No abstract

Exact expressions for finite-volume Kirkwood-Buff (KB) integrals are derived for hyperspheres in one, two, and three dimensions. These integrals scale linearly with inverse system size. From this, accurate estimates of KB integrals for infinite systems are obtained, and it is shown that they converge much better than the traditional expressions. We show that this approach is very suitable for the computation of KB integrals from molecular dynamics simulations, as we obtain KB integrals for open systems by simulating closed systems.

Accelerating progress in the discovery and deployment of advanced nanoporous materials relies on chemical insight and structure property relationships for rational design. Because of the complexity of this problem, trial-and-error is heavily involved in the laboratory today. A cost-effective route to aid experimental materials discovery is to construct structure models of nanoporous materials in silico and use molecular simulations to rapidly test them and elucidate data-driven guidelines for rational design. For example, highly-tunable nanoporous materials have shown promise as adsorbents for separating an industrially relevant gaseous mixture of xenon and krypton. In this work, we characterize, screen, and analyze the Nanoporous Materials Genome, a database of ca. 670,000 porous material structures, for candidate adsorbents for xenon/krypton separations. For over half a million structures, the computational resources required for a brute-force screening using grand-canonical Monte Carlo simulations of Xe/Kr adsorption are prohibitive.To overcome the computational cost, we used a hybrid approach combining machine learning algorithms (random forests) with molecular simulations. We compared the results from our large-scale screening with simple pore models to rationalize the strong link between pore size and selectivity. With this insight, we then analyzed the anatomy of the binding sites of the most selective materials. These binding sites can be constructed from tubes, pockets, rings, or cages and are often composed of non-discrete chemical fragments. The complexity of these binding sites emphasizes the importance of high-throughput computational screenings to discover new materials. Interestingly, our screening study predicts that the two most selective materials in the database are an aluminophosphate zeolite analogue and a calcium based coordination network, both of which have already been synthesized but not yet tested for Xe/Kr separations.

We show how density and energy fluctuations of small nonperiodic systems embedded in a reservoir can be used to determine macroscopic thermodynamic properties like the enthalpy density and the thermodynamic correction factor. For mixtures, the same formalism leads to a very convenient method to obtain so-called total correlation function integrals, also often referred to as Kirkwood-Buff integrals. Using finite size scaling, the properties obtained for small systems can be extrapolated to the macroscopic system limit provided that the system is sufficiently far from the critical point. As derived in our previous work (Chem. Phys. Lett. 2011, 504, 199-201), the finite size scaling is significant and depends on 1/L, where L is the length of the small system in one dimension. By considering a reservoir with an ensemble of embedded small systems, we can use the scaling arising from surface effects to determine properties for macroscopic systems by extrapolation. We demonstrate this method for the WCA and LJ fluids, as well a for a heterogeneous system, i.e., argon adsorbed in silicalite-1 zeolite.