Question on CRYSOL

Calculation of SAXS and SANS profiles (CRYSOL, CRYSON), superposition of models (SUPCOMB, DAMAVER, DAMCLUST), database DARA
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kimjs70
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Joined: 2015.01.08 19:56

Question on CRYSOL

Hello,

I would like to figure out what type of function of space is used in calculating intensity profile given PDB coordinates.
In 1995 CRYSOL paper, I found that CRYSOL uses a five-Gaussian formula (Cromer-Mann) to compute the form factor of individual atom (From there, mathematical calculation including the spherical harmonics etc. follows).
But I could not find the function of space corresponding to that formula.
For example, I have heard that a gaussian sphere is used for the coordinates of each atom.
I wonder if that means the following:
Given the coordinates of the i-th atom, denoted as x_i,
rho(x) ~ exp (-1/(2 \sigma^2) (x - x_i)^T (x - x_i)) ,
or there is any other function type for rho(x).
Thanks so much for any kind help, in advance.

Sincerely,
Jin

SaxsMax
Posts: 349
Joined: 2007.08.03 19:16

Re: Question on CRYSOL

There might be some confusion between the five-Gaussian approximation and the Gaussian sphere.
The five-Gaussian approximation is related to the atomic scattering in vacuum.
Corresponding theory and parameters can be found in the International Tables for X-ray Crystallography,
Volume IV, page 71 (2.2 Atomic Scattering Factors for X-rays) and in Table 2.2B, page 99 hereof.
The Gaussian sphere is related to the scattering from the excluded volume.
The density of the Gaussian sphere taken from Fraser et al. J. Appl. Cryst. (1978) 11, 693-694 is:
rho(r)=exp(-(r/r0)^2)
Hope this helps.

kimjs70
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Posts: 2
Joined: 2015.01.08 19:56

Re: Question on CRYSOL

Thank you very much, SaxsMax, for your kind reply.
I was not clear on the Gaussian sphere.
Back to my original question, I wonder what is the function of space corresponding to the given PDB coordinates.
It seems to me that the Dirac delta functions with additional factors are used: for example, let x_i denote the cartesian coordinates of the i-th atom, then something like sum_{i=1}^{N} \delta (x - x_i) is used to calculate the scattering intensity profile.
I wonder what the exact form of this spatial function might be.
Again, thanks so much for any help on this, in advance.

Sincerely,

Jin

SaxsMax