Real-space solution to the electronic structure problem for nearly a million electrons.

We report a Kohn-Sham density functional theory calculation of a system with more than 200 000 atoms and 800 000 electrons using a real-space high-order finite-difference method to investigate the electronic structure of large spherical silicon nanoclusters. Our system of choice was a 20 nm large spherical nanocluster with 202 617 silicon atoms and 13 836 hydrogen atoms used to passivate the dangling surface bonds. To speed up the convergence of the eigenspace, we utilized Chebyshev-filtered subspace iteration, and for sparse matrix-vector multiplications, we used blockwise Hilbert space-filling curves, implemented in the PARSEC code. For this calculation, we also replaced our orthonormalization + Rayleigh-Ritz step with a generalized eigenvalue problem step. We utilized all of the 8192 nodes (458 752 processors) on the Frontera machine at the Texas Advanced Computing Center. We achieved two Chebyshev-filtered subspace iterations, yielding a good approximation of the electronic density of states. Our work pushes the limits on the capabilities of the current electronic structure solvers to nearly 106 electrons and demonstrates the potential of the real-space approach to efficiently parallelize large calculations on modern high-performance computing platforms.

Space-Filling Curves for Real-Space Electronic Structure Calculations.

Hamiltonian matrices for Kohn-Sham calculations implemented in real space are often large (millions by millions) but very sparse. This poses challenges and opportunities for iterative eigensolvers, which often require a large number of matrix-vector multiplications. As a consequence, an efficient parallel sparse matrix-vector multiplication algorithm is desired. Here, we investigate the benefits of using Hilbert space-filling curves (SFCs) in domain partitioning. We show that the use of Hilbert SFCs in grid-point partitioning brings better locality of the grid points, improves balance of communication, and reduces communication overhead. We also demonstrate an extension of Hilbert SFCs coupled with blockwise operations. The use of blockwise operations helps exploit the vector-processing units in contemporary computational platforms. We illustrate speedup and scalability improvements for an iterative eigensolver based on the Chebyshev-filtered subspace iteration method. Using blockwise Hilbert SFCs, we solve the Kohn-Sham problem for silicon nanocrystals up to 10 nm in diameter, which contain over 26,000 atoms. We illustrate how the density of states of silicon nanocrystals evolves to the bulk limit, where Van Hove singularities are clearly apparent.

Investigation of the Water Adsorption Properties and Structural Stability of MIL-100(Fe) with Different Anions.

Investigating metal-organic frameworks (MOFs) as water adsorbents has drawn increasing attention for their potential in energy-related applications such as water production and heat transformation. A specific MOF, MIL-100(Fe), is of particular interest for its large adsorption capacity with the occurrence of water condensation at a relatively low partial pressure. In the synthesis of MIL-100(Fe), depending on the reactants, structures with varying anion terminals (e.g., F-, Cl-, or OH-) on the metal trimer have been reported. In this study, we employed molecular simulations and density functional theory calculations for investigating the water adsorption behaviors and the relative structural stability of MIL-100(Fe) with different anions. We also proposed a possible defective structure and explored its water adsorption properties. The results of this study are in good agreement with the experimental measurements and are in support of the observations reported in the literature. Understanding the spatial configurations and energetics of water molecules in these materials has also shed light on their adsorption mechanism at the atomic level.

Investigating the Potential of Single-Walled Aluminosilicate Nanotubes in Water Desalination.

Water shortage has become a critical issue. To facilitate the large-scale deployment of reverse-osmosis water desalination to produce fresh water, discovering novel membranes is essential. Here, we computationally demonstrate the great potential of single-walled aluminosilicate nanotubes (AlSiNTs), materials that can be synthesized through scalable methods, in desalination. State-of-the-art molecular dynamics simulations were employed to investigate the desalination performance and structure-performance relationship of AlSiNTs. Free energy profiles, passage time distribution, and water density map were also analyzed to further understand the dependence of transport properties on diameter and water dynamics in the nanotubes. AlSiNTs with an inner diameter of 0.86 nm were found to fully reject NaCl ions while allowing orders of magnitude higher water fluxes compared to currently available reverse osmosis membranes, providing opportunities in water desalination.

Relationships among the structural topology, bond strength, and mechanical properties of single-walled aluminosilicate nanotubes.

Carbon nanotubes (CNTs) are regarded as small but strong due to their nanoscale microstructure and high mechanical strength (Young's modulus exceeds 1000 GPa). A longstanding question has been whether there exist other nanotube materials with mechanical properties as good as those of CNTs. In this study, we investigated the mechanical properties of single-walled aluminosilicate nanotubes (AlSiNTs) using a multiscale computational method and then conducted a comparison with single-walled carbon nanotubes (SWCNTs). By comparing the potential energy estimated from molecular and macroscopic material mechanics, we were able to model the chemical bonds as beam elements for the nanoscale continuum modeling. This method allowed for simulated mechanical tests (tensile, bending, and torsion) with minimum computational resources for deducing their Young's modulus and shear modulus. The proposed approach also enabled the creation of hypothetical nanotubes to elucidate the relative contributions of bond strength and nanotube structural topology to overall nanotube mechanical strength. Our results indicated that it is the structural topology rather than bond strength that dominates the mechanical properties of the nanotubes. Finally, we investigated the relationship between the structural topology and the mechanical properties by analyzing the von Mises stress distribution in the nanotubes. The proposed methodology proved effective in rationalizing differences in the mechanical properties of AlSiNTs and SWCNTs. Furthermore, this approach could be applied to the exploration of new high-strength nanotube materials.