Chemical self-assembly is the process by which ‘programmed’ molecular subunits spontaneously form complex supramolecular frameworks1,2. This approach has been applied to many model systems, in which hydrogen bonds3,4, metal–ligand coordination5 or other non-covalent interactions6 typically control the self-assembly process. In biology, self-assembly is generally dynamic and depends on the cooperation of many such non-covalent interactions. Water can play an important role in these biological self-assembly processes, for example by stabilizing the native conformation of biopolymers7,8,9. Hydrogen-bonded (H2O)n clusters10,11 can play an important role in stabilizing some supramolecular species, both natural and synthetic, in aqueous solution. Here we report the preparation and crystal structure of a self-assembled, three-dimensional supramolecular complex that is stabilized by an intricate array of non-covalent interactions involving contributions from solvent water clusters, most notably a water decamer ((H2O)10) with an ice-like molecular arrangement. These findings show that the degree of structuring that can be imposed on water by its surroundings, and vice versa, can be profound.

An intermolecular (H2O)10 cluster in a solid-state supramolecular complex

The tight-binding method of modelling materials lies between the very accurate, very expensive, ab initio methods and the fast but limited empirical methods. When compared with ab initio methods, tight-binding is typically two to three orders of magnitude faster, but suffers from a reduction in transferability due to the approximations made; when compared with empirical methods, tight-binding is two to three orders of magnitude slower, but the quantum mechanical nature of bonding is retained, ensuring that the angular nature of bonding is correctly described far from equilibrium structures. Tight-binding is therefore useful for the large number of situations in which quantum mechanical effects are significant, but the system size makes ab initio calculations impractical. In this paper we review the theoretical basis of the tight-binding method, and the range of approaches used to exactly or approximately solve the tight-binding equations. We then consider a representative selection of the huge number of systems which have been studied using tight-binding, identifying the physical characteristics that favour a particular tight-binding method, with examples drawn from metallic, semiconducting and ionic systems. Looking beyond standard tight-binding methods we then review the work which has been done to improve the accuracy and transferability of tight-binding, and moving in the opposite direction we consider the relationship between tight-binding and empirical models.

https://iopscience.iop.org/article/10.1088/0034-4885/60/12/001/pdf

Tight-binding modelling of materials

The diversity of molecular structures exhibited by fullerenes1 suggests a wide range of interesting and useful properties. Several fullerenes are now considered to be well characterized, but only minor variations in their chemical and physical properties have been observed2. Here we show that there are in fact two distinct classes of fullerenes, with some very different chemical properties. Members of the first class, typified by C60 and C70, have large energy gaps between the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO), and are soluble in many organic solvents. The second, previously unrecognized class is represented by C74 and selected isomers of the higher fullerenes, such as that of C80 with icosahedral symmetry: these are either free radicals or have small HOMO–LUMO gaps. Like radical metallofullerenes, they are kinetically unstable and react readily to form insoluble, polymerized solids. These intermolecular bonds can be broken by electrochemical reduction. After reducing them to soluble anions, we have been able to isolate and characterize these new fullerenes.

Isolation and properties of small-bandgap fullerenes

Optimisation of geometries of all 40 fullerene isomers of C40, using methods from molecular mechanics and tight-binding to full abinitio SCF and DFT approaches, confirms minimisation of pentagon adjacency as a major factor in relative stability. The consensus predictions of 11 out of 12 methods are that the isomer of lowest total energy is the D2 cage with the smallest possible adjacency count, and that energies rise linearly with the number of adjacencies. Quantum mechanical methods predict a slope of 80–100 kJ mol-1 per adjacency. Molecular mechanics methods are outliers, with the Tersoff potential giving a different minimum and its Brenner modification a poor correlation and much smaller penalty.

Pentagon adjacency as a determinant of fullerene stability

A theoretical study of buckminsterfullerene reaction products: C60+C60

Combining an efficient simulated annealing scheme for generating closed, hollow, spheroidal cage structures with a tight‐binding molecular‐dynamics method for energy optimization, the ground‐state structure of every even‐numbered carbon fullerene from C72 to C102 is determined. As a general trend, most ground‐state structures of the large fullerenes have relatively low symmetries. In many cases, several isomers of a fullerene are found to have competitively low energies, which suggests that a mixture of these isomers can be observed in experimental prepared samples.

CZ Wang

Papers

The geometry of large fullerene cages: C72 to C102