Hi Alan,
I also find it hard to understand the rationale behind this approach.
G(r) can suffer from fourier truncation artifacts due to the finite q
range of the data, but there seems to be no such limitation in a model.
Isn't there a risk of fitting to truncation ripples with G(r)?
As for computational costs, Bricogne has explained this somewhat better
than I can in section 1.3.4.4.4 (.5 and .7) of International Tables
Volume B (reciprocal space). To paraphrase; when N.Nhkl is huge an FFT
helps. The reciprocal space R factors (and gradients) can be found via
an FFT of an electron density map with cost savings for large problems.
Not having a unit cell for liquids and amorphous materials does present
a conceptual problem, which seems to need the Debye formula, see eg:
http://srs.dl.ac.uk/arch/dalai/Formula.html
It seems that function is mainly used for small angle scattering, where
the q range is too small to make a pdf. The distance histogram method
mentioned there also looks interesting for computational speeds.
Looking forwards to hearing some more opinions...
All the best,
Jon
AlanCoelho wrote:
HI all
Looking at the Pair Distribution Function and refinement I come away
with the following:
Fitting in real space (directly to G(r)) should be equivalent to
fitting to reciprocal space except for a difference in the cost
function. Is this difference beneficial in any way. In other words
does the radius of convergence increase or decrease.
The computational effort required to generate G(r) is proportional to
N^2 where N is the number of atoms within the unit cell. The
computational effort for generating F^2 scales by N.Nhkl where Nhkl is
the number of observed reflections. Is there a speed benefit in
generating G(r) - my guess is that it’s about the same. Note,
generating G(r) by first calculating F and then performing a Fourier
transform is not considered.
In generating the observed PDF there’s an attempt to remove
instrumental and background effects. In reciprocal space these
unwanted effects are implicitly considered. This seems a plus for the
F^2 refinement.
From my simple understanding of the process, there seems to be good
qualitative information in a G(r) pattern but can someone help in
explaining the benefit of actually refining directly to G(r).
Cheers
Alan
