Article Cite This: Cryst. Growth Des. XXXX, XXX, XXX−XXX
pubs.acs.org/crystal
Bottom-Up Design and Generation of Complex Structures: A New Twist in Reticular Chemistry Ashlee J. Howarth,‡ Peng Li,‡ Omar K. Farha,*,‡,§ and Michael O’Keeffe*,† ‡
Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States Department of Chemistry, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia † School of Molecular Sciences, Arizona State University, Tempe, Arizona 85287, United States §
S Supporting Information *
ABSTRACT: The design and subsequent construction of complex structures using simple building blocks represent an interesting challenge in the field of chemistry. In this paper we describe complex nets of the mtn family and their relationship to the most common binary structure in chemistry, MgCu2. In this bottom-up approach we start by linking simple shapes in space and show the inevitable evolution to highly complex, low density structures.
1. INTRODUCTION The art and science of reticular chemistry is concerned with linking molecular modules of well-defined shapes into symmetrical frameworks. Although applied mainly to metal− organic frameworks (MOFs),1 it also is relevant to the design of related materials such as metal−organic polyhedra (MOPs)2 and covalent organic frameworks (COFs).3,4 A basic principle of reticular chemistry is that the underlying topologies of such materials will correspond to nets with the minimal number of topologically distinct vertices (nodes) and edges (links). In the jargon, these are nets of minimal transitivity consistent with the local geometry of the components.5,6 As such, minimal transitivity in the context of topological analysis and/or design is a “bottom-up” principle. The most important nets in this connection are uninodal and binodal with just one kind of link (i.e., transitivity 1 1 and 2 1, respectively) as these types of nets are most commonly generated in practice and can serve as templates for structural design. Recent developments emphasize the need, in some instances, to design the geometry of the component modules as well as consider the topology of the underlying net when building new architectures.7−9 Occasionally MOFs are reported with giant cubic cells that are in striking contrast to the minimal-transitivity principle. Notable examples, setting successive new records for cubic unit cell size (all with symmetry Fd3m ̅ ), are (1) MIL-100 with unit cell a = 72.9 Å10 and MIL-101 with a = 88.8 Å,11 (2) “mesoporous MOF 1” with a = 123.9 Å,12 and (3) NU-1301 with a = 173.3 Å.13 This last material has the largest unit cell volume (>5 × 106 Å3) of any known nonbiological material (30 times larger than the next largest porous crystal14) and has an underlying net of (vertex edge) transitivity 17 18. Strikingly, it © XXXX American Chemical Society
was shown that a simple bottom-up principle was sufficient to explain the occurrence of this structure. In this paper, we show that a generalization of that bottomup principle accounts for all the previously mentioned structures and leads to a large family of complex low-density structures derived from joining one or two simple shapes in a prescribed way. Given that such structures are clearly designable, we consider this to be an important addition to the canon of reticular chemistry.
2. STRUCTURAL ANALYSIS A salient feature of the complex structures described herein is the presence of two kinds of pores arranged as the Mg and Cu atoms of MgCu2, and as such, it is instructive to consider the geometry of that structure first. 2.1. The MgCu2 and Type II Clathrate Structures. It is well-known that regular tetrahedra cannot fill Euclidean threedimensional space.15,16 The dihedral angle is 70.5° (
