**Examples**

#### Assembling, Analyzing, and Steering the Design of New Materials

**Maciek Haranczyk**

Pore Accessibility by "Molecular Worms"

Predicting whether a molecule can traverse chemical labyrinths of channels, tunnels, and buried cavities usually requires performing computationally intensive molecular dynamics simulations. Often one wants to screen molecules to identify ones that can pass through a given chemical labyrinth or screen chemical labyrinths to identify those that allow a given molecule to pass. Because it is impractical to test each molecule/labyrinth pair using computationally expensive methods, faster, approximate methods are used to prune possibilities, “triaging” the ability of a proposed molecule to pass through the given chemical labyrinth. Most pruning methods estimate chemical accessibility solely on geometry, treating atoms or groups of atoms as hard spheres with appropriate radii. Here, we explore geometric configurations for a moving “molecular worm,” which replaces spherical probes and is assembled from solid blocks connected by flexible links. The key is to extend the fast marching method, which is an ordered upwind one-pass Dijkstra-like method to compute optimal paths by efficiently solving an associated Eikonal equation for the cost function. First, we build a suitable cost function associated with each possible configuration, and second, we construct an algorithm that works in ensuing high-dimensional configuration space: at least seven dimensions are required to account for translational, rotational, and internal degrees of freedom. We demonstrate the algorithm to study shortest paths, compute accessible volume, and derive information on

topology of the accessible part of a chemical labyrinth. As a model example, we consider an alkane molecule in a porous material, which is relevant to designing catalysts for oil processing.

1. “Navigating molecular worms inside chemical labyrinths”, Haranczyk, M. and Sethian, J.A., Proc. National Acad. Sciences, 106 pp. 1472-21477, 2009. http://www.pnas.org/content/106/51/21472

High-throughput Analysis of Porous Materials

One important aspect of the structural analysis of materials such as zeolites and metal organic frameworks is the investigation of the geometrical parameters describing pores. Here, we present algorithms and tools to efficiently calculate some of these important parameters. Our tools are based on the Voronoi decomposition, which for a given arrangement of atoms in a periodic domain provides a graph representation of the void space. The resulting Voronoi network is analyzed to obtain the diameter of the largest included sphere and the largest free sphere, which are two geometrical parameters that are frequently used to describe pore geometry. Accessibility of nodes in the network is also determined for a given guest molecule and the resulting information is later used to retrieve dimensionality of channel systems as well as in Monte Carlo sampling of accessible surfaces and volumes. The presented algorithms are implemented in a software tool, Zeo++, which includes a modified version of the Voro++ library.

Zeo++ also provides many additional capabilities which build upon and modify the fundamental Voronoi decomposition underlying porous structure analysis. For instance, the Voronoi diagram can be abstracted as a histogram or “Voronoi hologram”, by encoding the frequency of occurrence of particular edge lengths and radii of the vertices they connect (i.e., denoting sizes of adjacent cavities inside a structure). Materials can thereby be rapidly compared based on these histograms; since similar materials exhibit similar histograms, databases can hence be rapidly searched, screened and sampled based on these novel descriptors.

In general, the Voronoi tessellation is only appropriate when atoms all have equal radii, and the natural generalization to structures with unequal radii leads to cells with curved boundaries, which are computationally expensive to compute. Therefore, high-throughput structure analysis codes, such as Zeo++, utilize the radical Voronoi tessellation, which approximates the curved cells by polyhedra. This approximation can lead to errors in largest included sphere calculations of ca. 0.6 Å. Following the work of Phillips et al. (Soft Matter, 2010, 6, 1693–1703), we describe a strategy to systematically decrease observed errors, and demonstrate that high accuracy (errors below 0.1 Å) can be obtained within the same algorithmic framework and at the expense of only an order of magnitude increase in computational cost.

“Algorithms and tools for high-throughput geometry-based analysis of crystalline porous materials”, T.F. Willems, C.H. Rycroft, M. Kazi, J.C. Meza, M. Haranczyk – Microporous and Mesoporous Materials, 149, pp. 134-141., 2012.

“Addressing challenges of identifying geometrically diverse sets of crystalline porous materials”, R.L. Martin, B. Smit, M. Haranczyk. Jour. Chem. Information and Modeling 52, 308-318, 2012. http://pubs.acs.org/doi/abs/10.1021/ci200386x

“High accuracy geometric analysis of crystalline porous materials”, M. Pinheiro, R.L. Martin, C.H. Rycroft, M. Haranczyk, CrystEngComm 15 7531-7538, 2013. http://pubs.rsc.org/en/content/articlelanding/2013/ce/c3ce41057a.

Materials Design by Optimization

Discovering materials with the optimal characteristics for a particular application is a great challenge. Due to the vast chemical space of possible structures, exhaustive synthesis of materials is not a feasible strategy; therefore alternative, computation-driven strategies for materials discovery are in demand. Much of the recent computation work concerns the enumeration of large databases of feasible material structures, and their subsequent exhaustive analysis. While this approach has led to numerous insights into the design of high performing materials, a significant computational cost is associated with both enumerating and storing a large database of structures, and running exhaustive calculations.

The automated design of high-performance materials through mathematical optimization is an intriguing alternative strategy for materials discovery. In this complementary strategy, material structures are iteratively modified with respect to property; many optimization algorithms from steepest ascent through genetic algorithms can be applied to converge to optimal material designs, and this approach has been demonstrated in the efficient design of high surface area materials. This work reveals that not only can individual materials with outstanding properties be automatically achieved, but that design rules for realizing these properties can also be discovered. Materials can be design with respect to a wide variety of objective functions, and indeed, multiple functions simultaneously, as demonstrated through multiobjective optimization.

“Exploring frontiers of high surface area metal-organic frameworks“, R.L. Martin, M. Haranczyk, Chemical Science 4 ,1781-1785, 2013. http://pubs.rsc.org/en/Content/ArticleLanding/2013/SC/C3SC00033H

“Insights into Multi-Objective Design of Metal-Organic Frameworks”, R.L. Martin, M. Haranczyk , Crystal Growth and Design 13m 4208-4212 2013. http://pubs.acs.org/doi/abs/10.1021/cg401240f