[GSoC 2025 Project Idea] Implementing Particle Mesh Ewald-based Structure Factor Calculation

[shehan807]

The static structure factor, $S(q)$, provides essential insight into the governing length-scales of a physical system. The X-ray and neutron $S(q)$ specifically can be determined experimentally and theoretically, which has allowed the study of numerous bulk-phase liquid systems. $S(q)$ is computed in one of two ways: (1) as a sum in real space that gets Fourier transformed or (2) directly in reciprocal space. This is nicely outlined by Araque et al., 2015 in Equations 2 and 3, respectively.

Equation 2 is relatively more convenient and prevalent--the "real space sum" is obtained by computing the radial distribution function, $g_{ij}(r)$, after which the user needs to determine an atomic form factor as well as consider finite-size effect corrections.

Alternatively, Equation 3 provides (1) advanced partitioning capabilities (e.g., decomposing $S(q)$ into specific molecular components) & (2) theoretical insights at asymptotic limits. The reciprocal space equation is dependent on an "ensemble average of Fourier space densities", $\rho(k)$, which McDaniel et al, 2015 show that, functionally, it resembles the electrostatic energy of the system at some wavevector $k$. This fact allows for one to compute the $S(q)$ via the particle mesh Ewald method originally introduced by Essman et al, 1995. Explicit details of this approach are provided in McDaniel et al, 2015 SI.

I propose to implement the PME-based $S(q)$ algorithm as an MDAkit given that there are numerous user inputs one may wish to control (i.e., atomic form factor, partitioning scheme, etc). Perhaps this could be a downstream addition to MDAnalysis.analysis given the overlap in base functionality for computing a standard rdf. Any initial feedback would be greatly appreciated!

[orbeckst]

An MDAKit would be a good framework.

I think you'll need to make a case that this is something that is needed in the community, i.e., the potential impact. For instance, is this functionality available elsewhere, are their other papers that make use of such analysis but using custom code, etc.

(S)PME is computationally intensive. You should comment on performance considerations (e.g., using a FFT library, writing the core of the code in a compiled language, ...).