reduction in the Debye-Waller factors, so it
should only be taken as a reasonable guide. Thus the use of as large a k
range as possible not only improves the determinacy of the problem, but it
also improves the precision and accuracy to which individual metal-ligand
bond lengths are determined, and whether individual bond lengths can be
resolved. With the typical k ranges used in SS XAFS analysis, M-L bond
differencs have to differ by 0.1-0.2 Å for the oscillations in the XAFS to
be sufficiently resolved to distinguish between these two bond lengths. By
contrast, MS analysis of XAFS data has the ability to distinguish between
metal-ligand bond distances that differ by a factor that is less than the
~0.1 Å limit imposed by the SS resolution, provided that the groups to
which the ligand donor atoms are attached have quite different MS
contributions, which is often the case. The differentiation of M-L bond
distances that are less than the resolution obtainable with SS analysis
relies on the MS contributions of other atoms within the ligands, since
these normally have sufficiently different frequencies of oscillations in
the XAFS so that they can be resolved.
The MS contributions are most important in the low k range [18] and hence,
the most accurate and precise bond length determinations in terms of
resolution of different shells (and three-dimensional structural
determination) will be obtained when both a large k range and all of the
low k range data are used in the fitting procedure.
What do the above comments mean in practice? It means that if a complex
has ligands all of the same type and angles that involve the M-ligand bond
and the ligand are essentially the same, then MS analysis cannot improve
over SS on separating bond distances that differ by less than the SS
resolution in the FT. However, if ligands of the same type are at
different angles with respect to the metal-ligand axes or have different
ligands adjacent or opposite to them, or if different ligands are at
similar distances, then there is almost certainly a range of MS paths that
have half distances that differ by more than the resolution given by the
equation and, hence, the individual metal-ligand distances can be
distinguished by the use of MS fitting within the constraints of the
equation that was given, when they cannot be distinguished by SS fitting.
2. With regard to point 2, yes the equation should have been more
accurately described as the number of independent observations rather than
the number of independent points in reference to equation 24 in the
review. The number of independent observations is a combination of the
number of independent points in the EXAFS data plus the number of
independent observations obtained from crystallography that are included in
the restrained model, as described in the Binsted, Strange and Hasnain
article. The equation (or variations of it, as pointed out by the comments
below) is, however, appropriate for use in estimating the value of the
number of independent observations that are included in restrained MS
modeling for fits to EXAFS data. This is not only used in such EXAFS
analyses but also extensively, and for a long time, in protein
crystallography to increase the degree to which a fit is overdetermined or
to prevent an underdetermined fit to the data. As pointed out by Matt,
this is often used for relatively rigid ligands, such as imidazoles; it can
also be used for flexible ligands where the internal bond lengths vary over
a narrow range that is defined by X-ray crystallography, but one of more
angle(s) have significant flexibility. For the former case, the whole
ligand is moved as an essentially rigid entity, in much the same way as a
single atom in the fitting procedure. The essentially fixed (within small
ranges) bond angles and bond lengths involving this group lead to the extra
term in the equation that is the number of independent observations that
are included in the model and, in a restrained model, this increases the
value of N/p, even though the value of p does not change (i.e., the
positional parameters within the imidazole, for instance, are also fitted
but within a very narrow range that is consistent with the variation
observed in accurate X-ray crystallography structures). If these bond
lengths and angles (and/or Debye-Waller values) were constrained, then the
value of p would also decrease making the problem more overdetermined. The
Debye-Waller factors can be calculated for atoms in a ring in order to
reduce the value of p, but extreme care has to be taken in the use of these
values in constrained fits, since they take no account of disorder problems
in the crystal or solution and, hence, could result in constrained values
that are artificially low and which would lead to problems in the fitting
procedure.
The answer to the question is that the Stern paper discusses the number of
independent points in the EXAFS data and applies to both SS and MS
fitting. However, for restrained MS fits, the number of independent
observations that should be used in assessing the degree to which the
problem is determined in the fitting procedure is that described in the
Binsted, Strange and Hasnain paper (or something similar). The latter type
of fitting was that described in the Coordination Chemistry Rev article and
presumably has been used in the work described by Mark.
All the best
Peter
HI Mark,
> Any thoughts and opinions would be greatly appreciated as this relates
directly to corrections suggested to be made to my PhD thesis!
This is going to re-iterate most of what Bruce said, but since you asked:
> 1)Does the equation for bond distance resolution (r = pi/2deltak) only
apply to SS?
No. It applies to all EXAFS.
> I have held the opinion that this can be applied to MS analysis
You have been right.
> however I have recently been informed that this equation does not
correctly describe distance > resolution in MS analyses. The paper in
Coord. Chem. Rev. 2005, 249, 141-160 describes this > and is this
concordant with the views of the wider EXAFS community?
