[Wien] atomic form factor calculation

[Semen Gorfman]

Dear Howard Sheng!

Generally speaking there are no any unambiguous ways to subdivide
electron density in solids into independent atomic fragments /
pseudoatom. In other words there are no individual atoms in crystal
unit cell.

For X-ray structure analysis several different approximation are
used. Bader(zero flux surfaces) atomic partitioning is one possible
way, but there are also some other ones. For example: multipole model
or Hishfelld approaches. Finally, free atoms model may be used.
Depending on the type of pseudoatoms (Bader volumes, multipole or
Hirshfeld pseudoatoms) you get different Fourier transformation of
them, and accordingly different form factors of a model pseudoatom in
a crystal.

Hirshfeld approach might be technically the simplest one. First you
get the weight function, dividing electron density in a crystal by
electron density in pro-crystal (superposition of free atomic
densities). Then you just multiply this weight function with the free
atomic density of an atom.

Best regards
Semen Gorfman


> Dr. Marks,

> Thanks for the paper. I have read it and it's an excellent paper.

> I understand that the chemical bonding introduces changes to the atomic
> factor(s), due to charge redistribution and orbital hybridization. It's not
> surprising that dstart generates the same atomic factor as the tabulated
> values, since dstart basically superposes the charge densities of all atoms,
> without relaxing to their electronical ground states.

> My problem still remains: how can I generate the atomic form factor of
> individual atoms in the unit cell? In my simulation of the X-ray structure
> factor (e.g. of a liquid), I need not only <f>^2, but also <f^2>. It's the
> latter that I found difficult to get.

> I come by a solution, but am not sure if it will work. One may do the Bader
> analysis first, and the charge density can be divided into regions of
> different atoms. The subsequent Fourier transform of the charge density (of
> different atoms) then gives the atomic form factors. How do you think? Are
> there other simpler workarounds?

> Thank you,

> Howard

>>-----Original Message-----
>>From: wien-bounces at zeus.theochem.tuwien.ac.at
>>[mailto:wien-bounces at zeus.theochem.tuwien.ac.at]On Behalf Of L. D. Marks
>>Sent: Tuesday, April 25, 2006 10:18 PM
>>To: A Mailing list for WIEN2k users
>>Subject: Re: [Wien] atomic form factor calculation
>>
>>
>>See http://scripts.iucr.org/cgi-bin/paper?lc5043 . The tabulated x-ray
>>scattering factors and those from dstart are essentially the same, the
>>changes on bonding are much larger.
>>
>>On Tue, 25 Apr 2006, HW Sheng wrote:
>>
>>> Dear Wien users,
>>>
>>> I wonder if I can use lapw3 to calculate the atomic form factor for
>>> individual atoms in an alloy.
>>>
>>> If I understand this correctly, lapw3 computes the atomic form factor
>>> (so-called X-ray structure factor) of a unit cell, including
>>contributions
>>> from all elements (if not an elemental solid) in the unit cell.
>>The is the
>>> averaged atomic form factor <f>. Any guidance/suggestions how to
>>calculate
>>> the form factor of individual atoms?  I need this in order to compare how
>>> the atomic form factor in an alloy ( or a compound) differs from the
>>> tabulated value of  "neutral atoms", and this information will help me to
>>> simulate X-ray diffraction experiments with high accuracy.
>>>
>>> Your help would be greatly appreciated.
>>>
>>> Howard Sheng
>>>
>>> Dept. Materials Science & Engineering
>>> Johns Hopkins University
>>>
>>>
>>
>>Note: if you have an old email address for me, please note that "nwu" has
>>been changed to "northwestern".
>>-----------------------------------------------
>>Laurence Marks
>>Department of Materials Science and Engineering
>>MSE Rm 2036 Cook Hall
>>2225 N Campus Drive
>>Northwestern University
>>Evanston, IL 60208, USA
>>Tel: (847) 491-3996 Fax: (847) 491-7820
>>email: L-marks at northwestern dot edu
>>http://www.numis.northwestern.edu
>>-----------------------------------------------
>>
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