I am trying to reproduce the 2D SAXS interference pattern of bulk water via ab initio MD methods as shown in the figure below:

enter image description here

The main aim is to recreate figure (a) via averaging MD configurations of bulk water. To do this. I ran QM/MM simulations of water in CP2K to get the electron density of bulk water. The water molecules were selected so as to create a spherical volume in the middle of the simulation box.

The structure factor $S_{\vec{G}}$ can be written as the fourier transform of the electron density:

$$ n_{\vec{G}} = \frac{1}{V}\sum\limits_j e^{-i\vec{G}\cdot\vec{r}_j}\int n_j\left(\vec{r}'\right)e^{-i\vec{G}\cdot\vec{r'}}d\vec{r}'\tag{1}$$

\begin{equation} S_{\vec{G}} =Vn_{\vec{G}} = \sum\limits_j f_j\left(G\right)e^{-i\vec{G}\cdot\vec{r}_j}, \tag{2}\end{equation}

so the simplest way to reproduce the above figure seem to be to perform the fourier transform of the electron density cube files obtained from the MD simulations and average them over multiple configurations. However in my case, I am getting a spike in the q-space corresponding to the center zero frequency.

enter image description here

Does anyone here has any experience with this type of scenario or has tried to replicate the SXRS spectra of water? Any suggestions would be helpful.

  • $\begingroup$ The g(r) graph looks like the gyration radii that it is a discrete quantity (depend on the position of each particle). I m not seen how to calculate it from electronic density (continuous function of x,y,x). $\endgroup$
    – Camps
    Mar 9, 2021 at 15:46
  • 1
    $\begingroup$ @Camps The g(r) graph is the radial distribution function of water which can be experimentally determined by X-ray (hence based on electronic structure of the system). For ex: A.K. Soper's 2013 paper on water RDF (doi.org/10.1155/2013/279463) $\endgroup$
    – mykd
    Mar 11, 2021 at 19:19


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