Design of a Molecular Quasicrystal

Abstract

A revolutionary discovery in solid state science was made in 1984 when Schechtman and co-workers [1] showed that certain metal alloy materials (typified by Al x Mn y ) can exhibit diffraction patterns with 10-fold symmetry. The apparent dilemma was that the diffraction patterns of these materials comprise sharp Bragg-like reflections characteristic of ordered crystalline materials, whereas the accepted dogma maintained that 10-fold or 5-fold symmetry is impossible in a crystalline material with long-range periodic order.[2] Resolution of this issue [3][4][5] rests on the fact that certain quasiperiodic tilings (e.g. the Penrose tiling [6] ) have diffraction patterns that contain sharp Bragg-like reflections based on a 10-fold symmetric reciprocal space, [7] resembling those observed for the metal alloy materials. Such tilings [6,8,9] are constructed from a set of geometrically welldefined tiles, assembled according to well-defined rules, but do not have translational periodicity. Following the pioneering work in this field, several other materials have been discovered that exhibit diffraction patterns with 10-fold symmetry, and their properties have been investigated experimentally and theoretically; [10][11][12][13][14] the term "quasicrystal" is now widely adopted for such materials. Despite the huge interest in quasicrystals during the intervening period, [14,15] all examples reported to date have been metal alloy materials, and there has been no example of a quasicrystal composed of discrete molecular entities. In this paper, we demonstrate for the first time that it is feasible to construct a quasicrystal using organic molecules as the building units, based on exploiting similar principles to those used for the structural design of crystalline molecular materials. Our designed molecular quasicrystal, which is based on a standard Penrose tiling, is shown to be energetically stable and to give rise to a 10-fold symmetric diffraction pattern.Within the field of crystalline organic molecular materials, there is currently much interest in understanding the fundamental factors that control the observed structural properties, as such knowledge is an essential pre-requisite for the design of molecular crystals for specific applications, an area of activity often called "crystal engineering". [16][17][18][19][20][21] However, rationalization of the factors that control the structural properties of such materials is often far from straightforward, as the observed crystal structure generally arises from the subtle inter-play of several different types of intermolecular interactions of comparable strengths. Nevertheless, for cases in which one specific intermolecular interaction (or a small number of interactions) has a dominant role in directing the structure, it can become possible to develop a reliable rationalization of the observed arrangement of molecules in the crystal, and hence to exploit such understanding as the basis for reliable a priori prediction of the structural properties of other (related) materials. ...

Crystal Engineering: A Holistic View

“…[71] There is even an in silico design of a molecular quasicrystal. [72] As far as intermolecular interactions are concerned, the last frontier in terms of grappling with them lies indubitably in understanding the supramolecular chemistry of the CÀF group, the so-called "organic" fluorine. Fluorine is so electronegative and nonpolarizable that it forms nonbonding contacts only with great reluctance.…”

Anisotropy in two-dimensional arrays of collinear in-plane rotated identical particles with arbitrary charge or polarization distribution

“…4͒. 31,32 The technical relevance of quasicrystals might be questionable 33 ͑in several cases long-range order seems to be antiferromagnetic in quasicrystals, 34 if present at all 35 ͒, but they are used in nonlinear optics 36 and-by laser interference-can be produced by rather standard lithographic methods. A quasicrystalline light field, e.g., due to interfering laser beams, may also trap dielectric particles on a surface and force them into a nonperiodic structure.…”

Kristall‐Engineering: eine holistische Darstellung

“…[71] Es gibt sogar einen rechnergestützten Entwurf eines molekularen Quasikristalls. [72] Was intermolekulare Wechselwirkungen betrifft, liegt die supramolekulare Chemie der CF-Gruppe -des "organischen" Fluors -an der äußersten Grenze dessen, womit man sich in diesem Zusammenhang beschäftigt. Fluor ist so elektronegativ und unpolarisierbar, dass es nur sehr widerwillig nichtbindende Wechselwirkungen eingeht.…”