You were mis-informed. This paper is profoundly wrong, and is not
concordant with the views of the wider EXAFS community, as defined by
the standards and criteria documents at
http://www.i-x-s.org/OLD/subcommittee_reports/sc/err-rep.pdf
This paper states that the number of independent points in an XAFS data set is:
N_i = [ 2*(rmax - rmin) * (kmax -kmin) / pi ] + Sum D*(N-2) + 1
Here rmin,rmax,kmin, and kmax are the spectral ranges. I cannot tell
what the sum is over, but
D is the "dimension with a restrained part of the model (ie, three for
a three-dimensional model)"
and N is "the number of independent atoms within the restrained group
of the model".
The ( Sum D*(N-2) ) term asserts that the number of independent
points in the data is dependent on the model. This is complete
nonsense.
For what it's worth, the standards and criteria report cited above
recommends using
N_i = [ 2*(rmax - rmin) * (kmax -kmin) / pi ]
rounded to the nearest integer. The report is has a bit more to say,
but note that it is carefully (and deliberately) silent on "+1", "+2",
etc. This is because N_i is an estimate of the maximum number of
parameters that can be extracted from a signal. If you're quibbling
whether to add 1 or 2 to this number, it probably means you should
really subtract 4.
Now, one may apply a variety of modeling approaches (tricks??
assumptions??) to the analysis of multiple scattering in highly
constrained three-dimensional models that are often associated with
organo-metallics. For example, a histidine ring attached to a metal
will give multiple scattering, and you can usually assert that the
ring is rigid, though you may need to refine its location and
orientation relative to the metal. That makes the bond distances and
angles (and MS amplitudes) for all the scattering paths from this ring
all dependent on a reduced number of variables. It does not add
information to the data.
Cheers,
--Matt
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Cc: MarkBondin <mibondin at three.com.au>
Subject: Re: [Ifeffit] bond distance resolution and correlation of
parameters in MS analyses?
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On Wednesday 06 June 2007, MarkBondin wrote:
> 2) What is the actual equation which defines the determinacy of a fitting
> procedure and does this differ between SS and MS analyses? For MS analyses
> there has been a recently published equation (Coord. Chem. Rev. 2005, 249,
> 141-160) which takes into acount the number of dimensions used in the
> analyses and is this only relevant to MS analyses of data? This has also
> been expressed in the paper by Binsted (Biochemistry. 1992, 31,
> 12117-12125) however a different equation has been detailed by Stern (Phys.
> Rev. B. 1993, 48, 9825-9827) which I have been using as a guide in my MS
> analyses. Is this acceptable?
1. I don't know what you mean by the word "determinacy". In any
case, I thought I made it clear in my last post that, in my
opinion, the differences between SS and MS analysis are in the
physical interpretation and not in the statistical interpretation.
Feff, Ifeffit, and Artemis certainly go to great lengths to
downplay the differences between SS and MS paths in the context of
the formalism of the theory and analysis, instead emphasizing
their differences only in the context of physical interpretation.
2. Argonne's library only has access to the last year of
Coord. Chem. Rev. and I don't have time this week to go fetch it
from the stacks. So I cannot comment on that paper.
3. The paper by Stern should be read with some care. The argument Ed
makes in that paper can only be true in the case of a perfectly
packed signal. EXAFS data, although treated as signal processing
problem, is never perfectly packed. The Nyquist criterion is an
upper bound on the information content, but the actual content of
the data is always somewhat less. There are some very fine papers
by Rossner and Krappe about using Baysian techniques to find the
actual information content of the EXAFS signal. The executive
summary is that if think you need Ed's magic "+2", you are
probably overusing the information content of your data.
Most of us here in this list aren't as careful in practice as all
that Baysian stuff. In general, one tries to stay "well below"
the Nyquist upper bound. If your fitting parameters make sense
physically, if the correlations are not "too high", and if the
error bars on your parameters are not "too big", then you are
probably not overusing the information content of your data.
What is "too high" and "too big"? Well, I am purposefully using
squishy language. It is kind of difficult to use Gaussian
statistical techniques on EXAFS data, despite the fact that that's
exactly what Ifeffit does. The reason is that Gaussin statistics
presumes that your measurememt errors are statistical and normally
distributed. In practice, exafs analysis is dominated by
systematic uncertainties. Things like detector or sample
non-linearities and the approximations made by Feff are much
bigger sources of error than shot noise for most experiments.
Most of those systematic problems are present in your analysis,
but I have no idea how you could possibly quantify them. Hence I
find myself using squishy language to discuss fit statistics.
Read the papers by the frequent contributors to this mailing
list. Scott Calvin and Shelly Kelly in particular are careful
EXAFS practitioners who work on tough analysis problems and deal
well with these issues. Doing what they do may not be as right as
possible, but it certainly ain't wrong.
