Yes, in my gnuplot "form factor" functions, "x" is the real-space
distance from the center of the atom in Angstrom and the "return value"
is electron density in electrons/A^3.
I did not realize the gnuplot file would be so interesting! If anyone
wants the reciprocal-space version (which is simpler), it is here:
http://bl831.als.lbl.gov/~jamesh/pickup/all_atomsf.gnuplot
Where the "s" value is sin(theta)/lambda and the return value is simply
"electrons". This is because the structure factor is defined as the
ratio of the scattering to the atom (or any other object) to the
scattering from a single point electron at the origin (Debye & Scherrer,
Phys Z. 1918; Hartree, Philo Mag. 1925).
The incorporation of a B factor is formally a convolution in real space
(blurring function), which translates into a simple multiplication in
reciprocal space. The funky (4*pi/B)**1.5 factors in the real-space
functions arise because the total number of electrons must not change
when you apply a B factor. This is why the peak height goes down with
increasing B, and you also rapidly loose any "atomic radius" information
as the width of the B-factor Gaussian becomes large when compared to the
width of the relevant Ee_ff(x,0) function.
Ian has also pointed out that none of this considers the mechanics of
how you actually calculate maps, where things like "series termination
error" come into play. But perhaps that is a topic for a new thread?
-James Holton
MAD Scientist
On 11/2/2011 7:17 PM, Ivan Shabalin wrote:
Hi James!
Thank you very much for the gnuplot-ish version of ${CLIBD}/atomsf.lib!! It
works very nice and is very useful for education!
As I understand, the form factor is the Fourier transform of electron charge
density. It is plotted as f(electrons) vs sin(tetta)/lambda and is approximated
as 5 Gaussian (Cromer and Mann) in REFMAC. And you made reverse Fourier
transform of the approximation and plotted the electron density distribution in
the real space.
So, can I ask, what unit is x? Is it angstrom?
And what is Y? is it e/A3 (electron density)?
I found, that at Bf=20, density profiles look almost the same for ions and
atoms (Mg2+ and Mg, Cl- and Cl). Does that means, there is no sense to specify
atomic charge in refmac refinement? It looks a bit strange, because the numbers
of electrons are different. Or decreasing in number of electrons is compensated
with significant decrease in atom size (that can have the same effect as Bf
lowering)? With Bf=0 the difference in curves is significant.
With best regards,
Ivan Shabalin
