[Ifeffit] Using more than one E0

[Bruce Ravel]

On Thursday 27 May 2004 02:18 pm, Wojciech Gawelda wrote:
WG> My question is the following: does anyone of you have some experience
WG> with such procedure? And if yes, shall than distinguish between the
WG> first shell of nearest neighbors and the rest of the atoms in terms of
WG> their E0 corrections (using 2 parameters)? Or perhaps one can use
WG> separate E0's for each path?

Hi Wojciech,

Feff makes approximations when it computes the potentials.  The
farther away from a muffin tin the real material is, the worse those
approximations will be.  For a material that is centro-symmetric or
not so far away, the potentials should be pretty trustworthy in the
extended spectrum.  For an assymmetric material, the muffin tin
approximation may be suspect.  In particular, there is no real
concept of a bond in a muffin tin potential.  In a real material,
there might be phase shifts seen by the photoelectron as it scatters
in one direction that are different in another direction.

One empirical way of accommodating the shortcomings of a muffin tin
potential is to introduce more than one e0 into a fit.  But doing so
is like approaching the part of an ancient map that says "Here there
be dragons."

The dragon in this case is the argument that you are just throwing a
non-physcial parameter at the problem in order to obtain a fit that is
numerically superior.  In slangy English, we call these fudge factors.

Fudge factors may be bad because they may be highly correlated with
the parameters we want to measure.  A fudge factor that improves the
fit but which cannot be ascribed any physical interpretation should be
viewed with suspicion.

You should note that the first e0 is NOT a fudge factor.  As I
mentioned in response to Stefano's mail yesterday, the first e0 is
needed to make sure the absolute energy scales of the data and the
calculation line up.  Thus the first e0 does have a physical
interpretation.

The bottom line for considering a second e0 is that it must be
physically justifiable.  If it no more than a fudge factor, it's
probably best to stay away.

I would insist that all the parameters affecting the various delta_R
values all behave sensibly as I change some extrinsic parameter.  By
this I mean that if I measure, say, a temperature sequence, all the
delta_R parameters show a dependence on temperature that is sensible
and consistent with anything I might know about the behavior of the
material.  Temperature is a good way of putting a prior constraint on
parameters.  There are other ways as well.  Similarly sigma^2 values
should be sensible, as should any other parameters.

I would not expect the best fit values to be hugely different, perhaps
not even outside their error bars, when I add the second e0.  If
adding the second e0 improves the fit quality and tightens other
uncertainties without significantly changing best fit values, then I
might begin to consider it -- especially if there is some correlation
between the paths that need a different e0 and a suspected shortcoming
of the muffin tin approximation.

Another case where a second e0 might be justifiable is if you expect
there to be interstitial electron density in a particular direction
(due to strong bonding that the muffin tin approximation knows nothing
of) and the use of multiple e0's in particular paths correlates very
strongly with what you expect from the real electron density
distribution.  Again, things that can be justified physically can be
considered in the analysis.


Actually the argument that parameters should be physically justifiable
applies to all parameters, not just your e0 parameters ;-)

HTH,
B



-- 
 Bruce Ravel  ----------------------------------- ravel at phys.washington.edu
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