Determining Nanoscale Structures from Pair Distribution Function and Density Functional Theory via Multi-Objective Optimization*

The structures of nanoparticles are challenging to determine. Various techniques have been proposed, each with its own limitations. Computational predictions require approximations and extensive sampling to find low-energy structures, and lowest-energy structures are not guaranteed. Experimental characterization, such as pair distribution function (PDF), provides information on the specific structure, but the inversion of such data is non-trivial.

Combining experimental and computational data into one framework to solve for nanostructures can reduce or eliminate these difficulties. We report our development of a framework that uses multi-objective genetic algorithm to optimize the structure by simultaneously minimizing the energy calculated by density functional theory (DFT) and the PDF residual. We benchmark this framework on gold nanoclusters, compare them to a one that minimizes one data type (i.e. the energy or PDF only), and show that the multi-modal optimization approach is more often able to find the target structures.