These tiny structures could offer architectural designs for the cities of the future. The authors explore the foam-like carbon structures, which relate to schwarzites and which are infinite periodic minimal surfaces of negative curvature. They show that the periodicity of close repeat units of such structures is evident not only in these formations but also in all of the carbon allotropes. The text provides literature and data on the field of nanostructure periodicity and the authors own results on nanostructure building and energy calculations.

In Periodic Nanostructures, the authors demonstrate that structural periodicity in various nanostructures has been proven experimentally. The text covers the coalescence reactions, studied by electronic microscopy, and shows that the nanoworld is continuous, giving rise to zero- (fullerenes), one- (tubules), two-(graphite) and three-(diamond, spongy carbon) dimensional carbon allotropes.

The authors explore foam-like carbon structures, which relate to schwarzites, and which represent infinite periodic minimal surfaces of negative curvature. They show that these structures contain polygons (with dimensions larger than hexagons w.r.t. to graphite) that induce this negative curvature. The units of these structures appear as nanotube junctions (produced via an electron beam) that have wide potential molecular electronics applications. Self-assembled supramolecular structures (of various tessellation) and diamond architectures are also proposed. The authors propose that the periodicity of close repeat units of such structures is most evident not only in these formations but also present in all of the carbon allotropes. It is also shown that depending on the lattice tessellation, heteroatom type, and/or doping, metal nanostructures (nanotubes in particular) can display both metallic and semiconductor characteristics. Therefore, their properties can be manipulated by chemical functionalization. The authors therefore suggest that nanostructures have heralded a new generation of nanoscale biological, chemical, and physical devices.

The text also provides literature and data on the field of nanostructure periodicity and the authors own results on nanostructure building and energy calculations as well as topological characterization by means of counting polynomials of periodic nanostructures. The aromaticity of various coverings of graphitic structures is also discussed.

This book is aimed at scientists working in the field of nanoscience and nanotechnology, Ph.D. and MSc. degree students, and others interested in the amazing nanoarchitectures that could inspire the cities of the future."

Novel carbon allotropes, such as spherical fullerenes and nanotubes, have been added, in the last three decades, to the traditionally recognised diamond and graphite. Although fullerene C60 has been speculated about for a long time. A fullerene is, according to a classical definition, an all-carbon molecule consisting entirely of pentagons (exactly 12) and hexagons (n/2-10). Non-classical fullerene extensions to include rings of other sizes have been considered. Fullerenes are commonly synthesised by arc-discharge or laser ablation methods. Spherical fullerenes became nowadays parts of real chemistry: they can be functionalised or inserted in supramolecular assemblies.

Most, yet not all, chemical substances consist of molecules. The fact that molecules have a 'structure' is known since the middle of the 19th century. Since then, one of the principal goals of chemistry is to establish the relationships between the chemical and physical properties of substance and the structure of the corresponding molecules. Countless results along these lines have been obtained along these lines and presented in different publications in this field. One group uses so-called topological indices. About 20 years ago, there were dozens of topological indices, but only a few with noteworthy chemical applications. Over time, their numbers have increased enormously. At this moment here is no theory that could serve as a reliable guide for solving this problem. This book is aimed at giving a reasonable comprehensive survey of the present, fin de siecle, state of art theory and practice of topological indices.

The central problem in QSPR (Quantitative Structure-Property Relationship) I QSAR (Quantitative Structure-Activity Relationship) is to convert chemical structures into molecular descriptors that are relevant to a certain physico-chemical property or biological activity. Although various physico-chemical properties may be subjected to QSPR/QSAR studies, the major application field of these models is drug discovery. Classically, drug discovery mainly relied on chance and massive screening of large libraries of synthesised or natural compounds. By contrast, computer-aided drug design, GADD, is an approach to rational drug design made possible by the recent advances in computational chemistry (in its various fields, such as molecular graphics, quantum chemistry, molecular mechanics, molecular dynamics, library searching, prediction of physicochemical and biological properties) and, of course, in computer science. Many physico-chemical properties can be satisfactorily correlated with the topostructural or topochemical features. Topological indices are among the simplest and efficient descriptors for QSPR/QSAR. In principle, these are mathematical objects, without a precise physical meaning. However, they may express the topological shape or may correlate with the molecular volume or surface area, as is shown in the pages of this book.