HTH,
B
--
Bruce Ravel ---------------------------------------------- bravel at anl.gov
Molecular Environmental Science Group, Building 203, Room E-165
MRCAT, Sector 10, Advanced Photon Source, Building 433, Room B007
Argonne National Laboratory phone and voice mail: (1) 630 252 5033
Argonne IL 60439, USA fax: (1) 630 252 9793
My homepage: http://cars9.uchicago.edu/~ravel
EXAFS software: http://cars9.uchicago.edu/~ravel/software/
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Subject: Re: [Ifeffit] bond distance resolution and correlation of parameters
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On Wednesday 06 June 2007, MarkBondin wrote:
>1)Does the equation for bond distance resolution (r = pi/2deltak) only
>apply to SS? I have held the opinion that this can be applied to MS
>analysis however I have recently been informed that this equation does not
>correctly describe distance resolution in MS analyses. The paper in Coord.
>Chem. Rev. 2005, 249, 141-160 describes this and is this concordant with
>the views of the wider EXAFS community?
>
>
>Mark,
>
>Strictly speaking, that equation doesn't have anything to do with
>EXAFS. That is the equation that tells you what your Fourier
>component resolution is in a general Fourier analysis problem. It
>just so happens that, in the case of single scattering EXAFS analysis,
>that equation is easily interpreted in terms of photoelectron
>wavenumber k and SS path length r.
>
>The equation is neither different nor incorrect for MS analysis.
>That's true becuase MS analysis isn't any different from SS analysis.
>In either case, you do a Fourier transform. In either case, you
>attempt to model Fourier components using the contributions from some
>number of scattering geometries as computed by theory. In either
>case, you are asking yourself if you can actually resolve small
>differences in phase of the various things that contribute to the fit.
>
>The only difference lies in how you *interpret* the physical meaning
>of the Fourier components. And even then, things aren't so very
>different. In the case of SS analysis, you assert that the R axis is
>a measure of "bond length" while for MS analysis the R axis is a
>measure of "half path length" -- acknowledging, of course, that there
>is a phase shift in the EXAFS equation such that the R axis actually
>measures something a bit shorter than the bond or half path length.
>
>Off the top of my head, I don't recall the paper you cite and I most
>certainly cannot speak for the "wider EXAFS community". Speaking for
>myself, the physical interpretation of the equation for Fourier
>component resolution may change when you consider MS paths, but to
>claim that a property of the Fourier transform somehow becomes invalid
>when you change the details of the fitting model is just silly.
>
>B
>
>
>--
>Bruce Ravel ---------------------------------------------- bravel at anl.gov
>
>Molecular Environmental Science Group, Building 203, Room E-165
>MRCAT, Sector 10, Advanced Photon Source, Building 433, Room B007
>
>Argonne National Laboratory phone and voice mail: (1) 630 252 5033
>Argonne IL 60439, USA fax: (1) 630 252 9793
>
>My homepage: http://cars9.uchicago.edu/~ravel EXAFS software:
>http://cars9.uchicago.edu/~ravel/software/
>
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>Subject: [Ifeffit] bond distance resolution and correlation of parameters
> in MS analyses?
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>Hi, I would like general opinions of some EXAFS practioners in regards to
>the most widely accepted methods for bond distance resolution and
>correlation of parameters in both single scattering (SS) and multiple
>scattering (MS) EXAFS refinements and if these can be said to differ?
>
>1)Does the equation for bond distance resolution (r = pi/2deltak) only
>apply to SS? I have held the opinion that this can be applied to MS
>analysis however I have recently been informed that this equation does not
>correctly describe distance resolution in MS analyses. The paper in Coord.
>Chem. Rev. 2005, 249, 141-160 describes this and is this concordant with
>the views of the wider EXAFS community?
>
>2) What is the actual equation which defines the determinacy of a fitting
>procedure and does this differ between SS and MS analyses? For MS analyses
>there has been a recently published equation (Coord. Chem. Rev. 2005, 249,
>141-160) which takes into acount the number of dimensions used in the
>analyses and is this only relevant to MS analyses of data? This has also
>been expressed in the paper by Binsted (Biochemistry. 1992, 31,
>12117-12125) however a different equation has been detailed by Stern
>(Phys. Rev. B. 1993, 48, 9825-9827) which I have been using as a guide in
>my MS analyses. Is this acceptable?
>
>Any thoughts and opinions would be greatly appreciated as this relates
>directly to corrections suggested to be made to my PhD thesis!
>
>Many thanks,
>
>Mark
>
>_
Professor Peter A. Lay FAA
ARC Australian Professorial Fellow and Personal Chair in Inorganic
Chemistry
Centre for Heavy Metals Research
School of Chemistry
The University of Sydney
NSW 2006
Australia
Tel: +61-2-9351 4269
Fax: +61-2-9351 3329
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