Covalent Carbon Compounds: From Diamond Crystallites to Fullerene-Assembled Polymers

Conclusion

As is clear from the work discussed here and elsewhere in this book there are a variety of ways in which cluster calculations are impacting the understanding and design of solid state properties. Also illustrated in the above discussion is the fact that each theory and numerical algorithm has specific subfields where it is most appropriate and the discussion of this topic necessitates equal emphasis on both the specific theory and the application. With respect to density-functional based calculations several known results have been reiterated here. First, it is possible to obtain very accurate geometries, vibrational modes, electronic densities, polarizabilities and hyper polarizabilities within a local approximation of the theory. Second, the overbinding that is present in existing local approximations to the density-functional theory can be circumvented if the cluster energies are calculated within the generalized gradient approximation. Finally, we presented results that show one example where the generalized gradient approximation significantly improves results. In contrast to the local-density-approximation which leads to qualitatively incorrect results for the methyl-methane hydrogen abstraction energy, we show that the generalized gradient approximation leads to results that are almost quantitatively correct.

With respect to applications we have shown that the density-functional method can be used to learn about growth processes that occur during the fabrication of solid-state materials, calculate barriers associated with formation, understand the optical response of an assembly of clusters, and use theoretical geometries, electronic structures and vibrational modes to aid experimentalists in the characterization of solids composed of clusters. While the examples discussed here touch upon a reasonably wide range of uses for cluster calculations in solid-state physics many other uses have been discussed elsewhere. There is little doubt that calculations on such systems will become increasingly important as theorists continue to improve their computational means for exploring such problems and as experimentalists enhance their abilities to fabricate cluster based materials.