Differential PDF from MD trajectory--real or reciprocal space calculation?

[Niklas Thompson]

Hi all,

Our group is interested in modeling PDF data collected on dilute solutions of organometallic species using molecular dynamics. (The idea is to see if we can extract information from the experimental PDF data regarding the molecule--solvent interface.) In practice, this means we obtain our data as a differential PDF ([solvent + solute scattering] - pure solvent scattering).

In principle, the experimental scattering should contain contributions from:

1. Solute-solute (intramolecular) correlations

2. Solute-solvent (intermolecular) correlations

3. Solvent-solvent correlations (if the solute induces restructuring that is locally distinct from bulk solvent, a la nanoparticles suspended in solvent)

The first two contributions should be obtainable from a single MD trajectory. I have approached simulating PDF data from such a trajectory using the two methods provided in diffpy, namely, using the Debye equation to calculate the scattering in reciprocal space (via diffpy.srreal.pdfcalculator.DebyePDFCalculator) and using the real-space calculator (via diffpy.srreal.pdfcalculator.PDFCalculator). In either case, I calculate the scattering from the desired pairs of atoms for each frame in the MD trajectory, and then average over all frames. 

However, I observe quantitative (and qualitative) differences between these two approaches. In particular, the relative intensity of the solute-solute versus solute-solvent contributions differ by about a factor of 2 between the real space and the reciprocal space calculation. I attach an example below: The top lines show the (normalized) solute-solute G(r), while the bottom lines show the solute-solvent G(r) (normalized to the intra-molecular scattering) using both simulation approaches. The dashed line at the bottom is the reciprocal space calculation multiplied by a factor of 2.

My question is simply: What is the origin of this discrepancy? The only thing I can think of is there's some normalization condition imposed from periodic boundary conditions accounting for this factor of 2.

The qualitative differences bother me less than this quantitative difference, considering that the two calculators are fundamentally different. I will note that the real-space approach gives a prediction that is in much better agreement with experiment than the reciprocal space one. 

Thanks,

Nik