[Ifeffit] bond distance resolution and correlation of parameters in MS analyses?

[Matt Newville]

Hi Peter,

Mark's  questions seemed fairly straightforward to me, and not
uncommon for this forum.   In the quest to get as much information as
possible from XAFS data, the issue of how many parameters can be
determined from an XAFS spectra is a perennial topic of discussion.

Neither Bruce nor I addressed the important point that the 'bond
distance resolution'  of
     pi / (2* Delta_k)
does not determine the accuracy or precision that XAFS normally
achieves.    It's normal to have Delta_k <~ 15Ang^-1, which gives a
typical "bond distance resolution" of 0.1 Ang.   Thirty years of
literature put typical precisions in bond distances an order of
magnitude better than that.      A recent paper by Pettifer et al,
(Nature 435, p78, 2005)  showed sensitivity of XAFS to distance
changes of 10fm (0.0001A),  The data they show in the paper extends to
about 200 eV (kmax ~=  7Ang^-1)!!    They certainly did not have data
with a "spectral resolution" of 10pm, which would require data to
kmax = pi/(2*0.0001) ~= 15700 Ang^-1, or nearly 1GeV above the edge.

But this was not the question.  The question was instead whether this
formula applied equally to single- and multiple-scattering paths.   It
does apply equally.

>  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.

We're doing our best to educate and advance science in this forum.  If
incorrect things are published here or elsewhere, we try to correct
them.

>  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.

I don't understand how a question can be incorrectly phrased.    The
question was whether the spectral resolution was different for SS and
MS paths.  The answers were (and are) "no".

> 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.

Well, I definitely agree with that.

> 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.

This might be read to mean that there is a "SS resolution" and a "MS
resolution" and that they are somehow different.   Which may have led
to the confusion.

>  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.

I don't think that Bruce or I really addressed or disagreed with any
of this (I believe Bruce was clear that he hadn't seen the paper and
my own objections were elsewhere in the paper).   MS is definitely
sensitive to small changes in distance and angles between ligands.
If we disagree on anything here, it's probably on the implication that
pi/(2*Delta_k) sets the precision for SS paths.
But again, the phrase "SS resolution" has strange connotation that the
resolution is somehow different for SS and MS, which was Mark's
original question.


>  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.

Just to clarify my objection to the phrasing used in the paper, and to
be sure that I don't misrepresent it in any way, I'll quote (Coord
Chem  Rev 249, page 148 and 149):

    A crucial factor in the fitting procedure is to ensure that there
are more independent
    data points than there are variables.  The determinacy of the
system (Ni/p) is calculated
    from the estimated number of independent data points collected in
the XAFS data set
    (Ni), and fitted parameters included in the model (p), where Ni is
given by Eq. (3) [24].
                 Ni =  2(rmax − rmin)(kmax − kmin)/π  + D(N − 2) + 1
                (3)
    Here, rmax, rmin and kmax, kmin are the maximum and minimum values
used in the FT
    and XAFS filtered data, respectively; D is the number of
dimensions within a restrained
    part of the model (i.e., three for a three-dimensional model); and
N is the number of
    independent atoms within the restrained group of the model.

That pretty clearly states that the "number of independent data points
collected in the XAFS data set"  depends on the details of the
restraining model.   This equation was exactly what Mark asked about,
and I stick by my earlier answer (the short version of which is: "it's
wrong").

>  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.

I'm not sure we disagree here, but the terminology might be slightly
different.   You seem to be using "restrained MS fits" to mean fits
that include MS and also include restraints imposed by knowledge
derived from crystallographic data.

The "Number of independent points" represents the information content
of the XAFS signal, which is set by its spectral range (and noise
level -- typically ignored except to determine what Kmax should be,
and to stress that the estimated value is an upper bound), not by how
much other knowledge you have.    Certainly, having other knowledge
(say, from diffraction) and being able to relate that to the modeling
of XAFS data is immensely valuable.

Cheers,

--Matt Newville